Copyright by Kha Xuan Tran 2019

Copyright

by

Kha Xuan Tran

2019

The Dissertation Committee for Kha Xuan Tran Certifies that this is the approved version

of the following disseration

Exciton and Valley Properties in Atomically Thin Semiconductors and

Heterostructures

Committee

Xiaoqin Li Supervisor

Chih-Kang Shih

Ananth Dodabalapur

Keji Lai

Nanshu Lu


Heterostructures

by

Kha Xuan Tran

Dissertation

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy


May 2019

Dedication

Dedicate to my parents family and friends

v

Acknowledgements

Six years ago in summer 2013 I arrived in Austin Texas eager to start a new journey of

earning a PhD in physics Looking back at the time I spent at The University of Texas at

Austin there are certainly many challenges as well as many fond memories I am grateful for the

opportunity to study and work here with a lot of hardworking people

First of all I would like to thank my supervisor professor Xiaoqin Elaine Li Although

she is a tough mentor with a lot of demands to her students she cares about her students success

Ultimately her knowledge determination and perseverance have shown me that I can achieve

goals that I thought were never possible

Members of the Li group were fun to work with Akshay Singh helped me a great deal

when I first joined the group He has patiently taught me how to operate instruments in the lab

and how to run the pump-probe setup We had many engaging and stimulating scientific

discussions as well as conversations about not too important things Kai Hao and Liuyang Sun

helped me with tips and tricks about setting up optics and troubleshooting problems from time to

time I especially enjoy discussing the sample fabricating process with Junho Choi and Jiamin

Quan They often have great ideas on how to improve the sample making process to achieve

better quality samples Last but not least I would like to thank Li group undergraduate team

Andreacute Zepeda and Marshall Campbell have stayed in the lab very late with me trying to finish

making a TMD heterostructure Matt Staab Kayleigh Jones Carter Young Dennis Hong

Eduardo Priego Tiffany Pham-Nguyen Samantha Smith Michael Alexopoulos all provided

helps with exfoliating monolayers for my samples Jacob Embley who is taking over the setup

vi

after I leave was fun to work with I hope that I have left a decently working lab behind for him

to continue his PhD

I am also very grateful to work with a lot of excellent collaborators in the field Galan

Moody provides help with writing and scientific knowledge Fengcheng Wu and professor Allan

MacDonald provide theory support for my experiment Xiaobo Lu and professor Li Yang

provide band structure calculations that further consolidate my experimental results

In the end I thank my parents Theyve provided me advice support and encouragement

throughout my entire academic career

vii


Heterostructures

Kha Xuan Tran PhD

The University of Texas at Austin 2019

Supervisor Xiaoqin Elaine Li

Two dimensional van der Waals (vdW) materials recently emerged as promising

candidates for optoelectronic photonic and valleytronic applications Monolayer transition

metal dichalcogenides (TMD) are semiconductors with a band gap in the visible frequency range

of the electromagnetic spectrum Their unique properties include evolution from indirect band

gap in bulk materials to direct band gap in monolayers large exciton binding energy (few

hundred meV) large absorption per monolayer (about 10) strong spin-orbit coupling and

spin-valley locking Moreover two or more TMD monolayers can be stacked on top of one

another to create vdW heterostructures with exciting new properties

Optical properties of semiconductors near the band gap are often dominated by the

fundamental optical excitation the exciton (Coulomb-bound electron-hole pair) Excitons in

TMD monolayers (intralayer exciton) exhibit a large binding energy and a very short lifetime

The excitons in TMD monolayers are formed at the boundary of the Brillouin zone at the K and

viii

K points The time-reversal symmetry dictates that spins are oriented with opposite directions

leading to distinct optical selection rules for the excitons at these two valleys a property known

as the spin-valley locking Valley polarization is often characterized by circularly polarized

photoluminescence (PL) We show that the degree of valley polarization in a WSe2 monolayer

depends on the degree of disorder evaluated by the Stokes shift between the PL and absorption

spectra Intrinsic valley dynamics associated with different optical resonances can only be

evaluated using resonant nonlinear optical spectroscopy We discovered exceptionally long-lived

intra-valley trions in WSe2 monolayers using two-color polarization resolved pump-probe

spectroscopy

A different type of excitons (interlayer excitons) may rapidly form in TMD

heterostructures with a type-II band alignment Because of the spatial indirect nature interlayer

excitons have a much longer lifetime which is tunable by the twist angle between the two layers

Especially we discover that multiple interlayer excitons formed in a small twist angle

heterobilayer exhibit alternating circular polarization - a feature uniquely pointing to Moireacute

potential as the origin We assign these peaks to the ground state and excited state excitons

localized in a Moireacute potential and explain how the spatial variation of optical selection rule

within the moireacute superlattice can give rise to multiple peaks with alternative circular polarization

The twist angle dependence recombination dynamics and temperature dependence of these

interlayer exciton resonances all agree with the localized exciton picture Our results suggest the

feasibility of engineering artificial excitonic crystal using vdW heterostructures for

nanophotonics and quantum information applications

ix

Table of Contents

List of tables xi

List of figures xii

Chapter 1 Introduction and overview 1

I Definition of semiconductor 1

II Early experiments on semiconductor 2

III From vacuum tube to transistor 4

IV Some concepts and ideas of band theory 6

Chapter 2 Introduction to monolayer transition metal dichalcogenides (TMDs) 10

I TMD lattice structure and polymorphs 10

II Evolution from indirect band gap in bulk material to direct band gap in

monolayer 12

III Excitons13

IVK-K valleys in monolayer TMD 19

V Dark excitons 20

VI Valley property of excitonic states (ie exciton trion) 23

VII Trions28

Chapter 3 Introduction to TMD heterostructures 33

I TMD heterobilayer band alignment and optical properties 33

II Moireacute pattern in TMD heterobilayer 36

Chapter 4 Experimental Techniques 39

I Photoluminescence 39

II White light absorption measurement41

III Pump probe spectroscopy 42

x

IV Second harmonic generation (SHG) techniques 53

Chapter 5 Steady state valley properties and valley dynamics of monolayer TMD 61

I Disorder dependent valley properties in monolayer WSe2 61

II Long lived valley polarization of intravalley trions in monolayer WSe2 76

Chapter 6 Evidence for Moireacute excitons in van der Waal heterostructure 89

I Motivation 89

II Moireacute theory overview 91

III Sample details and experimental methods 94

IV Moireacute exciton model 97

V First principles calculation of the bandgaps of MoSe2-WSe2 bilayer

heterostructure101

VI Thermal behavior and recombination dynamics103

VII Additional heterostructures 105

VIII PL emission from Sz = 1 and Sz = 0 exciton transitions 107

IX Conclusion 108

Chapter 7 Conclusion and outlook110

Appendix Sample fabrication techniques 113

I Exfoliation 113

II Transfer 119

III Encapsulated heterostructure fabrication 126

IV Atomic Force Microscope (AFM) images of the fabricated sample 131

References 134

xi

List of tables

Table 61 Summary of peak positions full-width half-maximum (FWHM) and Stokes Shift

(SS) using Lorentzian (L) Gaussian (G) and Half-gaussian fitting methods for different

samples 71

Table A1 Pros and cons of the two types of PDMS 114

Table A2 Pros and cons of two commercial bulk TMDs 115

xii

List of Figures

Figure 11 Comparison of electrical conductivities of insulators metals and semiconductors

2

Figure 12 First semiconductor diode the cats whisker detector used in crystal radio Source

wikipedia 3

Figure 13 a) Schematic of the vacuum tube that only permits electricity to flow in one

direction Electrons can flow from hot cathode to anode but not the other way

around b) Metal grid inserted in the space between the anode and cathode can

control the current flow between anode and cathode Source wikipedia 5

Figure 14 Top views of probability density plots for an electron in hydrogen atom Brighter

area corresponds to region with higher probability of finding the electron 7

Figure 15 Energy band gaps for (a) metal -- zero energy gap (b) semiconductor -- 1 to 2 eV

gap (c) insulator -- larger than 3 eV gap 8

Figure 16 In a direct (indirect) bandgap material the CB minimum and the VB maximum

occur at the same (different) position in momentum space as illustrated in panel a

( panel b) 9

Figure 21 Two main structure polymorphs of TMD 2H trigonal prismatic and 1T

octahedral The crimson (gray) circle represents chalcogen(metal) atom The red

(gray) shadow represents primitive (computational) cell 12

Figure 22 a) The Brillouin zone of monolayer TMD showing the path in which the band

structure is drawn in part b b) Calculated band structure of bulk and 1 layer

MoS2 The solid arrows indicate the lowest energy transitions Bulk (1 layer) has

indirect (direct) bandgap c) PL measurement with different layers 1 layer MoS2

has much higher luminescence than 2 layer MoS2 13

xiii

Figure 23 a) Schematic of real space representation of an exciton b) The modulus squared of

the electron wave function of an exciton in which the hole position is fixed at the

center black circle The inset shows the corresponding wave function in

momentum space across the Brillouin zone Figure adapted from ref [6] c)

Representation of the exciton in reciprocal space d) Dispersion curve for the

exciton with different excited states in a direct band gap semiconductor with

energy gap Eg and exciton bind energy EB labeled e) Exciton series measured in

the absorption spectrum of a multi-layer MoS2 Figure adapted from ref [14] f)

Derivative of the reflectance contrast spectrum of a monolayer WS2 showing the

emergence of higher excited exciton states 16

Figure 24 a) Schematic represents exciton in 3D (bulk) and 2D (monolayer) TMD b) The

effect of increased binding energy in 2D system due to reduced dielectric

screening The binding energy is indicated by the dash red double arrows Figure

adapted from ref [5] c) Logarithm of a typical dIdV curve obtained from

scanning tunneling microscopy measurement of monolayer MoSe2 used to obtain

band gap value 18

Figure 25 a) The Brillouin zone of monolayer TMD with the reciprocal lattice vectors b1

b2 b) Band structure of monolayer WSe2 around K and Krsquo points Exciton at K

and Krsquo valley couples to light with σ+ and σ- polarization respectively 20

Figure 26 Different types of dark excitons a) Spin forbidden dark exciton in

tungsten(molybdenum) based monolayer TMD denoted WX2 and MoX2

respectively b) Momentum indirect dark exciton in which electron and hole are

not in the same valley c) Momentum indirect dark exciton in which same valley

electron located outside of the light cone 22

Figure 27 a) The circular polarized photoluminescence spectrum of monolayer MoS2 at

14K The excitation energy is indicated by the arrow which is 196 eV b) The

circular polarized photoluminescence spectrum of monolayer WSe2 at 4K excited

with the same energy as part a) X0 and X

- denote the exciton and trion peak

respectively 25

Figure 28 a) The linear polarized PL of monolayer WSe2 at cryogenic temperature excited

with 188 eV CW laser Different gate voltages are used to control the emergence

of neutral exciton X0 negative trion X- and positive trion Co(cross) linear

detection is plotted as the black(red) curves b) Normalized neutral exciton

intensity peak as a function of detection polarization angles 27

xiv

Figure 29 a) Microscopic image of a monolayer MoSe2 and the two metal contact b) Device

schematic to control the doping level in the sample c) PL spectrum of the

monolayer as a function of gate voltage The labels are as followed X0 exciton

X- negative trion X

+ positive trion X

I impurity peak d) Contour plot of the first

derivative of the differential reflectivity in a charge tunable WSe2 monolayer

Double trion peaks emerge at the n-dope regime 30

Figure 210 Charge configuration of (a) intravalley trion (b) intervalley trion of monolayer

WSe2 and (c) intervalley trion of monolayer MoSe2 31

Figure 31 a) Type II band alignment of MoSe2-WSe2 heterobilayer The conduction band

minimum (valence band maximum) is belong to monolayer MoSe2(WSe2)

Charge transfer intra- and interlayer exciton recombination timescales are

indicated b) Band structure of the aligned TMD heterostructure at 0 degree

stacking angle Conduction band K(K) valley from MoSe2 is aligned with valence

band K(K) valley from WSe2 in momentum space c) The low temperature PL

spectrum of an aligned heterobilayer MoSe2-WSe2 featuring interlayer exciton

(IX) peak around 14 eV 35

Figure 32 a) Twist angle increasing makes the IX becoming indirect in momentum Optical

transition requires the participation of Δk momentum phonon Figure adapted

from ref [13] b) The PL intensity of IX decreases as the twist angle increase from

0o and increases again as the twist angle approaching 60

o c) Time resolved PL of

IX detected at 1320 meV for three samples with increasing twist angles showing

increased lifetime of IX for larger twist angle sample 36

Figure33 a) STM image of rotational aligned WSe2-MoS2 heterobilayer showing the moireacute

superlattice period of 87 nm b) Moireacute supercell with

denoting the

locations that retain the three fold symmetry c) Zoom in view showing the

specific atomic alignment d) and e) Layer separation and band gap variation of

the TMD moireacute pattern respectively 38

Figure 41 Schematic of the photoluminescencewhite light absorption optical setup 41

Figure 42 Simplest form of pump probe technique Two pulses split from the Ti-sapphire

out with variable delays between them interact co-linearly with the sample The

intensity of the probe is monitored as a function of the delay while the pump is

filtered out before the detector 43

xv

Figure 43 Two color pump probe optical setup In addition to the simple pump probe in the

previous figure the pulse shapers are inserted to independently vary the

wavelength or photon energy of two pulses 45

Figure 44 Schematic details the working principle of the pulse shaper in two color pump

probe setup 47

Figure 45 Schematic of the RF (radio frequency) generation and AOM (acousto-optic

modulator) 48

Figure 46 Schematic of lockin amplifier illustrating signal (S) and reference frequency (R)

convolution using the integrator 50

Figure 47 Schematic of the autocorrelation setup to measure the pulse duration 52

Figure 48 a) Monolayer TMD crystal axis b) Same as in a) but rotated 60o clockwise or

counter clockwise 120o rotation will make the crystal structure identical to a) 55

Figure 49 a) Schematic of the polarization resolved SHG setup b) SHG polarized intensity

as the sample is rotated 360o in the plane to which the laser beam is perpendicular

to 56

Figure 410 a) Schematic of the spectral phase resolved SHG setup b) SHG phase resolved

spectra between the monolayers and the BBO crystal with signal in phase for a

near twist angle stacking c) Similar to b) but with out-of-phase signals for a

near twist angle 58

Figure 411 Coordinate systems used in SHG signal calculation XOY is the lab frame of

reference in which OX(OY) is the horizontal(vertical) direction XOY is the

sample frame of reference in which OX(OY) is the armchair(zigzag) direction

Angle between OX and OX is 60

xvi

Figure 51 a) The band structure of monolayer WSe2 at two degenerate K and K valleys

Valley contrasting spins allow left (right) circular polarized light to excite

excitons in the K (K) valley b) Bloch Sphere representation of valley pseudospin

degree of freedom Circular polarized light prepares an exciton in |Kgt or |Kgt

state ie states at the poles whereas linear polarized light prepares an exciton in a

superposition of |Kgt and |Kgt ie states at the equator 63

Figure 52 a) PL spectrum of monolayer WSe2 excited with 188 eV CW laser Blue shaded

Gaussian represents the fits to the exciton resonance b) Zoomed in spectrum

around the exciton resonance shows co (cross) linear PL signal with respect to

the excitation laser polarization Corresponding VC is plotted on the right hand

side c) PL spectra taken with co- and cross- circular PL signal with respect to a

circularly polarized excitation laser PL intensity and VP are plotted on the left

and right vertical axes respectively 66

Figure 53 a) Stoke shift is shown as the difference in energy between the absorption

spectrum and PL from the exciton resonance Inset SS dependence on

temperature b) VC (VP) is plotted with respect to SS VC shows an inverse

dependence versus SS whereas VP shows no recognizable trend 69

Figure 54 Absorption linewidth of sample E4 fitted using different profiles Lorentz Gauss

and half Gauss 72

Figure 55 The absorption spectra are fitted with Gaussian profile and the FWHMs are

extracted and plotted against SS 73

Figure 56 a) Trion resonances on both co and cross signal are fitted with Gaussians Since

trion doesnt show any valley coherence the fits are essentially the same Valley

coherence is shown here before the trion subtraction from the co and cross

signals b) After trion subtraction the valley coherence is essentially the same

signifying that trion has minimal contribution to exciton valley coherence 74

Figure 57 Degree of a) valley coherence and b) valley polarization plotted across the exciton

resonance of omitted CVD sample c) Valley coherence and valley polarization

plotted against SS included the omitted data point 75

xvii

Figure 58 (a) Possible configurations of charged and neutral bright excitons in WSe2 (b)

Differential transmission spectrum of WSe2 (dots) The black line is an

interpolation curve serving as a guide to the eye The solid Gaussians illustrate

the spectral position of the exciton and the two trion (inter- and intravalley)

resonances The spectral positions of probe energies for data in figure 69 and

610 (dashed colored lines) and the pump energy for figure 610 (gray line) are

also illustrated 80

Figure 59 Co- (solid dots) and cross-polarized (open dots) signals recorded in resonant

excitation experiments across the trion resonance at probe energies of (a) 17268

meV (b) 1722 meV and (c) 17196 meV (d) Valley polarization for the

measurements displayed in (a) and (c) 84

Figure 510 Co- (solid dots) and cross-polarized (open dots) signals recorded in nonresonant

excitation experiments for pumping at the exciton resonance and probing at (a)

17244 meV (b) 1722 meV and (c) 17196 meV (d) Valley polarization for the


Figure 511 Schematic of the suggested valley polarization dynamics exciton and trion

conversion processes and their respective time scales as measured in the

experiment Dashed lines suggest that such processes are possible in principle but

do not compete favorably with other faster processes 88

Figure 61 (a) Different local atomic alignments occur in an MoSe2WSe2 vertical

heterostructure with small twist angle The three highlighted regions correspond

to local atomic configurations with three-fold rotational symmetry (b) In the K

valley interlayer exciton transitions occur between spin-up conduction-

band electrons in the MoSe2 layer and spin-up valence-band electrons in the WSe2

layer K-valley excitons obey different optical selection rules depending on the

atomic configuration within the moireacute pattern

refers to -type stacking

with the site of the MoSe2 layer aligning with the hexagon center ( ) of the

WSe2 layer Exciton emission at the (

) is left-circularly (right-circularly)

polarized Emission from site is dipole-forbidden for normal incidence (c)

Left The moireacute potential of the interlayer exciton transition showing a local

minimum at site Right Spatial map of the optical selection rules for K-valley

excitons The high-symmetry points are circularly polarized and regions between

are elliptically polarized 93

xviii

Figure 62 (a) Optical image of an hBN-encapsulated MoSe2WSe2 stacked heterostructure

The hBL region is indicated inside the black dotted line (b) Comparison of the

photoluminescence spectrum from an uncapped heterostructure (dashed curve)

and an hBN-encapsulated heterostructure (solid curve) Neutral (X0) and charged

(X-) exciton emission is observed from the MoSe2 and WSe2 monolayers The

interlayer exciton (IX) emission is observed ~300 meV below the intralayer

resonances (c) Illustrative band diagram showing the type-II alignment and the IX

transition 96

Figure 63 (a) Representative PL spectra shown for hBLs with 1deg and 2deg twist angles Each

spectrum is fit with four (1deg) or five (2deg) Gaussian functions (b) The center

energy of each peak obtained from the fits at different spatial positions across

each sample The average peak spacing increases from 22 plusmn 2 meV to 27 plusmn 3 meV

with twist angle (c) Circularly polarized PL spectrum for + excitation of the 1deg

sample (d) The degree of circular polarization versus emission wavelength

obtained from the spectra in (c) 97

Figure 64 (a) Illustration of the spatial variation of the moireacute potential and the confined multiple IX resonances (b) Optical conductivity of IXs in the K valley in response to (blue line) and (red line) polarized light (c)-(f) Real-space map of the center-of-mass wave functions for peaks (1) (2) (3) and (4) respectively (g)-(h) The spatial variation of the components of the optical matrix elements 101

Figure 65 (a) The three stacking types (

) of the bilayer MoSe2-WSe2

heterostructure and corresponding DFT-calculated band structures (b) Interlayer

distance and the band gap of three stacking types (c) First principles GW-BSE

calculation results for quasiparticle band gap and exciton binding energy for

different stacking types 103

Figure 66 (a) Temperature dependence of the PL between 25 K and 70 K (b) Time-resolved

PL dynamics (points) at energies near the four IX transitions labeled in the inset

The solid lines are biexponential fits to the data The inset shows the emission

energy dependence of the fast and slow decay times 104

Figure 67 (a) Steady state PL spectra from 1o sample (sample 1) and 2

o sample (sample 2)

(b) Time-resolved PL dynamics for IX emission at 1320 meV as indicated by the

shaded area in (a) 106

xix

Figure 68 Comparison between IX resonances from H-type sample (upper panel) and R-type

sample (lower panel) 107

Figure A1 a) and b) Home-made (thicker film) and commercial PDMS (thinner film) on

microscope slide respectively c) Bulk TMD thinned down on a piece of blue

tape One can tell the quality of the bulk TMD by looking at the flakes Good

quality bulk usually appears with flat cleaved surface In this case the bulk is not

that good but still exfoliatable d) Huge monolayer WSe2 exfoliated on home-

made PDMS 117

Figure A2 a) Schematic of the transfer microscope showing different components b) Actual

picture of the microscope 120

Figure A3 a) 12 PPC liquid inside the glass vial ready to be spin coated b) PMDS dot 122

Figure A4 Watch for contact region during dry transfer process Here the monolayer (on the

PDMS) is at the lower left corner outside the field of view 126

Figure A5 a) PPC transfer steps and b) dry transfer steps for making TMD heterostructure

128

Figure A6 PL spectra from monolayer MoSe2 at 10 K excited using 660 nm CW laser with

30 W power The exciton (X) and trion (T) peaks are labeled Keep monolayer

from contact with any chemical during transfer process 130

Figure A7 Temperature chart for annealing TMD sample 131

Figure A8 a) Topography image showing the roughness of monolayer MoSe2 from 2D

semiconductor dry transferred on top of an annealed hBN b) Zoom-in region

from a showing super flat surface c) Lateral force image shows atomic resolution

of the region d) Sample schematic 131

xx

Figure A9 a) and b) Topography image showing the roughness of monolayer MoSe2 from

HQ graphene on top of an annealed hBN 132


semiconductor dry transferred on silicon b) Line cut showing various peaks and

troughs c) Sample schematics 133

1

Chapter 1 Introduction and Overview

One shouldnt work on semiconductor that is a filthy mess who knows if they really exist --

Wolfgang Pauli 1931

The semiconductor is the most significant factor that contributes to the development of the

personal computer cell phone internet camera ie the digital world as we know of today

Semiconductor makes data communication and processing become much faster and electronic

devices much smaller and cheaper than before ie at the time of vacuum tubes Before the advent

of quantum mechanics and band theory experiments on semiconductor were patchily driven by

the needs of technology[1] The purpose of this chapter is to give a brief overview of the

development of semiconductor as well as the introduction of band theory of material This is the

background knowledge in which subsequence chapters are built upon

I Definition of semiconductor

The textbook definition of the semiconductor is the material whose electrical

conductivity is between that of metals and insulators As shown in figure 11 the electrical

conductivity of a semiconductor can vary by three to four orders of magnitude Moreover this

variation can be controlled by various mean ie either by introducing a minute amount of

impurity atoms in the semiconductor or impose an external electric field through electrical

contacts In contrast with metals the electrical conductivity of semiconductor increases as the

temperature increases We can also increase semiconductors electrical conductivity by shining

light with an appropriate wavelength on them - a phenomenon called photoconductivity For a

long time people didnt understand these physical phenomena until the advent of the quantum

theory of solids

2

II Early experiments on semiconductors

Earliest work on semiconductors is by Michael Faraday[16] He found that the electrical

conductivity of silver sulfide increases as a function of temperature - a signature of

semiconductor which is the opposite trend as that of the temperature dependence of metal This

behavior was not understood at the time and was hence labeled as anomalous We now know

that this is due to the exponential increase of charge carriers according to Boltzmann distribution

that more than offset the decrease in mobility due to phonon (lattice vibration) scattering

whereas the near constant number of charges in metal with respect to temperature makes its

electrical conductivity susceptible to phonon scattering[1]

Figure 11 Comparison of electrical conductivities of insulators metals and

semiconductors Figure adapted from ref [1]

3

Rectification is the ability of an electrical device to conduct electricity preferentially in

one direction and block the current flow in the opposite direction In 1874 Carl F Braun and

Arthur Schuster independently observed rectification between semiconductor and metal junction

Braun studied the flow of electrical current between different sulfides and the thin metal wires

Whereas Schuster studied electrical flow in a circuit made of rusty copper wires (copper oxide)

bound by screws[18] The copper oxide and the sulfides were not known as semiconductors at

the time Rectification is the basic principle behind the diode The early version of which (termed

cats whisker-see figure 12) played a major role in radio communication and radar detection in

world war II[18]

The electrical conductivity of a semiconductor can also be increased by shining light

upon it --the property called photoconductivity It enables semiconductor to be used as optical

detectors and solar cells Willoughby Smith while working on submarine cable testing in 1873

discovered that the electrical resistance of selenium resistors decreased dramatically when being

exposed to light [19] In 1883 Charles Fritts constructed the very first solar cells out of

selenium[20] However the efficiency of the device was very small less than 1 of photon

energy converted into electricity

Figure 12 First semiconductor diode the

cats whisker detector used in crystal radio

Source wikipedia

4

III From vacuum tube to transistor

The cat whisker detector was difficult to make The material acting as a semiconductor

(usually lead sulfide PbS crystal) often had lots of impurities A good crystal with the favorable

conducting property was hard to be found There was also no way to distinguish between good

versus bad crystal[21] When operating cat whisker required careful adjustment between the

metal wire (whisker) and the semiconducting crystal Moreover this alignment could easily be

knocked out of place[1] Needless to say the cat whisker was cumbersome and was impossible

to mass produced

John Ambrose Fleming invented the vacuum tube in 1904[22] The device consists of

two electrodes inside an airtight-sealed glass tube (Figure 13a) The design of the vacuum tube

evolved from that of the incandescent light bulb The cathode which was often a filament

released electrons into a vacuum when heated -- the process called thermionic emission The

anode which was a metal plate at positive voltage attracted those electrons floating around In

this way the vacuum tube acted as a rectifying device or diode which permits current to flow in

only one direction This current flow can also be controlled if a metal grid is inserted between the

anode and cathode (Figure 13b) By applying the various voltage to the metal grid it was

possible to amplify the current flowing between the anode and cathode This was also the

working principle behind the transistor based on the semiconductor junctions which was later

invented in the 1940s Because of the simple design vacuum tube became a basic component in

electronic devices in the first half of the 20th century The broadcast industry was born[1]

Although vacuum tube performance was better than that of cat whiskers diode electronics

devices made from vacuum tube were bulky and consumed a lot of power After World War II

the proposal was underway to find the replacement for the vacuum tube

5

As mention above point contact detector such as the cats whisker diode performed

poorly due to the bad quality of the semiconductor Thus there was a push for producing high-

quality material particularly silicon and germanium Russel Ohl melts silicon in the quartz tube

and allowed it to cool down slowly 99999 purity silicon was available in 1942[1] In 1947

William Shockley John Bardeen and Walter Brattain successfully demonstrated a working

model of the point contact transistor at Bell Labs made from the high-quality germanium[23]A

few years later Shockley proposed a design for the junction transistor which consisted of 3

layers n-doped layer sandwiched between two p-doped layers[24] In 1950 Shockleys design

was experimentally realized by the work of Gordon Teal Teal made the p-n-p junction transistor


direction Electrons can flow from hot cathode to anode but not the other way around b)

Metal grid inserted in the space between the anode and cathode can control the current

flow between anode and cathode Source wikipedia

a) b)

6

from high purity germanium he grew in the lab[25] From there the transistor was ready to be

mass produced and gradually replaced the use of vacuum tubes in everyday electronics

IV Some concepts and ideas of band theory

Much of the development of semiconductor technology in the early 20th century owed to

the success of band theory - a manifestation of quantum mechanics in a solid state system In

quantum mechanics an electron can be mathematically described by its wave-function which is

often a complex number function of the position and time The magnitude squared of the wave-

function gives the probability density of the electron ie the probability to find the electron at a

given moment in time in a particular unit volume of space In this framework the electron

behaves like a wave So if its being confined (by some energy potential) its wave-function and

energy will be quantized very much like the guitar string being held fixed on both ends The

situation can be generalized for electron confined in hydrogen atom by the electrostatic Coulomb

potential The probability densities of this electron as functions of the position for different

energy levels[2] are depicted in figure 14

7

In solid atoms are closely packed in a lattice structure Electrons in the highest energy

level are affected by the Coulomb potential of the nearby atoms Neighbor electrons can interact

with each other Discreet energy levels in atom become energy bands in solid Because atoms

can have a lot of electrons there are a lot of energy bands when atoms form crystal structure in

solid However there are three energy bands that are very important because they entirely

determine the optical and electrical properties of solid conduction band valence band and band

gap The energetically highest band which is fully occupied by electrons is called the valence

band In the valence band electrons are not mobile because there is no room to move The


area corresponds to region with higher probability of finding the electron Figure adapted

from ref [2]

8

conduction band is the next higher energy band which is generally empty Electrons in the

conduction band are free to move and are not bound to the nucleus The energy difference

between the valence band and the conduction band is called the band gap The size of the band

gap (in electron-volt unit) determines whether the material is conductor semiconductor or

insulator (figure 15)

In solid state physics one usually encounters two types of energy band plots band

diagram and band structure Band diagram is the plot showing electron energy levels as a

function of some spatial dimension Band diagram helps to visualize energy level change in

hetero-junction and band bending Band structure on the other hand describes the energy as a

function of the electron wavevector k - which is also called the crystal momentum

Semiconductors fall into two different classes direct and indirect bandgap In direct (indirect)

gap semiconductors conduction band minimum occurs at the same (different) point in k-space as

the valence band maximum as illustrated in the band diagram figure 16 Since a photon or light

has negligible momentum compared to an electron ( ) the process


gap (c) insulator -- larger than 3 eV gap

9

of absorbing or emitting a photon can only promote or induce an electron to undergo a vertical

(with nearly zero momentum change) transition in the dispersion curve An electron (hole)

electrically injected or optically promoted to the conduction quickly relaxes to the bottom (top)

of the conduction (valence) band Consequently optical absorption or emission processes are

much more efficient in direct-gap semiconductors than those in the indirect gap semiconductors

Well-known examples of direct (indirect) gap semiconductors are GaAs and GaN (Si and

Ge)[26]

Figure 16 In a direct (indirect) bandgap material the CB minimum and the VB

maximum occur at the same (different) position in momentum space as illustrated

in panel a ( panel b)

gEgE

k k

0 0

a) b)

10

Chapter 2 Introduction to monolayer transition metal dichalcogenides

(TMDs)

Two dimensional (2D) materials consist of a single layer of element or compound

Interest in 2D material started since the isolation and characterization of graphene in 2004 Since

then tens of thousands of papers on graphene has been published[27] In 2010 Nobel prize in

physics was awarded for Geim and Novoselov for groundbreaking experiments regarding the

two-dimensional graphene[28] Graphene itself is an excellent electrical conductor[29]

However its lack of band gap has limited its applications in electronic and optoelectronic

devices Over the years new types of 2D materials with diverged properties have emerged such

as the ferromagnetic Cr2Ge2Te6[30] CrI3[15] superconductive such as 1T-SnSe2[717]

insulating such as hBN[31]

Transition metal dichalcogenides (TMDs) are members of 2D materials family and are

semiconductors with a band gap in the visible range of the electromagnetic spectrum Two

studies in 2010 simultaneously reported these new 2D semiconductors [332] Their properties

are especially interesting including an evolution from indirect in bulk material to direct bandgap

in monolayer[332] tightly bound excitons (coulomb bound electron-hole pairs) due to two-

dimensional effect [533] large absorption per monolayer (~10) [34] and spin-valley coupling

[1235-37] This chapter will briefly survey the physics behind some of these interesting

properties of monolayer TMD

I TMD lattice structure and polymorphs

Transition metal dichalcogenide (TMD) has the chemical formula of MX2 where M

stands for a transition metal and X stands for a chalcogen The atomic structure of bulk TMD

11

consists of many layers weakly held together by van der Waal (vdW) forces[14] Within each

monolayer the metal layer is sandwiched between two chalcogen layers and is covalently

bonded with the chalcogen atoms ie strong in-plane bonding[4] as shown in figure 21 It is the

former that allows TMD to be easily mechanically exfoliated into thin layer forms monolayer

bilayer trilayer etc

Monolayer TMDs mainly have two polymorphs trigonal prismatic (2H) and octahedral

(1T) phases The difference in these structures is how the chalcogen atom layers arranged around

the metal layer In the 2H(1T) phase chalcogen atoms in different atomic planes are located right

on top of (a different position from) each other in the direction perpendicular to the monolayer

(side view in fig II1) Either 2H or 1T can be thermodynamically stable depending on the

particular combination of transition metal (group IV V VI VII IX or X) and chalcogen (S Se

or Te) For example MoS2 MoSe2 WS2 WSe2 form 2H phase[38] These materials are the

main focus of our study In contrast WTe2 thermodynamically stable phase is 1T at room

temperature[39]

12

II Evolution from indirect bandgap in bulk material to direct bandgap in

monolayer

Most TMDs (eg MoS2 MoSe2 WSe2) are found to exhibit an indirect to direct gap

transition as the layer thickness is reduced to a monolayer leading to the drastic increase in

photon emission efficiency[332] Monolayer TMDs reciprocal lattice is a hexagon with the

center of Brillouin zone denoted as the gamma point G and the vertices at the K points (see

figure 22a) In the bulk material the maximum of the valence band is at G point whereas the

minimum of the conduction band is at the Q point - between G and K point (see figure 22b left

panel) The conduction band states and the valence band states near K point are mainly

composed of strongly localized orbitals at the Mo atoms (valence band) and

states (conduction band) slightly mixed with the chalcogen orbitals They have minimal


octahedral The crimson (gray) circle represents chalcogen(metal) atom The red (gray)

shadow represents primitive (computational) cell Figure adapted from ref [4]

Top

vie

wSi

de

vie

w

13

interlayer coupling since Mo atoms are sandwiched between two layers of S atoms[32] On the

other hand conduction at the Q point and valence band at G point originate from the linear

combination of anti-bonding pz orbital of S atoms and d orbitals of Mo atoms They have strong

interlayer coupling and their energies depend on layer thickness As layer thickness reduces the

indirect gap becomes larger while the direct gap at K point barely changes By tracking the shift

the photoluminescence (PL) peak position with layer number in MoS2 it has been shown that

indirect gap shifts upwards in energy by more than 06 eV leading to a crossover from an

indirect gap in bulk to direct gap in monolayer[3] As a consequence monolayer TMD is much

brighter than the bilayer TMD shown in figure 22c

III Excitons

Excitons (X) are electron-hole pairs bound together by Coulomb force ie an electron in

the conduction band binding with a hole in the valence band (figure 23c) Classically in the real


structure is drawn in part b b) Calculated band structure of bulk and 1 layer MoS2 The

solid arrows indicate the lowest energy transitions Bulk (1 layer) has indirect (direct)

bandgap c) PL measurement with different layers 1 layer MoS2 has much higher

luminescence than 2 layer MoS2 Figure adapted from ref [3]

G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14

space representation exciton can be thought of as negative electron and positive hole orbiting

around each other (figure 23a) and freely move to abound in the crystal In fact the quantum

mechanics picture of the exciton is slightly more complicated We take a look at the wave

function of the ground state exciton in a crystal The concept of correlated electron-hole motion

is illustrated in figure 23b in which the position of the hole is assumed to be at the origin

indicated by the black circle The electron wave function is spanning over many lattice sites

Quantitatively we can model the exciton similarly to a hydrogen atom using the effective

electron(e) mass and effective hole(h) mass[26] We can also separate the X wave-function into

two parts the relative motion between e and h and the center of mass motion The center of

mass motion behaves like a free particle with the reduced mass m of e and h given by

whereas the relative motion results in hydrogen-like energy level We note the basic equation

describing the energy of an exciton here which has contributions from both relative and center

of mass motion

The first term is the band gap of the semiconductor The second term is the primary

correction to the band gap and causes the X energy to be lower than the band gap energy by the

amount EB which is the X binding energy which is often written as

where aB is the

exciton Bohr radius Often the exciton Bohr radius is used as a measure of how large the exciton

is In monolayer TMD the exciton binding energy is huge because of the reduced

dimensionality Therefore the exciton Bohr radius in monolayer TMD is small about few

nanometers compared to tens of nanometers exciton in the traditional quantum well[26]

15

Formally exciton in monolayer TMD can be thought of as Wannier-Mott exciton whose

mathematical description is shown in the preceding equation

The third term of the energy equation gives rise to the parabolic form of the exciton

dispersion curve - see figure 23c corresponding to the kinetic energy arise from the free motion

of the center of mass When the exciton energy level n is large only the energy band gap Eg and

the kinetic energy term dominate Indeed a series of exciton excited states can often be observed

in the absorption spectrum from a multilayer MoS2 with gradually decreasing oscillator strength

for higher excited states[14] as shown in figure 23d In monolayer TMD the absorption of the

exciton higher excited states (ngt2) are very weak - barely visible in the absorption spectrum One

often needs to take the derivative of the reflectance contrast[5] - see figure 23e

16

Exciton in monolayer TMD is very robust due to strong binding energy between electron

and hole which is in the order of a few hundred mili-electronvolts making it stable at room

temperature These excitons have such strong binding energy is due to the reduced dielectric

screening in two-dimensional system The electric field lines between electron and hole extend

outside the sample plane in monolayer as shown in figure 24a bottom panel The electron and

hole are being pulled closer together giving rise to smaller exciton Bohr radius On the other

Figure 23 a) Schematic of real space representation of an exciton b) The modulus squared

of the electron wave function of an exciton in which the hole position is fixed at the center

black circle The inset shows the corresponding wave function in momentum space across

the Brillouin zone Figure adapted from ref [6] c) Representation of the exciton in reciprocal

space d) Dispersion curve for the exciton with different excited states in a direct band gap

semiconductor with energy gap Eg and exciton bind energy EB labeled e) Exciton series

measured in the absorption spectrum of a multi-layer MoS2 Figure adapted from ref [14] f)

Derivative of the reflectance contrast spectrum of a monolayer WS2 showing the emergence

of higher excited exciton states Figure adapted from ref [5]

gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17

hand the Coulomb interaction in the 3D system is screened out by the surrounding bulk material

effectively weaken the binding energy between electron and hole The distance between electron

and hole is also further than the 2D case (figure 24a top panel)

To measure the exciton binding energy experimentally one must identify the absolute

energy positions of both exciton resonance EX and free particle band gap Eg The binding energy

is then easily calculated by the relation EX can be measured by the optical

method such as absorption shown in figure 23f Here EX corresponds to the energy position of

the 1s state On the other hand Eg cannot be determined by the optical measurement which is

strongly influenced by excitonic effects A direct approach is to use scanning tunneling

spectroscopy (STS) technique which measures tunneling currents as a function of the bias

voltage through a tip positioned very close to the sample STS can probe the electron density of

states in the vicinity of the band gap revealing the energy levels of free electrons in the valence

band and the conduction band A typical STS spectrum for monolayer MoSe2 on bilayer

graphene is shown in figure 24c The band gap is the difference between onsets which is 216

eV for monolayer MoSe2

18


effect of increased binding energy in 2D system due to reduced dielectric screening The

binding energy is indicated by the dash red double arrows Figure adapted from ref [5] c)

Logarithm of a typical dIdV curve obtained from scanning tunneling microscopy

measurement of monolayer MoSe2 used to obtain band gap value Figure adapted from ref

[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15

Bias Voltage (Volts)

(c)

19

IV K-K valleys in monolayer TMD

Valley refers to the energy extrema in the band structure (energy minima in the

conduction band and energy maxima in the valence band) As mention in the previous chapter

the reciprocal lattice of a monolayer TMD is a hexagon with three-fold rotational symmetry

corresponding to three-fold symmetry of the real lattice Although the Brillouin zone of a

monolayer has 6 vertices only two of the K and K are inequivalent because other vertices can be

mapped back to either K or K by either b1 or b2 - the reciprocal lattice vector The direct band

gap of the monolayer TMD occurs at the K and Krsquo valley The exciton at K and K valley only

interact with σ+ and σ- circularly polarized light respectively due to chiral optical selection rules

which can be understood from group theory symmetry argument The orbital Bloch functions of

the valence band states at K K points are invariants while the conduction band states transform

like the states with angular momentum components plusmn1 inherited from the irreducible

representations of the C3h point group[3540] Therefore the optical selection rules of the

interband transition at KK valley can only couple to σplusmn light respectively as illustrated in figure

25b

20

V Dark excitons

As we discussed in the previous section exciton can be modeled as the hydrogen atom in

which the negative electron orbits the positive hole This gives rise to different excited state 1s

2s 3s (see figure 23) Among them the 1s exciton state dominates the optical properties of

the monolayer TMD By definition bright(dark) exciton can(cannot) interact (absorbemit) with

photon As a result bright exciton has a much shorter lifetime than dark exciton because electron

and hole in bright exciton can recombine and emit a photon There are many reasons that make

an exciton dark

1 Spin forbidden dark exciton

Spin forbidden dark exciton consists of the anti-parallel spin conduction band and

valence band as illustrated in figure 26a Here the arrow next to the band indicates the direction

of electron spin To be able to interact with a photon the total spin of electrons forming an


b2 b) Band structure of monolayer WSe2 around K and Krsquo points Exciton at K and Krsquo

valley couples to light with σ+ and σ- polarization respectively

a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21

exciton must add up to 1 This is the familiar conservation of angular momentum in which the

spin-forbidden dark exciton is not satisfied

The order and energy difference between bright and dark exciton is given by the sign and

amplitude of the spin splitting in the conduction band[741] As a result for the tungsten-based

monolayer TMD such as WS2 and WSe2 the bright exciton is the second lowest energy 1s

exciton (left side of figure 26a) Whereas in molybdenum case the bright exciton is the lowest

energy exciton (right side of figure 26a) This difference is one of the reasons leading to the

contrasting behavior of exciton luminescence with respect to temperature For example

monolayer WX2(MoX2) is brighter(dimmer) as the temperature increases Also monolayer WX2

exciton has more robust valley polarization and valley coherence in steady-state PL than that of

monolayer MoX2 These differences are thought to be the result of the interplay between the

spin-forbidden dark exciton momentum indirect dark exciton and phonon which is discussed in

great details in ref [41]

There are several experimental techniques to measure the energy splitting between the

bright and spin forbidden dark exciton Strong in-plane magnetic field (~30T) mixes the bright

exciton and the dark exciton states which allow for the detection of dark transitions that gain

oscillation strength as the magnetic field increases[3142] Another method is to take advantage

of the emission polarization of the dark exciton Symmetry analysis shows that the spin-

forbidden dark exciton is not completely dark It couples to light whose polarization in the z-axis

(normal to the plane of the monolayer) In fact if the monolayer is excited and collected from the

edge of the monolayer strong peak 40 meV below the neutral exciton peak emerges in the PL

spectrum of monolayer WSe2[43] corresponding to the conduction band splitting High NA

objective also gives rise to the out of plane optical excitation polarization As a result the spin

22

forbidden dark exciton also shows up in normal incidence PL when high NA (numerical

aperture) objective is used[43]


tungsten(molybdenum) based monolayer TMD denoted WX2 and MoX2 respectively b)

Momentum indirect dark exciton in which electron and hole are not in the same valley

c) Momentum indirect dark exciton in which same valley electron located outside of the

light cone Figures adapted from ref [7]

K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23

2 Momentum indirect dark exciton

Momentum indirect dark exciton composes of parallel spin electrons but located at

separate valleys in the band structure (figure 26b) or the electron located outside of the light

cone (figure 26c) In order to interact with light the momentum indirect exciton needs to

exchange momentum with phonon to make up for the momentum difference Higher temperature

gives rise to more phonons Thus one would expect the indirect momentum exciton gets brighter

with respect to increased temperature

VI Valley property of excitonic states (ie exciton trion)

1 Valley polarization

Valley polarization often refers to the population difference between K and K valley

Based on the spin-valley locking one can selectively excite carriers with the excitation energy

above the band gap in K (K) valley using σ+ (σ-) circular polarized light Electrons and holes

then relax to the band edge to form excitons which can be radiatively recombined to emit

photons The degree of valley polarization for an excitonic state (exciton trion) in PL signal is

usually quantified by the formula

Where Ico_circ (Icross_circ) is the PL signal that emits at the same(opposite) circular polarization with

the excitation polarization By writing out the rate equation explicitly taking into account the

population generated by optical pumping population recombination and relaxation it can be

shown that[12]

24

Where τA and τAS are the total lifetimes and the intervalley relaxation time of the exciton Thus

if it takes longer or comparable time for the exciton to scatter across the valley (intervalley

scattering) than the exciton total lifetime the circularly polarized emission from exciton will be

observed Figure 27ab shows the circular polarized steady-state PL for monolayer MoS2 and

monolayer WSe2 respectively On the other hand the valley relaxation time of the exciton in

monolayer WSe2 at cryogenic temperature has been measured by the circular pump probe

technique to be less than 1ps[44] The total lifetime of the WSe2 monolayer exciton is even faster

~200 fs[45] Remarkably the spin lifetime of the free carrier electron and hole in monolayer

TMD is extremely long on the order of a few nanoseconds[46] The primary cause of the fast

depolarization of the exciton is the intervalley electron-hole exchange interaction [11] which can

quickly annihilate bright exciton in K valley accompanying with the creation of bright exciton in

opposite valley K[47]

25

2 Valley coherence

Valley coherence refers to the phase preservation (coherence) between K and K valley

exciton One can readily observe the valley coherence of exciton in monolayer TMD by

excitation using linear polarized light and measuring the linear polarized PL signal Linearly

polarized light can be considered as a superposition of σ+ and σ- polarization Thus if the linear

polarization of the emitted light from the exciton is preserved so is the coherence between K and


14K The excitation energy is indicated by the arrow which is 196 eV Figure adapted

from ref [12] b) The circular polarized photoluminescence spectrum of monolayer WSe2

at 4K excited with the same energy as part a) Figure adapted from ref [11] X0 and X-

denote the exciton and trion peak respectively

co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26

K valley excitons Following the definition of the degree of valley polarization we can define

the degree of valley coherence as

Where Ico_lin (Icross_lin) is the PL signal that emits at the same(orthogonal) linear polarization with

the excitation polarization By pumping above the exciton resonance the valley coherence of the

exciton in monolayer TMD has readily observed if the excitation energy is close to that of the

exciton Figure 28a shows the linear polarized PL signal on monolayer WSe2 pumping at 188

eV[11] Figure 28b shows that the intensity of the neutral exciton is maximized whenever the

detection polarization is in the same polarization of the excitation

27

Figure 28 a) The linear polarized PL of monolayer WSe2 at cryogenic temperature

excited with 188 eV CW laser Different gate voltages are used to control the

emergence of neutral exciton X0 negative trion X- and positive trion Co(cross) linear

detection is plotted as the black(red) curves b) Normalized neutral exciton intensity

peak as a function of detection polarization angles Figures adapted from ref [11]

28

VII Trions

1 Definition and basic properties

Trion or charged exciton is the exciton bound with an extra electron ie negative trion or

an extra hole ie positive trion The binding energy of trion is defined as the energy difference

between exciton peak and trion peak either in PL or absorption measurement Trion binding

energy in monolayer TMD is about 20 to 40 meV which is one order of magnitude stronger than

trion in GaAs quantum well[848] The samples fabricated by CVD or mechanical exfoliation are

often n-type (negatively doped with extra electrons) The formation of trions is very

likely[4950] Strong trion binding energy is also due to reduced dielectric screening discussed in

the previous section In contrast to exciton trion is a charged particle Therefore it directly

influences electrical transport in a semiconductor The process of the exciton capturing an extra

charge to form trion is energetically favorable Indeed by using the pump probe technique we

have directly measured this process to be happening in a few pico-second timescales[51]

In fact one can adjust the doping level in the sample by fabricating metal contacts in

order to control the emergence of negative or positive trions One such example is shown in

figure 25a where a monolayer MoSe2 is put under two metal contacts The gate voltage is then

varied to p-dope the sample with extra holes (negative gate voltage) or n-dope the sample with

extra electrons (positive gate voltage) The PL spectrum of the monolayer is monitored as a

function of the gate voltage in figure 29c Four prominent features can be seen in figure 29c At

Vg=0 exciton sharp peak shows up at 1647 eV and impurity broad peak is at 157 eV Trion

shows up at either negative or positive gate voltage at energy 1627 eV Thus the trion binding

energy in monolayer MoSe2 is 20 meV The similarity in energy between positive and negative

29

trions indicates that the electron and the hole in monolayer TMD have approximately the same

effective mass which is consistent with the theoretical calculations [3052] More interestingly

n-dope regime gives rise to two types of trions intervalley and intravalley trion which show up

in the absorption spectrum of the monolayer if the linewidth is sufficiently narrow (figure 25d)

These two types of trions will be discussed in the next subsection

30


schematic to control the doping level in the sample c) PL spectrum of the monolayer as a

function of gate voltage The labels are as followed X0 exciton X- negative trion X+ positive

trion XI impurity peak Figures adapted from ref [8] d) Contour plot of the first derivative of

the differential reflectivity in a charge tunable WSe2 monolayer Double trion peaks emerge

at the n-dope regime Figure adapted from ref [17]

Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31

2 Intervalley and intravalley trion in monolayer TMD

Trion is a charged exciton - exciton bound to an extra hole or extra electron If the extra

electron or hole resides in the same(opposite) valley as the excited electron-hole pair the trion is

called intravalley(intervalley) trion Because the exfoliated monolayer TMD on a substrate is

unintentionally n-doped[4453] we will restrict our discussion to the negative trions only The

charge configurations of different species of trion are shown in figure 210

The conduction band splitting has a different sign for W-based monolayer and Mo-based

monolayer Because bright exciton is not the lowest energy exciton in monolayer WSe2 an extra

electron from either the same valley or from opposite valley can bind with the exciton to form

trion (figure 210a and b) On the other hand bright exciton in monolayer MoSe2 is the lowest

energy exciton so extra electron must come from the opposite valley to form trion Intravalley

trion in monolayer MoSe2 is much higher in energy than intervalley trion (figure 210c) and is

energetically unfavorable to form

Figure 210 Charge configuration of (a) intravalley trion (b) intervalley trion of

monolayer WSe2 and (c) intervalley trion of monolayer MoSe2

a) b) c)

Monolayer WSe2 Monolayer MoSe2

Intravalley trion Intervalley trion Intervalley trion

32

Inter- and intravalley trion in hBN encapsulated monolayer WSe2 has been observed

experimentally in PL signal at cryogenic temperature[54] The energy splitting between

intervalley and intravalley trion due to electron-hole interaction is predicted and observed to be 6

meV It turns out that because of the charge configuration intravalley trion can retain its valley

polarization about two orders of magnitude longer than intervalley trion This is one of our own

contributions to the field and will be discussed in more details in the later chapter

33

Chapter 3 Introduction to TMD heterostructure

In this chapter well look at the properties of TMD heterostructure particularly TMD

vertical heterobilayer (hBL) which possesses type II band alignment[55-57] and can host

interlayer exciton (IX)ndash with electron and hole localized in different layers Interlayer exciton

has a much weaker dipole moment about two orders of magnitude[58] and much longer lifetime

three order of magnitude than the intralayer exciton counterpart[13] Moreover heterobilayer

composed of monolayers with a slightly different lattice constant andor twist angle can give rise

to Moireacute superlattice[5960] with unique effects on the interlayer exciton potential landscape and

optical properties[61]

I TMD heterobilayer band alignment and optical properties

TMD vertical heterobilayer is made of two monolayers stacked on top of one another

either by transfer of mechanically exfoliated monolayer or CVD (chemical vapor deposition)

growth Due to different band gap and the work function of two constituent monolayers TMD

heterostructure has type II band alignment where the conduction band minimum is in one layer

and the valence band maximum is in other[55] Several experiments have measured the band

alignment directly in TMD heterobilayers Sub-micrometer angle-resolved photoemission

spectroscopy determines the valence band offset of MoSe2-WSe2 heterobilayer to be 300 meV

with the valence band maximum located at K and K points[62] Type II band alignment is also

found by scanning tunneling microscopy measurement on MoS2-WSe2 heterobilayer with

valence band (conduction band) offset of 083 eV (076 eV) at K and K points[57] Thus

electrons and holes once created quickly transfer and accumulate in the opposite layers in few

tens of femtoseconds timescale[63] Electron and hole residing in different layers bind together

34

by Coulomb attraction forming interlayer exciton (IX) Early experiment on MoSe2-WSe2

heterobilayer has reported the observation of interlayer exciton PL signal at the cryogenic

temperature around 14 eV(figure 31c) The spatial separation of electron and hole results in

much weaker dipole moment (around two orders of magnitude) of interlayer exciton than that of

the intralayer counterpart Thus as a consequence the interlayer exciton lifetime is much longer

in order of nanoseconds compared to just a few picoseconds of intralayer exciton[6465] at

cryogenic temperature

35

Valley physics of interlayer exciton is especially interesting In the simplest case with

zero twist angle the conduction band K (K) valley from MoSe2 is aligned with valence band K

(K) valley from WSe2 in momentum space (figure 31b) The interlayer exciton is thus a

momentum direct exciton As the twist angle increase the conduction band minimum moves

away from the valence band maximum at K point[66] The IX becomes indirect in momentum

space with decreasing dipole moment decreasing emission intensity and longer

lifetime[106167] At 60o Krsquo conduction band minimum is aligned with the K point valence


minimum (valence band maximum) is belong to monolayer MoSe2(WSe2) Charge transfer

intra- and interlayer exciton recombination timescales are indicated b) Band structure of

the aligned TMD heterostructure at 0 degree stacking angle Conduction band K(K) valley

from MoSe2 is aligned with valence band K(K) valley from WSe2 in momentum space c)

The low temperature PL spectrum of an aligned heterobilayer MoSe2-WSe2 featuring

interlayer exciton (IX) peak around 14 eV Figure adapted from ref [13]

WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36

band maximum Hence the twist angle is also an experimental knob that allows one to tune the

properties of the interlayer exciton in these heterostructures Furthermore mirror symmetry is

restored in TMD bilayer As a consequence both singlet Sz=0 and triplet Sz=1 excitons are

presented in heterobilayer[68] The triplet excitonrsquos dipole moment is estimated to be 23 of the

singletrsquos theoretically[60]

II Moireacute pattern in TMD hetero-bilayer

The moireacute pattern is the interference pattern resulted from two similar templates being

overlaid on top of one another In 2D material heterostructure Moireacute superlattices form when

two monolayers have slightly different lattice constant andor small twist angle (figure 33)

Moireacute superlattice imposes additional periodic potential that opens a new way to engineer

electronic band structure and optical properties[6069] For example in twisted bilayer graphene

a Moireacute superlattice has led to the observation of unconventional superconductivity and

Hofstadter butterfly spectra in the presence of a strong magnetic field[7071]


transition requires the participation of Δk momentum phonon Figure adapted from ref

[13] b) The PL intensity of IX decreases as the twist angle increase from 0o and increases

again as the twist angle approaching 60o Figure adapted from ref [10] c) Time resolved PL

of IX detected at 1320 meV for three samples with increasing twist angles showing

increased lifetime of IX for larger twist angle sample

IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37

Experimentally the potential landscape of WSe2-MoS2 heterobilayer has been directly

mapped out using a scanning tunnel microscope (STM) which shows Moireacute superlattice of 87

nm in size[9] Lattice mismatch between MoS2 and WSe2 monolayers gives rise to a spatial

variation of local atomic alignment Within the moireacute supercell there are three locations that

preserve the three-fold symmetry

refers to -type stacking (near zero degrees

twist angle) with the site of the MoS2 layer aligning with the hexagon center ( ) of the WSe2

layer can be h hexagonal site X chalcogen atom or M Mo metal atom The separation (Å)

of the two monolayers and the bandgap (meV) all vary periodically within the Moireacute supercell

and reach their optimal values at one of the sites

Local band gap and layer

separation can vary as much as 200 meV and 2 Å - more than twice each layer thickness (figure

33de)[9]

38

Figure 33 a) STM image of rotational aligned WSe2-MoS2 heterobilayer showing the moireacute


denoting the locations

that retain the three fold symmetry c) Zoom in view showing the specific atomic

alignment d) and e) Layer separation and band gap variation of the TMD moireacute pattern

respectively Figures adapted from ref [9]

25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)

Spatial dimension (nm)14

12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39

Chapter 4 Experimental Techniques

In this chapter we describe in details the working principle as well as the makeup

components of various optical techniques in the lab These include linear optical measurements

such as photoluminescence and white light absorption as well as nonlinear techniques such as

pump-probe spectroscopy and second harmonic generation

I Photoluminescence (PL)

PL measurement is one of the most widely used optical techniques for the

characterization of semiconductors PL is light emitted when photo-excited carriers decay from

the higher excited state to lower excited or ground state[72] These emission states may be defect

levels continuum levels in the conduction or valence bands or exciton states Thus the

interpretation of PL spectrum requires detailed knowledge of the energy levels of the sample

However PL measurement is a very quick simple and powerful characterization tool For

example the PL of the TMD sample at room temperature helps identify whether the sample is

monolayer or bilayer This is our method to verifyensure monolayer sample Exciton PL

linewidth of monolayer TMD sample at cryogenic temperature tells us about samples quality

Higher quality sample with low defect density gives rise to lower inhomogeneous broadening

and narrower linewidth[73] Other advantages of PL measurement include its ability to indirectly

measure the non-radiative recombination rate its ability to investigate very shallow levels and

yield information about the symmetry of an energy level[72] PL is also non-destructive requires

only a very small amount of material to work with PL can also be readily combined with other

tools to yield greater information about the material such as external magnetic field external

40

electric field and electrical doping (by means of metal contacts) pressure (by incorporating

pressure cell) temperature (cryostat)

Photoluminescence excitation (PLE) spectroscopy is a variation of PL measurement in

which the excitation energy is tuned through a particular energy level in order to excite

luminescence transitions related to the level being pumped PLE is an important tool for

investigating relationships between different luminescence transitions For example in this

report[74] PLE has been used to establish the moireacute exciton as the origin of multiple intralayer

exciton peaks

The PL optical setup is depicted schematically in figure 41 A laser (continuous wave or

pulsed) is focused on the sample by a microscope objective Here the laser and the luminescence

are transmitted through the sample to the spectrometer The laser is cut off by a filter so that only

the luminescence enters the spectrometer PL can also be set up in the reflection geometry in

which the luminescence is reflected back through the objective to the spectrometer

41

II White light absorption measurement

The white light absorption measures the absorption spectrum of a particular sample ie

how much light the sample absorbs as a function of photon energy This is different from PL

which measures how much light the sample emits Because some electronic and excitonic states

might only absorb without emitting (continuum states higher excited state) while other states

only emit instead of absorbing light (defect states) comparing PL and absorption spectra can

give valuable information about nature of different energy levels within the sample

The white light absorption setup is very similar to the PL setup (figure 41) except instead

of a laser a broadband white light source is used The white light is then focused on to the

Figure 41 Schematic of the photoluminescencewhite light absorption optical setup

42

sample and the transmission spectrum is revealed by the spectrometer subsequently Also the

wavelength filter is removed because the spectrum should not be cut off The transmission

spectra when the white light going through the sample (Tsamp) and when the white light only

going through the substrate (Tsub) are collected The absorption spectrum is calculated as

III Pump probe spectroscopy

1 Working principle

The pump probe spectroscopy is a very common type of ultrafast laser spectroscopy

There are variations of different types of pump probe In its simplest form the output pulse train

of an ultrafast laser is split into two optical paths (see figure 42) The difference in path lengths

of two beams can be changed by a mechanical delay stage which in turn controls the relative

arrival of the pulses on the sample The pump pulse is filtered out by either a polarizer or a

spectrometer after transmitted through the sample Only the probe pulse is measured by the

detector

43

Briefly the pump probe technique measures the transient absorption of the sample The

idea is that absorbing the pump decreases the samples capability to absorb the probe Recall that

the pump is completely blocked from entering the detector the probe intensity is monitored as a

function of the delay stage ie the relative arrival at the sample between the pump and the probe

The pump probe signal is defined by the difference in probe intensity with the pump present and

the probe intensity without the pump present

Where T(T0) is the intensity of the probe with(without) the presence of the pump The probe is

detected through a single channel detector connected to a lock-in amplifier We will discuss in

detail the lock-in detection technique later on in this chapter


out with variable delays between them interact co-linearly with the sample The intensity

of the probe is monitored as a function of the delay while the pump is filtered out before

the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44

The beauty of the pump probe technique is that the temporal resolution is determined by

the pulse duration and is not affected by the slow (~ nanosecond) single channel detectors

response The measurement temporal resolution is only limited by how broad the pulse widths

are when the pulse interacts with the sample Due to optical dispersion the pulse gets broader

and broader as it passes through optics with the finite index of refraction (lenses polarizers

waveplates ) By the time the pulse reaches the sample its width might be orders of

magnitude longer than the pulse width output of the laser cavity Thus it is important to

characterize the pulse width where the sample is located for it is determined how fast the

dynamics process of the sample we can measure The measurement of the pulse duration is

called auto-correlation and is discussed in more details later

2 Two color pump probe technique

We have discussed above that pump probe is analogous to transient absorption

measurement in which the delay between pump and probe pulses reveals the absorption overtime

of particular resonances ie trion and exciton Different resonances of the sample have different

dynamics due to differences in physical properties Degenerate pump probe in which the pump

photon energy equals the probe energy can be used to measure the dynamics of exciton and trion

separately However measurements of interaction between these quasi-particles cannot be

performed Degenerate pump probe thus has certain limitations in measuring interesting

interaction phenomena

Two color pump probe technique (figure 43) allows one to measure couplinginteraction

between resonances based on the fact that the pump and probe photon energies can be tuned

independently using grating based pulse shapers Using this technique one can for example

45

pumping on the exciton(trion) and probing on the trion(exciton) thus revealing important

dynamics about trionexciton coupling In addition two color pump probe technique can be used

to probe relaxation pathways In the following sub-sections we will discuss in details different

components that make up the two color pump probe optical setup

a Pulse shaper

The scanning range of the pump and probe wavelengths is limited by the bandwidth of

the pulsed laser In the case of the Tisapphire laser this range is about 30 nm for both pump and

probe pulse shaper Figure 44 describes the working principle of a pulse shaper It consists of a

diffraction grating a focusing lens a mirror and a movable slit First the output pulse train of a

Tisapphire laser (indicated by a big gray arrow in figure 44) is diffracted by the diffraction

Figure 43 Two color pump probe optical setup In addition to the simple pump probe in

the previous figure the pulse shapers are inserted to independently vary the wavelength

or photon energy of two pulses

46

grating which causes its spectrum to spread out in the spatial dimension A focusing mirror

collimates this 1st order diffracting light on to a mirror which sends the diffracting light back on

to its original path The distance between the diffraction grating and the lens is equal to that of

the lens and the mirror which is also the focal length of the lens For the setup in the lab we use

a 20 cm lens To select pulses with different photon energies a narrow movable slit is positioned

right in front of the mirror The width of the slit determines how broad the spectral bandwidth of

the pulse is which ultimately determines the spectral resolution of the measurement Typically

we choose the slit such that it gives the spectral resolution of 1 nm Broader slits however are

available and can be interchanged for broader bandwidth pulse with more optical power The

selected pulse (red color in figure 44) is then reflected back through the lens This selected pulse

will be caught by a small circular mirror and sent on the way to the sample Because of the

optical dispersion the pulse width coming out of the pulse shaper is broader than the input pulse

width as indicated in figure 43 Thus we sacrifice the temporal resolution for the corresponding

increase in spectral resolution

47

b Acousto-optic modulator (AOM)

The next optical component on the laser path (figure 45) is the AOM or acousto optic

modulator The AOMs (manufactured by Gooch-Housego) main component is the crystalline

tellurium dioxide and offers high-frequency modulation which is around megahertz regime

instead of kilohertz modulation of the mechanical chopper Briefly an RF (radio frequency)

carrier wave ( depending on the phonon frequency of the AOM crystal) is mixed

with the modulation wave The RF mixed signal drives a piezoelectric transducer

which effectively shakes the AOM crystal at the RF mixed frequency This shaking creates a

traveling sound wave within the AOM with trough and crest of varying index of refraction The

input laser is diffracted from this grating of the sound wave such that its intensity is modulated

by the modulation frequency (figure 45) The deflection angle of the refracted beam from the

input beam can be adjusted through varying the carrier frequency ie


probe setup

48

For the pump probe setup in our lab we modulate both the pump and probe beams using

the AOMs The pump(probe) is modulated at 175(178) MHz The carrier frequencies for the

pump and probe AOMs are 80 and 81 MHz respectively The probe carrier and modulation as

well as the pump modulation RF signals are generated by Novatech Instruments model 409B

The pump carrier signal is however generated by separate device HP 8656B The modulation

signal is mixed with a carrier signal and then is amplified before transferring to the AOMs The

lock-in detects the pump probe signal at the difference in modulation frequency between pump

and probe AOMs or 30 kHz

c Lock-in detection technique

The working principle of a lockin amplifier is illustrated in figure 46 A lockin can

extract a signal up to a million times smaller than the noisy background The lockin works by

looking for the pure signal oscillating at the reference frequency in a noisy background In other

words it locks on to the reference frequency to extract the pure signal oscillating at that

frequency In our case the noisy signal (S) comes from the balance detector which monitors the


modulator)

49

probe intensity The reference signal (R) is a sinusoidal function oscillating at the difference

between pump and probe modulation ie 30 kHz from the Novatech generator

How does the lockin extract the pure signal The reference frequency(R) is multiplied by

the noisy signal (S) and integrated over the chosen time interval t0 Consider the total signal

which is a function of multiple different frequency components input into the

lockin The desired signal (pure signal) oscillates at the difference frequency Then

the output of the lockin will have the form

where is the reference signal The result is a DC signal with contributions only

from signal components oscillating at the reference frequency Signal components at all other

frequencies average out to zero The integration time t0 is very long compared with the sample

rate of the lockin in order to average over slowly varying noise Typically we choose t0 to be

100 milliseconds or 300 milliseconds Further signal improvement can be achieved using passive

bandpass filters These filters are built-in the lockin For example to detect signal at 30 kHz we

use bandpass filters from 10 kHz to 100 kHz which help to improve the signal to noise ratio

tremendously These filters also help to block the probe signal which oscillating at 178 MHz

from overloading the lockin

50

Finally to illustrate the lockin detection technique we will look at a very simple

derivation The signal entering the detector is the intensity of the probe which is the function of

the intensity of the pump (because whether the sample absorbs the pump will change the

intensity of the probe)

where S(t) is the signal entering the detector is the probe(pump) intensity Since the

pump is modulated at frequency becomes

Expand S(t) only up to first order

where is the oscillation amplitude of the probe(pump) Here we also recall that the

probe is modulated at Thus our signal becomes


convolution using the integrator

51

Since the lockin only picks up the term at frequency The signal output of the lockin

is proportional to

Since the change in the probe intensity is small this term becomes

which is the pump probe signal

d Drift control of the sample inside the cryostat

TMD sample has lots of spatial inhomogeneity due to bubbles and residues accumulated

during the fabrication process That is small regions have a different optical signal from the rest

Thus it is important to limit our studies to a particular region of the sample Unfortunately there

is a thermal drift of the sample when it is cold This motion is random and is due to temperature

variation within the cryostat Thus it is crucial that we utilize a drift control that can correct for

this random motion from time to time

The drift control program is based on Labview image recognition software which can

recognize a pattern within an image and can extract the pattern coordinate within the image

When the selected pattern within the white light image is first chosen its initial coordinate (in

term of pixel number) is recorded Later on Labview looks for the selected pattern again and

extract its current coordinate Based on the difference between the current and the initial

coordinates Labview tells the mechanical stage on which the microscope objective is mounted to

52

move and correct for this difference If no difference is detected the stage doesnrsquot move

Labview corrects for drift every 5 seconds This time can be increased or decreased depending

on how much the sample is drifted during the measurement

2 Auto-correlation measurement

As mention in the beginning measuring the pulse duration at the sample location is very

important in characterizing the temporal resolution of the pump probe setup Since the response

of the electronics is very slow in order of nanoseconds we cant rely on them to measure the

pulse duration The autocorrelation measurement is to use the pulse to measure itself The

autocorrelation setup is almost identical to the two color pump probe setup except two-photon

detector is used in place of the sample The basic idea is to convert a measurement in the time

domain into a measurement in the space domain by increasing the path length of the pump with

Figure 47 Schematic of the autocorrelation setup to measure the pulse duration

53

respect to the probe by mean of a delay stage[26] Since the speed of light is 30 m100 fs in free

space it is easy to measure the pulse duration as short as few femtoseconds by precisely control

the delay distance with submicron accuracy The two-photon absorption detector connected to

lockin modulation yields the autocorrelation signal proportional to the temporal overlap of the

pump and probe pulses

where Ipu(Ipr) is the pump and probe intensities tD is the delay time between the two pulses Here

we assume that the two pulses have the symmetrical and identical shape (gaussian) and same

duration The width of the I(tD) divided by is the pulse duration

II Second Harmonic Generation (SHG) techniques

We use the second harmonic generation (SHG) signal from the TMD monolayer to

determine its crystal axis ie which direction is zigzagarmchair This information is critical to

making TMD heterostructures with various twist angles There are two types of SHG techniques

polarization-resolved SHG and spectral phase resolved SHG The polarization resolved

technique can determine the direction of zigzag and armchair of a monolayer Since monolayer

TMD has three-fold rotational symmetry aligning two zigzag or two armchair directions of two

monolayers will lead to either zero or 60 degrees stacking angle The spectral phase resolved

SHG completely specifies the crystal axes of monolayers which in turn determines 0o or 60

o

twist angle

1 Introduction to SHG

54

The optical response of a material is expressed in terms of the macroscopic polarization

When the optical power is small the relationship between the polarization and the incident

electric field is linear

where is the linear susceptibility Most of the optical phenomena can be described using

this linear relation A typical example is the familiar index of refraction which is given by

When the incident optical power increases the behavior of the sample deviates from the

linear regime The response of the material can now be described as a Taylor expansion of the

material polarization in powers of the electric field

In this section we will restrict ourselves to the discussion of the second order optical

response The incident electric field can always be written in term of plane waves

We obtain the second harmonic response of the form

is a third rank tensor In 3 dimensional space each index can be x y or z direction Thus

the tensor has components in total Most often this number is reduced For

example due to the commutative property of tensor contraction ie

the

number of distinct components becomes 18 Furthermore geometrical symmetry within a

55

specified crystal reduces this number further Eventually it is the symmetry information

contained in

that reveals the crystal axis of our monolayer

For monolayer TMD with the trigonal prismatic crystal structure

has only 4 non

zero components If we define the coordinate system as shown in figure 46 then these 4

components are

They give rise to different SHG signal polarizations depending on the crystal orientation

2 Polarization-resolved SHG setup

The polarization-resolved SHG is for determining the crystal axis of the monolayer

TMD The setup has been described in ref [7576] and is shown schematically in figure 49a

Briefly the output pulse train at 800 nm of a tisapphire laser is focused on to the monolayer


counter clockwise 120o rotation will make the crystal structure identical to a)

Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

which in turn generates the second harmonic signal at 400 nm The signal can be collected either

in the reflection or transmission geometry The excitation laser 800 nm is polarized linearly in

the horizontal direction The SHG signal 400 nm goes through an analyzer which is cross-

polarized (vertical polarization) with the excitation laser As the sample is rotated the SHG

intensity traces out six-fold degenerate signal as shown in figure 49b The maxima correspond to

the crystal axis ie when the crystal axis is parallel to the incident laser polarization

3 Spectral phase resolved SHG setup

One drawback of the polarization-resolved SHG is that it cannot distinguish between

monolayers differed by 60o rotation as shown in figure 48a-b This is important for making

bilayer with 0o or 60

o degree twist angles One can determine this before stacking by performing

the spectral phase resolved SHG measurement[77-80] after the polarization-resolved SHG The

spectral phase resolved SHG setup is described schematically in figure 410a The pulsed laser

centered at 800 nm ( ) is focused onto the sample using a 10X objective generating the SHG

Figure 49 a) Schematic of the polarization resolved SHG setup b) SHG polarized

intensity as the sample is rotated 360o in the plane to which the laser beam is

perpendicular to

b)a)

57

signal at 400 nm ( ) The laser power at the sample is kept about 5 mW with a 5 spot size

A beta barium borate (BBO) crystal generating a reference SHG signal ( ref) is positioned

right after the sample which is put on a standard microscope slide Because the group velocity of

the fundamental pulse ( ) is faster than that for the SHG pulse ( ) as they travel through the

sample substrate and the microscope slide the fundamental will arrive at the BBO crystal first

As a result the generated ref pulse precedes the sample by a delay time Δ which

depends on how much glass between the monolayer and the crystal through which the laser

pulses travels We find that the ~1 mm thickness of an amorphous SiO2 microscope slide gives

rise to 12 nm fringes in the interference spectrum between the ref and the sample pulses

shown in figure 410b-c Thicker glass or additional optics between the monolayer and the BBO

crystal causes larger time delay Δ and more finely spaced fringes rendering the SHG

interference undetectable During the measurement the BBO crystal orientation is fixed First

the SHG interference between monolayer WSe2 and the BBO crystal is measured in which the

WSe2 zigzag direction (determined in polarization-resolved SHG) is aligned in the horizontal

direction Similarly the monolayer MoSe2 SHG phase-resolved spectra are taken with its zigzag

direction aligned horizontally Two interference spectra are plotted on top of each other for

comparison If the spectra are in phase (out of phase) as shown in figure 410b (figure 410c) the

two stacked monolayers will have near 0o (60

o) twist angle

58

4 SHG signal calculation

In this subsection we briefly derive the SHG signal detected in the polarization SHG

measurement We see the reason why full rotation of the sample yield six-fold degenerate SHG

signal (figure 48b) and why the maxima correspond to the crystal axis First of all let define our

coordinate systems XOY(XOY) is the lab(sample) frame of reference Since our excitation

laser is polarized in the x-direction the SHG summation

only contain one

term for both

and

ie

Figure 410 a) Schematic of the spectral phase resolved SHG setup b) SHG phase

resolved spectra between the monolayers and the BBO crystal with signal in phase for a

near twist angle stacking c) Similar to b) but with out-of-phase signals for a near

twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59

Since we only know the components of

in the sample coordinate system we need to do the

tensor transformation

We are all very familiar with vector rotation which is a 1st rank tensor transformation

The relationship between vectors in XOY and XOY coordinates can be written as

This sum can be expressed in the matrix multiplication form

We therefore have identified the components of the transformation matrix being

The 3rd rank tensor transformation of

is similar to the above only has more terms in

the sum It is the relation

The sum for a particular component of

consists of only 4 terms instead of 27 because most of the components of

are zeros which

are discussed in the previous subsection Carrying out the summation for

we obtain

The transformation of

is very similar Thus the electric fields of SHG polarized in the x

and y directions are respectively

60

The intensity of SHG is the square of Px and Py Thus the polarization-resolved SHG is six-fold

degenerate Furthermore if which means the armchair is aligned with the horizontal

direction SHG signal is minimized in the x-direction and maximized in the y-direction We then

have a way to tell the crystal orientation of the monolayer


reference in which OX(OY) is the horizontal(vertical) direction XOY is the sample frame

of reference in which OX(OY) is the armchair(zigzag) direction Angle between OX and

OX is

61

Chapter 5 Steady-state valley properties and valley dynamics of monolayer

TMD

In this chapter we will take a look at two studies of monolayer TMD coming from our

group They are published as Physical Review B 96 041302(R) (2017) and Physical Review

Letter 117 257402 (2016) respectively

I Disorder-dependent valley properties in monolayer WSe2

We investigate the effect on disorder potential on exciton valley polarization and valley

coherence in monolayer WSe2 By analyzing polarization properties of photoluminescence the

valley coherence (VC) and valley polarization (VP) is quantified across the inhomogeneously

broadened exciton resonance We find that disorder plays a critical role in the exciton VC while

minimally affecting VP For different monolayer samples with the disorder characterized by their

Stokes Shift (SS) VC decreases in samples with higher SS while VP again remains unchanged

These two methods consistently demonstrate that VC as defined by the degree of linearly

polarized photoluminescence is more sensitive to disorder potential motivating further

theoretical studies

1 Motivation

Valley refers to energy extrema in electronic band structures Valley pseudo-spin in

atomically thin semiconductors has been proposed and pursued as an alternative information

carrier analogous to charge and spin [353781-84] In monolayer transition metal

dichalcogenides (TMDs) optical properties are dominated by excitons (bound electron-hole

pairs) with exceptionally large binding energy and oscillator strength [332] These excitons form

62

at the energy extrema ( ) points at the Brillouin zone boundary thus inheriting the ( )

valley index Valley contrasting optical selection rules make it possible to optically access and

control the valley index via exciton resonances as demonstrated in valley specific dynamic Stark

effect [85-87] as an example

For valleytronic applications particularly in the context of using valley as an information

carrier understanding both valley polarization and valley coherence are critical Valley

polarization represents the fidelity of writing information in the valley index while valley

coherence determines the ability to optically manipulate the valley index Earlier experiments

have demonstrated a high degree of valley polarization in photoluminescence (PL) experiments

on some monolayer TMDs (eg MoS2 and WSe2) suggesting the valley polarization is

maintained before excitons recombine [12378384] Very recently coherent nonlinear optical

experiments have revealed a rapid loss of exciton valley coherence (~ 100 fs) due to the intrinsic

electron-hole exchange interaction in WSe2 [47] In fact the ultrafast dynamics associated with

the valley depolarization (~ 1 ps) [44] and the even faster exciton recombination (~ 200 fs)

[7388] extracted from the nonlinear experiments are consistent with the PL experiments As

long as the valley depolarization and decoherence occurs on time scales longer or comparable

with exciton recombination lifetime steady-state PL signal shall preserve polarization properties

reflecting the valley-specific excitations

It is important to ask the question if disorder potential influences valley polarization and

coherence considering the fact that there are still a significant amount of defects and impurities

in these atomically thin materials This critical question has been largely overlooked in previous

studies Here we investigate how valley polarization and coherence change in the presence of

disorder potential First valley coherence is observed to change systematically across the

63

inhomogeneously broadened exciton resonance while there are no observable changes in valley

polarization We suggest that this systematic change is related to exciton localization by disorder

potential where the low energy side of the exciton resonance corresponds to weakly localized

excitons and the high energy side is associated with more delocalized excitons [5189]

Furthermore we investigated a number of monolayer WSe2 samples with different defect density

characterized by the Stokes shift between the exciton peak in photoluminescence and absorption

A higher degree of valley coherence is observed in samples with a smaller Stokes shift or lower

defect density [9091] These two observations consistently suggest that shallow disorder

potential reduces valley coherence without influencing valley polarization appreciably Our

studies suggest that a more qualitative evaluation of valley coherence may guide the extensive

on-going efforts in searching for materials with robust valley properties

2 Background

Figure 51 a) The band structure of monolayer WSe2 at two degenerate K and K valleys Valley contrasting spins allow left (right) circular polarized light to excite excitons in the K (K) valley b) Bloch Sphere representation of valley pseudospin degree of freedom Circular polarized light prepares an exciton in |Kgt or |Kgt state ie states at the poles whereas linear polarized light prepares an exciton in a superposition of |Kgt and |Kgt ie states at the equator

|Kgt

|Krsquogt

b)

K Krsquo

a)

64

The low energy bands with associated spin configurations in monolayer WSe2 are

illustrated in figure 51a A dipole allowed (ie an optically bright) transition can only occur if

the electron in the conduction and the missing electron in the valence band have parallel spins

Thus the transition between the lowest conduction band and the highest valence band is dipole

forbidden and the lowest energy exciton transition is between the second conduction band and

the highest valence band as illustrated in figure 51a Using ( ) polarized excitation light

excitons are preferentially created in the ( ) valley due to the valley contrasting optical

selection rules [35] As with any binary degree of freedom K and Krsquo valleys can be represented

as a vector on a Bloch sphere as shown in figure 51b The degree of valley polarization is

defined by the normalized difference in cross-circular and co-circular signals as

(1)

where represents co (cross) circular polarized PL intensity with respect to the

excitation polarization Previous studies on monolayer WSe2 have reported a large valley

polarization in steady-state PL experiments [124783] suggesting that valley scattering rate is

slower or comparable with exciton population recombination rate In the Bloch sphere picture a

large VP suggests that once the Bloch vector is initialized along the north pole it retains its

orientation during exciton population recombination time On the other hand when a linearly

polarized excitation laser is used a coherent superposition of two valley excitons is created [11]

Such a coherent superposition state corresponds to a Bloch vector on the equatorial circle

Previous experiments suggest that exciton valley coherence can be monitored by the linearly

polarized PL signal [92] Here we follow this method and further quantify the degree of valley

coherence by the following definition

65

(2)

where represents co (cross) linear polarized PL intensity with respect to the excitation

polarization

3 Steady-state photoluminescence measurements

We first investigate the change of VC and VP as a function of energy across the exciton

resonance on a mechanically exfoliated monolayer WSe2 sample It is known that the degree of

valley polarization depends strongly on the excitation wavelength [1193] In our experiments

the excitation energy is chosen to be energetically close to the exciton resonance to observe a

finite degree of VC but far enough so that resonant Raman scattering does not interfere with VC

[1193] Unless mentioned otherwise for all PL measurements presented in this manuscript we

use a continuous wave laser at 188 eV (ie 660 nm) and keep the power ~ 20 microW at the sample

with a focused spot size of ~ 2 microm diameter A typical PL spectrum of monolayer WSe2 is

shown in Figure 52a with two spectrally well-resolved resonances corresponding to exciton and

trion (a charged exciton) respectively There are two additional resonances at the lower energy

which may be due to either dark states or impurity bound states [41] Here we focus on valley

physics associated with the exciton resonance shaded in blue

66

Figure 52 a) PL spectrum of monolayer WSe2 excited with 188 eV CW laser Blue shaded Gaussian represents the fits to the exciton resonance b) Zoomed in spectrum around the exciton resonance shows co (cross) linear PL signal with respect to the excitation laser polarization Corresponding VC is plotted on the right hand side c) PL spectra taken with co- and cross- circular PL signal with respect to a circularly polarized excitation laser PL intensity and VP are plotted on the left and right vertical axes respectively

1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67

Figure 52b plots the co- and cross-linear polarized PL and the corresponding VC across

the exciton resonance The VC drops to zero beyond the lower energy edge of the exciton

resonance due to the presence of the trion which cannot exhibit VC in PL spectra due to photon-

spin entanglement [11] Interestingly we observe a monotonic increase of the VC across the

inhomogeneously broadened exciton resonance with varying from 0 to 035 as shown in

Figure 52b This monotonic change in VC across the exciton resonance is qualitatively repeated

on all measured samples VC reaches the maximum value at the high energy side of the exciton

and approaches zero at the low energy end Beyond the high energy side of the exciton

resonance because of low signal VC plateaus and becomes noisy We suggest that the increase

of VC across the exciton resonance arise from the degree of exciton localization [519495]

Valley coherence associated with the delocalized excitons is more robust than the weakly

localized excitons

In contrast VP remains constant across the exciton resonance with ~ 048 as

illustrated in Figure 52c It has been suggested that only atomically sharp potentials can induce

inter-valley scattering and depolarization of valley exciton [11] Thus the invariability of the VP

suggests that the inhomogeneously broadened exciton resonance is mainly due to slowly varying

spatial potentials (in contrast to atomically sharp potentials) Such disorder potential may be

attributed to local strain as well as shallow impurity potentials [519495] This speculation is

also consistent with the observation that strongly localized excitons likely due to deep

atomically sharp potentials appear at much lower energy ~ 100-200 meV below the exciton

resonance[9697] An important mechanism causing valley depolarization is electron-hole

exchange unaffected by shallow potential fluctuations [98-100] Other valley scattering

68

mechanisms such as Dyakanov-Perel (DP) and Eliott-Yafet (EY) mechanisms are slower and

considered unimportant for excitons in TMDs [98]

4 Correlation of VC and VP versus Stokes Shift

To further investigate the role of disorder potential on valley properties we studied a

total of 6 monolayer WSe2 samples prepared with both CVD (chemical vapor deposition) and

mechanical exfoliation We quantify the defect density using the spectral shift between exciton

resonances measured in PL and absorption known as the Stokes shift (SS) As a simple method

based entirely on commonly used linear optical spectroscopy methods SS has been used to

characterize a wide variety of material systems [90101] including defect density [102-104]

monolayer fluctuations in quantum wells [91105106] and size distribution in quantum dots

[107108]

A typical SS measurement is shown in figure 53a The PL and white light absorption

spectra of the same exfoliated monolayer WSe2 are taken at 13K Briefly the absorption

spectrum is taken using a broadband white light source in the transmission geometry to minimize

reflection induced spectral line-shape changes To achieve similar spot sizes in both absorption

and PL measurements a 100 m pinhole is placed in the focal plane between two focusing

lenses in the white light path to optimize the spatial mode The absorption spectrum is plotted as

a differential and normalized spectrum where is the transmission through the

substrate and is the transmission through both the substrate and monolayer sample The

exciton resonances in the PL and absorption are fitted with Gaussian functions The peaks

extracted from the fittings are indicated by the dotted lines yielding a 48 meV SS for this

sample

69

To quantify the dependence of valley properties on SS (and on defect potentials) the

above measurements are repeated on all 6 samples We confirmed SS of a particular sample has

little to no temperature dependence as shown in the inset of figure 53a For comparison across

different samples the VC (or VP) value for each sample is calculated by taking the average of

the VC (or VP) in a range spanning from the exciton peak where is the fitted linewidth

We found the range of the spectral integration does not change our qualitative conclusion The

results as summarized in figure 53b have a number of interesting features Firstly VC is found

Figure 53 (color online) a) Stoke shift is shown as the difference in energy between the absorption spectrum and PL from the exciton resonance Inset SS dependence on temperature b) VC (VP) is plotted with respect to SS VC shows an inverse dependence versus SS whereas VP shows no recognizable trend

1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)

Temperature (K)0 40 80 300

a

5a

a

4a

a

3a

Sample E2

Sample E3

70

to decrease with increasing SS of samples with a fractional drop of ~ 25 between the samples

with the lowest to highest SS Specifically varies from 032 to 025 as SS changes from 21

meV to 86 meV Secondly VP has similar values for all the samples ( ~ 045) and no

correlation between VP and SS is observed Based on the assumption that SS is correlated with

the defect density in different samples we infer that disorder potential reduces VC but has little

influence on VP This conclusion is consistent with the spectral dependence of VC and VP

across the exciton resonance observed on a single sample as reported in figure 52b and 2c In

addition a recent experiment [94] investigated spatial variations of VP and VC on a CVD grown

monolayer WSe2 While VP was found to be mostly constant VC showed significant changes

likely arising from disorder potential

5 Conclusion

In summary we report a systematic study of the effect of shallow disorder potential on

VC and VP in monolayer WSe2 The low energy side of the exciton resonance is associated with

weakly localized excitons and the high energy side with more delocalized excitons Using

steady-state polarization resolved PL we observe that the VC monotonically increases across the

inhomogeneously broadened exciton resonance The VP on the other hand remains constant

across the exciton resonance VP and VC are then measured for samples with different SS (a

measure of disorder) We find that VC varies inversely with SS and VP remains largely

invariant Our observations suggest that shallow disorder potentials have a crucial effect on the

exciton valley coherence Particularly weakly localized excitons lose valley coherence more

rapidly than the delocalized excitons On the other hand disorder potential does not affect the

valley polarization noticeably Our work should motivate future experiments and microscopic

71

theoretical studies necessary for a comprehensive understanding of the effect of disorder on

valley properties in TMDs

6 Extended Data

a Fitting comparison of the absorption spectrum and Sample information

We have used 6 samples They are labeled CVD1 E2 E3 E4 E5 E6 where the first one

is CVD grown sample and the others are made by mechanical exfoliation The sample order is

arranged so that they are in order of increasing Stoke Shift

We have fit absorption profiles with three different lineshapes- gaussian lorentzian and

half gaussian (see figure 54) The comparison of the three methods is summarized below in

Table 61 In S2 we also show an example of the lineshape fitted with the three methods We

emphasize that the stokes shift measured with all three methods is very similar and hence does

not change our treatment and conclusions in any way

Sample Peak position (meV) FWHM (meV) Stokes Shift (SS)

L G Half-G L G Half-G L G Half-G

CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83

Table 61 Summary of peak positions full-width half-maximum (FWHM) and Stokes Shift (SS) using Lorentzian (L) Gaussian (G) and Half-gaussian fitting methods for different samples

72

b Stokes Shift plotted against absorption linewidth

We fit Gaussian profiles to exciton absorption spectra and plot SS versus FWHM of the

fitted Gaussian for all 8 monolayer samples (see figure 55) The vertical errorbars of SS are due

to the combined fitting errors of both PL and absorption peak The horizontal errorbars of

FWHM are small and therefore not visible on the scale plotted The correlation between SS and

FWHM is only valid on a certain range of the FWHM We speculate that the lack of correlation

between the two quantities could be due to different types of defects causing inhomogeneous

broadening in different samples

Figure 54 Absorption linewidth of sample E4 fitted using different profiles Lorentz

Gauss and half Gauss

73

c Subtracting trion contribution to exciton valley coherence

The data shown in figure 56 and data figure 52 are from the same exfoliated sample

whose SS is 48 meV Here we plot the data over greater energy range to show the trion

resonances explicitly We fit the trion resonances of co and cross linear PL signals with

gaussians We then subtract the trion fitting curve from co and cross PL signals and compute the

degree of valley coherence from exciton Evidently the degree of valley coherence computed

before and after the trion subtraction is the same


extracted and plotted against SS

74

d Omitted data from CVD sample


trion doesnt show any valley coherence the fits are essentially the same Valley coherence

is shown here before the trion subtraction from the co and cross signals b) After trion

subtraction the valley coherence is essentially the same signifying that trion has minimal

contribution to exciton valley coherence

75

Figure 57 Degree of a) valley coherence and b) valley polarization plotted across the

exciton resonance of omitted CVD sample c) Valley coherence and valley polarization

plotted against SS included the omitted data point

76

II Long-Lived Valley Polarization of Intravalley Trions in Monolayer WSe2

We investigate valley dynamics associated with trions in monolayer tungsten diselenide

(WSe2) using polarization resolved two-color pump-probe spectroscopy When tuning the pump

and probe energy across the trion resonance distinct trion valley polarization dynamics are

observed as a function of energy and attributed to the intravalley and intervalley trions in

monolayer WSe2 We observe no decay of a near-unity valley polarization associated with the

intravalley trions during sim 25 ps while the valley polarization of the intervalley trions exhibits a

fast decay of sim4 ps Furthermore we show that resonant excitation is a prerequisite for

observing the long-lived valley polarization associated with the intravalley trion The

exceptionally robust valley polarization associated with resonantly created intravalley trions

discovered here may be explored for future valleytronic applications such as valley Hall effects

1 Motivation

The valley degree of freedom (DoF) indices the crystal momentum of a local energy

minimum within the electronic band structure and has been proposed as an alternative

information carrier analogous to charge and spin [35] In atomically thin transition metal

dichalcogenides (TMDs) fundamental optical excitations excitons (electron-hole pairs) and

trions (charged excitons) are formed at the hexagonal Brillouin zone boundaries at the K (K )

points As such they inherit the valley index which is locked with electron spins in TMDs Thus

exciton and trion resonances allow optical access and manipulation of the valley DoF in TMDs

using circularly polarized light [81237109110] The exceptionally large binding energies of

these quasiparticles (ie 200ndash500 meV for excitons and an additional binding energy of 20ndash40

meV for trions) further promise room temperature valleytronic applications

77

[58536573109111-113] High-efficiency valley initialization and a long lifetime of valley

polarization are preferred in valleytronic applications [46114-116] Initial experiments based on

steady-state photoluminescence have shown the possibility of creating a near unity valley

polarization in MoS2 and WSe2 via exciton resonances [1112] Time-resolved measurements

soon revealed that exciton valley polarization is quickly lost (sim1 ps) due to intrinsic electron-

hole exchange interaction The large exciton valley polarization observed in the steady-state PL

results from the competition between the valley depolarization time (sim1 ps) and the exciton

population relaxation time (sim100ndash200 fs) [7388] On the other hand trions offer an interesting

alternative route for optical manipulation of the valley index for a number of reasons First in

contrast to the ultrafast exciton population relaxation time trions exhibit an extended population

relaxation time of tens of picoseconds in monolayer TMDs [117-124] Second trions as charged

quasiparticles influence both transport and optical properties of TMDs and may be readily

detected and manipulated in experiments such as valley Hall effect [82] Last but not least

previous studies of negatively charged trions in conventional doped semiconductors suggest that

negatively charged trions leave the background electron gas spinpolarized after the electron-hole

recombination [99125-128] Thus trions may play a particularly important role in manipulating

electron spins and the valley DoF

2 Background

In this report we investigate valley polarization dynamics associated with negatively

charged trions in monolayer WSe2 using polarization resolved two-color pump-probe

spectroscopy with sub-nm spectral resolution Distinct valley polarization dynamics were

observed as the resonant pump-probe energy is tuned across the trion resonance and attributed to

the two types of trions known to exist in monolayer WSe2 intravalley and intervalley trions In

78

particular we discover a long-lived near-unity valley polarization (≫25 ps) associated with the

resonantly created intravalley trions This exceptionally robust valley polarization (in

comparison to excitons and intervalley trions) originates from the peculiar requirement of

simultaneous transfer of three carriers (two electrons and one hole) to the other valley with

proper spin and crystal momentum changes When the pump energy is tuned to the exciton

resonance the long-lived trion valley polarization dynamics can no longer be observed

highlighting the difficulty in accessing intrinsic trion valley dynamics under nonresonant

excitation conditions used in the majority of previous experiments [109129] The discovery of

an exceptionally robust trion valley polarization is significant since it suggests that information

encoded in the valley index can be stored and manipulated electrically via effects such as valley

Hall effect over long time scales

In monolayer WSe2 the particular band structure and optical selection rules suggest that

the energetically lowest interband transition is dipole forbidden [4198130] as illustrated in

figure 58(a) Thus two types of negatively charged trions intravalley and intervalley may form

represented with symbols T|1gt and T|2gt respectively The two electrons have the opposite

(same) spins for intravalley trions T|1gt (intervalley trions T|2gt) Because of the different spin

configurations the diagonal exchange interaction present in the intervalley trions T|2gt lifts the

energy degeneracy and leads to a shift of sim6 meV relative to the intravalley trions T|1gt as

illustrated in figure 58(a)[96131] The exciton resonance is approximately 30 meV higher than

T|2gt which has implications for optical phonon-assisted scattering between T|2gt and exciton

resonances [5493]

3 Experimental Method

79

We study a mechanically exfoliated monolayer WSe2 flake on a sapphire substrate (kept

at temperature sim13 K) using a pump-probe setup (see description in chapter 5) The sample is

considered to be n-doped based on similarly prepared samples from previous studies [1196]

The output from a mode-locked Ti-sapphire laser is split into pump and probe beams whose

wavelengths are independently varied by two grating-based pulse shapers After the pulse

shapers the pulse duration is sim1 ps (with sim07 nm bandwidth) After passing through linear

polarizers and 1 4 λ wave plates for circular polarization control the beams are focused to a spot

size of sim2 m The power for each beam is kept at sim10 W to obtain nonlinear signals in the χ(3)

regime and to avoid heating effects The transmitted differential transmission (DT) signal is

detected following further spectral filtering through a spectrometer which allows us to study

trion dynamics under resonant excitation conditions DT is defined as DT = (Tpump onminus Tpump

off)Tpump off where Tpump off(on) is the transmitted probe intensity when the pump is off (on) and it

measures the third-order nonlinear response

3 Experimental Results

We first performed a fully degenerate experiment using cross-linearly polarized pump-

probe beams to identify exciton and trion resonances at 1753 and 1719 meV respectively as

shown in figure 58(b) We note that intravalley and intervalley trions are not spectrally resolved

in our sample as those on BN substrates [54] Nevertheless both types of trions are intrinsic to

WSe2 and should be present under the inhomogeneously broadened trion resonance

80

a Quasi-resonance pump probe scans

We then investigate the trion valley dynamics by simultaneously tuning the pump-probe

energy across the trion resonance The pump energy is kept at 2 meV above the probe energy to

allow filtering of the scattered pump after passing through the spectrometer This quasiresonant

excitation condition is referred to as the resonant excitation condition in this paper for simplicity

In the following a σ+ polarized pump pulse is used to populate the K valley and the subsequent

dynamics in the K (K ) valley is investigated using a σ+ (σminus) polarized probe pulse The co- and

cross circularly polarized DT signals are displayed in the same panel as a function of time delay


Differential transmission spectrum of WSe2 (dots) The black line is an interpolation curve

serving as a guide to the eye The solid Gaussians illustrate the spectral position of the

exciton and the two trion (inter- and intravalley) resonances The spectral positions of

probe energies for data in figure 59 and 610 (dashed colored lines) and the pump energy

for figure 510 (gray line) are also illustrated

81

between the two pulses as shown in Figs 2(a)ndash(c) The co-circular experiments reflect trion

population relaxations within the same valley and have similar features in all scans after an

initial rise during the excitation pulse (solid grey area) there is a relatively fast decay of a few

picoseconds followed by a slower decay of sim35 ps The observed biexponential decay is

consistent with previous experiments and likely arises from scattering between the bright trion

states and dark states (or trap states) [117] The most intriguing feature is the drastic and

systematic change in the cross-circularly polarized scans as the pump probe energies are tuned

through the trion resonance as shown in Figs 2(a)ndash(c) In cross-circularly polarized experiments

trions created in the K valley are converted to trions in the K valley via spin flip and electron-

hole exchange interaction We attribute the dynamics on the higher (lower) energy side of the

trion resonance to intervalley trions T|2gt (intravalley trions T|1gt) For intervalley trions T|2gt

probed at 17244 meV the population in the opposite valley builds up and reaches its maximum

value after a few picoseconds [figure 59(a)] In contrast valley scattering is minimal for

intravalley trions T|1gt probed at 17196 meV during trion population relaxation time as shown in

figure 59(c) The robust valley polarization associated with T|1gt is reflected in the minimal

cross circularly polarized signal shown in figure 59 (c) As the excitation energy is tuned further

to the lower energy negative DT signal appeared only for the cross-circularly polarized scans

This negative DT signal for cross-circularly polarized scan likely arises from valley-dependent

many-body effects[120132133] We limit the following discussion to the spectral region with

only positive DT signal where the valley polarization can be defined meaningfully

We define valley polarization as VP =(co minus cross)(co + cross) following earlier work on

TMDs [12134] and calculate trion valley polarization for two particular probe energies at 17244

and 17196 meV respectively We focus on these two energies to highlight the distinct trion

82

valley dynamics associated with the two types of trions while minimizing spectral overlap

between them Trion valley polarization at these two energies as a function of time delay

between the pump and probe is shown in figure 59 (d) The valley polarization is only plotted

over a limited delay range because the error bars become very large at larger delays due to the

small DT signal in both the co- and cross circularly polarized scans The intervalley trion valley

polarization T|2gt exhibits a fast decay of sim4 ps which is consistent with earlier studies [117] In

contrast the valley polarization associated with the intravalley trion T|1gt persists much longer

and decays with a time constant much larger (gt25 ps) than the experimental observation range A

valley depolarization time longer than the population relaxation time associated with the

intravalley trions means that these trions recombine before valley scattering occurs leaving the

residual electron valley or spin polarized

83

b Non-resonant pumping of trions


excitation experiments across the trion resonance at probe energies of (a) 17268 meV (b)

1722 meV and (c) 17196 meV (d) Valley polarization for the measurements displayed in

(a) and (c)

84

This long-lived trion valley polarization associated with T|1gt is only observable under

resonant excitation conditions When we excited the mobile excitons at the higher energy side of

the exciton resonance (17588 meV specifically) while tuning the probe energy within the trion

resonance the difference between valley polarization dynamics for T|1gt and T|2gt disappears as

shown in figure 510(a)ndash(c) An apparent fast valley depolarization (sim2 ps) is observed for probe

energy tuned to both types of trions as shown in figure 510 (d) These experiments performed

under the nonresonant excitation conditions do not report on the intrinsic trion valley dynamics

Instead it is necessary to consider a number of physical processes including the valley

depolarization of excitons trion formation and phase space filling in the interpretation The key

feature of similar and rapid valley depolarization for probing at both trions mainly arises from

the rapid exciton valley depolarization ie excitons created at the K valley quickly scatter to the

K valley within the pulse duration (sim1 ps) due to electron-hole exchange interaction [4799]

The same DT signal amplitude in the co- and cross-circularly polarized experiments after 5 ps

support the interpretation of equal trion populations at the two valleys In the co-circular

experiments the DT reaches its maximal value immediately after the excitation pulse The

creation of excitons at the K valley prohibits the formation of either type of trions in the same

valley due to phase space filling leading to an instant and reduced absorption at the trion energy

In the cross-circular experiments the finite DT signal rise time (1ndash2 ps) is determined by the

time for the exciton to capture an extra charge ie the trion formation time [51] These

experiments unequivocally illustrate the importance of near-resonant excitation to access the

intrinsic dynamics associated with the trion valley DoF

85

4 Summary

Figure 510 Co- (solid dots) and cross-polarized (open dots) signals recorded in

nonresonant excitation experiments for pumping at the exciton resonance and probing at

(a) 17244 meV (b) 1722 meV and (c) 17196 meV (d) Valley polarization for the

measurements displayed in (a) and (c)

86

We summarize the various exciton and trion conversion and valley dynamics in a

diagram shown in figure 511 The top of the diagram illustrates the rapid exciton valley

depolarization (sim1 ps and shorter than the excitation pulses used in our experiments) due to

electron-hole exchange interaction Trion valley depolarization is expected to be slower than that

associated with excitons because it requires an additional carrier spin flip Interestingly the

drastically different valley polarization dynamics associated with the two types of trions in WSe2

have never been explicitly proposed or observed experimentally The K valley T|2gt can scatter to

the opposite valley and form K valley T|2gt without loss of energy This process however is not

as efficient as scattering to K valley T|1gt The latter process occurs through electron-hole

exchange interaction and is energetically favorable Thus we suggest that this K valley T|2gt to

K valley T|1gt conversion process is responsible for the sim4 ps intervalley trion valley

depolarization observed Intervalley trions created in the K valley can also be converted to

intravalley trion (the vertical dashed arrow) in the same valley via a spin flip which is likely a

slower process as illustrated by the vertical dashed lines Finally intravalley trion valley

depolarization is long-lived as illustrated in the bottom of the diagram The transfer of either a

single electron or an electron-hole pair to the other valley transforms the intravalley trion into an

intervalley trion which is an energetically unfavorable process Scattering of K valley T|1gt to

the opposite valley requires the simultaneous transfer of three carriers (two electrons and a hole)

to the other valley Thus valley polarization of the intravalley trions in monolayer WSe2 is

exceptionally stable consistent with our experimental observations Valley polarized PL from

the trion resonance was previously observed under nonresonant excitation conditions in MoS2

[109] In addition to being different TMD materials various time scales (population relaxation

valley depolarization and trion formation) are manifested differently in PL and DT experiments

87

Systematic studies are necessary to investigate how these time scales vary among different TMD

samples placed on various substrates at different doping levels

Microscopic theory of valley dynamics associated with trions with different spin

configurations and exchange interaction is not available yet The experiments presented here

provide further motivation and challenges for such theoretical studies on valley dependent

exchange interaction and many-body effects due to Coulomb interaction which is particularly

pronounced in monolayer semiconductors Most importantly this work suggests a possible

approach for creating and manipulating long-lived valley DoF potentially useful in valleytronic

applications


conversion processes and their respective time scales as measured in the experiment

Dashed lines suggest that such processes are possible in principle but do not compete

favorably with other faster processes

88

Chapter 6 Evidence for Moireacute excitons in van der Waal heterostructure

In this chapter we look at a paper from our group that first reports the influence of the

Moireacute potential on optical signal of van der Waal heterostructure Our study has been published

as Nature 567 71ndash75 (2019)

Recent advances in isolating and stacking monolayers of van der Waals (vdW) materials

have provided a new approach for creating quantum materials in the ultimate two-dimensional

limit[135136] In vdW heterostructures formed by stacking two monolayer semiconductors

lattice mismatch or rotational misalignment introduces an in-plane moireacute superlattice[9] While it

is widely recognized that a moireacute superlattice can modulate the electronic band structure and lead

to novel transport properties including unconventional superconductivity[137] and insulating

behavior driven by correlations[7071138] its influence on optical properties has not been

investigated experimentally Here we report the observation of multiple interlayer exciton

resonances with either positive or negative circularly polarized emission in a MoSe2WSe2

heterobilayer with a small twist angle We attribute these resonances to the excitonic ground and

excited states confined within the moireacute potential The twist angle dependence recombination

dynamics and temperature dependence of these interlayer exciton resonances all support this

interpretation These results suggest the feasibility of engineering artificial excitonic crystals

using vdW heterostructures for nanophotonics and quantum information applications

I Motivation

In vdW materials the usual constraint of lattice matching between adjacent layers is

lifted enabling different types of materials to be stacked to form atomically thin heterostructures

The twist angle between two layers can be adjusted arbitrarily in contrast to conventional

89

epitaxially grown heterostructures in which the orientation of adjacent layers is fixed by the

crystal axes These unique properties of vdW heterostructures present new possibilities for

engineering electronic band structure and optical properties via an in-plane moireacute superlattice

When two monolayers of semiconducting transition metal dichalcogenides (TMDs) are stacked

vertically a moireacute superlattice is not necessarily present The lattice constants of TMDs that

share common chalcogen atoms (eg MoX2 and WX2) only differ by ~01 In rotationally

aligned MoSe2WSe2 heterobilayers (hBLs) grown by chemical vapor deposition (CVD)

methods the minor lattice distortion in each layer leads to a commensurate atomic alignment

without a moireacute pattern[139] In mechanically stacked hBLs however a twist angle between the

two layers is most often present Thus a moireacute pattern is expected and has indeed been directly

imaged with high-resolution transmission electron microscopy[140]

In TMD hBLs with a typical type-II band alignment[5557141] rapid charge transfer[63]

of electrons and holes to different layers following optical excitation leads to emission from the

lower-energy interlayer exciton transitions[13142] Theoretically multiple interlayer exciton

resonances are expected to form due to the lateral confinement from the moireacute potential (figure

61)[5960143] The interlayer coupling determines the depth of the moireacute potential which is

predicted to be ~100-200 meV by first-principles calculations in TMD hBLs (see figure 65) and

confirmed by scanning tunneling spectroscopy experiments on a rotationally aligned MoS2WSe2

bilayer grown by CVD[9] Such a deep potential is expected to localize interlayer excitons as

long as the moireacute supercell has a period on the order of 10 nm or larger[5960] If and how the

moireacute potential manifests in far-field diffraction-limited optical measurements remains an

outstanding question

90

Here we report the observation of multiple interlayer exciton (IX) resonances in a high-

quality hexagonal boron nitride (hBN) encapsulated MoSe2WSe2 hBL Because the layers are

aligned with a small twist angle and the inhomogeneous spectral linewidths are reduced with the

capping layers several nearly equally spaced IX resonances are spectrally resolved at low

temperature Upon excitation with circularly polarized light the IX resonances exhibit

alternating co- and cross-circularly polarized photoluminescence (PL) We suggest that the

alternating polarized emission originates from the atomic-scale spatial variations of the optical

selection rules within a moireacute supercell The energy spacing and twist-angle dependence of the

resonances and helicity of the emitted light are consistent with calculations of multiple IX states

confined within a moireacute potential with ~150 meV lateral confinement in agreement with first-

principles calculations Time-resolved and temperature-dependent PL measurements support this

assignment of the ground and excited state IX excitons

II Moireacute theory overview

We first describe conceptually how the moireacute potential may give rise to multiple exciton

resonances with different optical selection rules as shown in figure 61 In MoSe2WSe2 hBLs

with a small twist angle ~1deg the exciton Bohr radius is large compared to the monolayer lattice

constant but small relative to the moireacute period (~20 nm) Thus the interlayer exciton can be

described as a particle moving in a slowly varying moireacute potential[60144] Within a moireacute

supercell there are three points where the local atomic registration preserves the three-fold

rotational symmetry as shown in Figs 1a and 1b These three sites are denoted by

respectively where

refers to -type stacking with the site of the MoSe2 layer aligning

with the hexagon center ( ) of the WSe2 layer These high symmetry points are local energy

extrema within the moireacute supercell where excitons can be localized In the case of sufficiently

91

deep energy modulation the moireacute pattern can provide an array of identical quantum dot

potential (left panel of figure 61c)

Another important consequence of the moireacute pattern is to impose spatially varying optical

selection rules[6066] Although the valley degree of freedom is still a good quantum number for

interlayer excitons the optical selection rules of exciton resonances are no longer locked to the

valley index as is the case of monolayers As shown in figure 61b an exciton residing directly at

site (

) only couples to ( ) polarized light Site has a dipole oriented perpendicular

to the plane which does not efficiently couple to normal incident light (see Methods) The

optical selection rules are determined not only by atomic quantum numbers but also by the

relative position between tungsten and molybdenum atoms in real space It is the latter

dependence that is responsible for distinct selection rules at different positions with the moireacute

supercell The optical selection rules change continuously in the moireacute pattern and are generally

elliptically polarized (right panel of figure 61c)

92

Figure 61 (a) Different local atomic alignments occur in an MoSe2WSe2 vertical heterostructure with small twist angle The three highlighted regions correspond to local atomic configurations with three-fold rotational symmetry (b) In the K valley interlayer exciton transitions occur between spin-up conduction-band electrons in the MoSe2 layer and spin-up valence-band electrons in the WSe2 layer K-valley excitons obey different optical selection rules depending on the atomic configuration

within the moireacute

pattern refers to -type stacking with the site of the MoSe2 layer aligning with the

hexagon center ( ) of the WSe2 layer Exciton emission at the (

) is left-circularly (right-circularly) polarized Emission from site

is dipole-forbidden for normal incidence (c) Left

The moireacute potential of the interlayer exciton transition showing a local minimum at site

Right Spatial map of the optical selection rules for K-valley excitons The high-symmetry points are circularly polarized and regions between are elliptically polarized

a

b

W atom Mo atom Se atom

σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50

Moireacute potential (meV)

-1 0 1

Degree ofcircular polarization

93

III Sample Details and Experimental Method

To examine the influence of the moireacute potential on interlayer excitons we perform

micro-PL measurements on multiple MoSe2WSe2 hBLs The samples were prepared following a

mechanical exfoliation and transfer process[145] We will focus on one encapsulated hBL with

1deg twist angle unless otherwise stated (see figure 67) An optical microscope image is shown in

figure 62a The hBL is held at 15 K and excited with a continuous wave 660 nm laser with a

full-width at a half-maximum spot size of 15 microm For an uncapped sample the PL spectrum

(dashed curve in figure 62b) features intra-layer neutral and charged excitons and a broad IX

resonance consistent with earlier reports[13146147] When the hBL is encapsulated between

hBN layers four spectrally resolved IX resonances emerge (solid curve in figure 62b) due to

reduced inhomogeneous broadening The IX spectral region is replotted in the lower panel of

figure 63a and fit with four Gaussian functions The central emission energies extracted from the

fits are 1311 meV 1335 meV 1355 meV and 1377 meV The resonance energies are

repeatable across different locations on the hBL with a nearly constant peak spacing of 22plusmn2

meV (figure 63b) Some moderate inhomogeneous broadening remains possibly due to multiple

moireacute domains or small variations in strain and layer spacing within the excitation spot that

covers ~1000 moireacute supercells

Multiple IX peaks may be indicative of quantized energy levels due to the lateral

confinement imposed by the moireacute potential as predicted in the calculations below The fact that

the resonances span an energy range of ~70 meV suggests that the moireacute potential depth is on the

order of 100 meVmdashsufficient to justify the picture of an array of quantum dot potential

Polarization-resolved PL experiments provide additional compelling evidence in support of this

interpretation Using polarized excitation we collected co- ( detection) and cross-circularly

94

( detection) polarized PL spectra which are shown in figure 63c We define the circular

polarization of emission as

where is the measured PL intensity We plot as a

function of energy in figure 63d The IX resonances exhibit a variation of between 02 and -

02 A negative indicates that the PL signal with cross-circular polarization is stronger than

that from the co-circular polarization We propose that the alternating co- and cross-circular

emission arises from the unique spatial variation of the optical selection rules predicted based on

rotational symmetry considerations[60]

To relate the observed PL signal to the optical selection rules we first assume that the

above-gap -polarized light optically creates spin-polarized intralayer excitons in the MoSe2

and WSe2 monolayers primarily in the K valley This spin-valley locking in TMD monolayers

has been established by previous studies[1236110] Second we assume that the charge transfer

process leading to the IX formation conserves the valley and spin index which is supported by a

previous polarization-resolved pump-probe spectroscopy[77] It then follows that an IX state

created in the K valley following optical excitation emits ( ) polarized light if it is

localized near the (

) high-symmetry point within the moireacute potential landscape (refer to

Figs 1b and 1c) We show in the calculations below for a deep moireacute potential that confines

excitons at the site the wave functions associated with the quantized exciton states can

acquire additional angular momentum and sample the potential landscape in a way that leads to

multiple resonances with alternating and light emissionmdasha characteristic consistent with

our experimental observations Because the valley relaxation and charge transfer dynamics can

be very complex the above assumptions do not strictly hold leading to reduced below unity

Because observing the alternating circular selection rules of IX resonances requires that the

valley polarization time is longer or comparable to IX recombination lifetimes[12] valley-

95

conserving PL can only be observed in bilayers with the smallest twist angle that exhibit

relatively short IX recombination lifetimes (~ 1 ns)

Figure 62 (a) Optical image of an hBN-encapsulated MoSe2WSe2 stacked heterostructure The hBL region is indicated inside the black dotted line (b) Comparison of the photoluminescence spectrum from an uncapped heterostructure (dashed curve) and an hBN-encapsulated heterostructure (solid curve) Neutral (X0) and charged (X-) exciton emission is observed from the MoSe2 and WSe2 monolayers The interlayer exciton (IX) emission is observed ~300 meV below the intralayer resonances (c) Illustrative band diagram showing the type-II alignment and the IX transition

a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL

Emission Energy (meV)1300 1400 1500 1600 1700

PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96

IV Moireacute exciton model

Here we provide a detailed description of the theory which has some overlap with the

main text The full theory can be found in Ref [59] In the moireacute pattern the local band gap

varies in real space and acts as a periodic potential for excitons IXs can be viewed as a

wavepacket moving in the potential with a center-of-mass (COM) motion described by

where is an energy constant is the COM kinetic energy is the moireacute

potential energy and is the exciton mass For IXs in a WSe2MoSe2 hBL where

Figure 63 (a) Representative PL spectra shown for hBLs with 1deg and 2deg twist angles Each spectrum is fit with four (1deg) or five (2deg) Gaussian functions (b) The center energy of each peak obtained from the fits at different spatial positions across each sample The average peak spacing increases from 22 plusmn 2 meV to 27 plusmn 3 meV with twist angle (c) Circularly polarized PL spectrum for + excitation of the 1deg sample (d) The degree of circular polarization versus emission wavelength obtained from the spectra in (c)

97

is the electron bare mass is a smooth potential and is approximated by the lowest-order

harmonic expansion where are the first-shell moireacute reciprocal lattice vectors The parameter

is the energy scale of the potential while determines where the potential extrema are

located We choose to be such that the potential minima are located at sites The

motivation of this choice is to be consistent with experimental observation as lowest-energy

excitons confined by the potential near site have an s-wave symmetry COM wave function

and emit light at the K valley Near sites the potential has the form of a harmonic

oscillator

where is the moireacute period An exciton confined

in this potential has quantized energy levels

where are non-

negative integers We take the twist angle to be resulting in of ~19 nm To be consistent

with the experimentally observed energy spacing (~25 meV) we take to be 18 meV The

overall range of the potential variation is meV

Both K and -K valley excitons are governed by the Hamiltonian in Eqn 1 but they have

different optical responses due to valley-dependent optical selection rules Below we focus on K

valley excitonsmdashproperties of -K valley excitons can be inferred by using time-reversal

symmetry Following the convention used in Ref [59] the bright IXs are located at the moireacute

Brillouin zone corners The optical matrix element for the bright IXs at the K valley is

98

where is the semiconductor ground state of the heterobilayer is the IX state is the in-

plane current operator and is the system area In the integral of Eqn 3 is the periodic

part of the Bloch wave state and captures the position dependence of the optical

matrix element in the moireacute pattern In Eqn 4 and represent the

components The spatial dependence is given by and

where are constants and | | is about 133

[60] At a generic position has both and components There are three notable

positions with high symmetry At the site ( ) vanishes and has a purely

component In contrast at site (

) has a purely component Finally

vanishes at site (

) These local optical selection rules are illustrated in Figs 1b and

1c of the main text The spatial variation of is plotted in Extended Data Figs 3c-d Around

site ( ) is nearly a constant while has a vortex structure

Based on Eqns 1-4 we calculate the theoretical optical conductivity of IXs at the K valley as

shown in figure 64b of the main text We have chosen such that the lowest-energy IX has

the experimental energy 1310 meV Four resonances with alternating valley optical selection

rules appear in the energy window shown in figure 64b Both the energies and helicities of these

resonances agree with the experimental observation The corresponding exciton COM wave

function can be understood as Bloch wave states composed of Wannier functions confined to the

potential minimum position ( sites) We show for the four peaks in figure 64c-f For

peak (1) has s-wave symmetry centered at sites and the integral in Eqn 3 only

acquires the components in In peak (2) the Wannier function associated with is

still centered at a site but it has a chiral p-wave form with an additional angular momentum

99

compared to Due to this difference peak (2) has the opposite valley optical selection rule

with respect to peak (1) The behavior of peaks (3) and (4) which have d-wave and f-wave

forms can be understood in a similar way

As expected our model calculation cannot reproduce all experimental features such as

the linewidths and relative intensity between the IX resonances For example the PL intensity of

the excited states is higher than the ground state a feature that may originate from disorder and

has been previously observed in an ensemble self-assembled quantum dots[148] The assignment

of the observed IX peaks as ground and excited states localized near the moireacute potential

minimum is consistent with the measured thermal behavior and recombination dynamics (see

figure 66)

100

V First-principles calculation of the bandgaps of MoSe2-WSe2 bilayer heterostructure

We employ the density function theory (DFT) with the Perdew-Burke-Ernzerh (PBE)

exchange-correlation functional including spin-orbit coupling (SOC) to calculate the electronic

structure of three specific stacking styles within the moireacute superlattices in a twisted MoSe2-WSe2

hBL (figure 65) The interlayer van der Waals (vdW) interaction is included within the DFT-D2

functional implemented in the Vienna ab initio simulation package (VASP) package[149150]

Figure 64 (a) Illustration of the spatial variation of the moireacute potential and the confined multiple IX resonances (b) Optical conductivity of IXs in the K valley in response to (blue line) and (red line) polarized light (c)-(f) Real-space map of the center-of-mass wave functions for peaks (1) (2) (3) and (4) respectively (g)-(h) The spatial variation of the components of the optical matrix elements

a

hf g

101

The cutoff of plane-wave energy is set to be 500 eV with a 16x16x1 k-point sampling in the

reciprocal space The atomic structures are calculated with a perpendicular vacuum larger than

18 angstroms which is enough to avoid artificial interactions between adjacent supercells

Because of the strong SOC splitting at the K-K point the band structures of the three stacking

types exhibit a direct bandgap at the K-K point as shown in figure 65 Therefore without

considering phonons we expect the lowest-energy interlayer exciton to be a direct exciton

Figure 65 shows the relaxed interlayer distances and bandgap values which are substantially

different with different stacking types and sensitive to the interlayer couplings vdW interaction

is the consequence of dynamical correlation effects which may not be well captured by DFT To

evaluate possible variations we perform additional calculations using another vdW functional

the DFT-D3 in which the interlayer distances and band gaps are different Despite different

choices of vdW functionals the band gaps vary more than 100 meV from different stacking

types within the moireacute superlattice ie a deep moireacute potential is consistently found in the first-

principle calculations Since electron self-energy corrections and excitonic effects are known to

dominate quasiparticle band gaps and optical spectra of 2D semiconductors we have applied the

first-principles GW-Bethe-Salpeter Equation (BSE) to obtain the energy of the lowest

exciton[151] The quasiparticle energies are calculated by the single-shot G0W0 approximation

using the general plasmon pole model We use a k-point grid of 24x24x1 for calculating the e-h

interaction kernel and a k-point grid of 48times48times1 for converged excitonic states These GW-BSE

simulations are performed using the BerkeleyGW code with the slab Coulomb truncation

included It is found that the exciton binding energy varies less than 5 within the moireacute

supercell Our calculations also confirm that the moireacute potential depth (ie quasiparticle gap)

102

in H-stacked samples (~20 meV) is significantly reduced compared to R-stacked samples (gt100

meV)

VI Thermal behavior and recombination dynamics

We show the steady-state PL at elevated temperatures between 25 K and 70 K in figure

66 With increasing temperature the rate at which the intensity of the two highest-energy peaks

decreases is significantly faster than the lower-energy peaks Because excitons in the excited

states are less-confined within the moireacute pattern they are more susceptible to phonon-induced

activation out of the potential[152] Excitons in the excited states can also relax to the lower

energy states which can enhance the recombination rate from these transitions Indeed we



heterostructure and corresponding DFT-calculated band structures (b) Interlayer distance and the band gap of three stacking types (c) First principles GW-BSE calculation results for quasiparticle band gap and exciton binding energy for different stacking types

PBE-D2 PBE-D3

Stacking

W-Mo Interlayer Distance (Aring) 708 644 646 711 652 651

Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking

Quasiparticle band gap (eV) 158 156 158 158 151 162

Exciton energy (eV) 117 117 120 120 112 122

b

c

a

103

observe a faster decay of the excited states shown by the time-resolved PL dynamics in figure

66b The dynamics of the highest energy peak are fit by a single exponential with a 09 ns time

constant As the emission energy decreases the dynamics become slower and biexponential

approaching decay times of 2 ns and 10 ns for the lowest energy state The slight increase in the

fast and slow decay times with decreasing energy shown in the inset to figure 66b is often

observed in other systems with spatially localized excitons such as in self-assembled InAsGaAs

quantum dots[153]

Figure 66 (a) Temperature dependence of the PL between 25 K and 70 K (b) Time-resolved PL dynamics (points) at energies near the four IX transitions labeled in the inset The solid lines are biexponential fits to the data The inset shows the emission energy dependence of the fast and slow decay times

a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450

Emission Energy (meV)

25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104

VII Additional heterostructures with interlayer exciton splitting R-type samples

Here we give additional details about sample 1 (1o twist angle) and sample 2 (2

o twist

angle) presented in the main text The Gaussian fit of the sample 2 PL spectrum shows the

emergence of five IX peaks 1306 meV 1336 meV 1366 meV 1386 meV and 1413 meV

The average energy spacing of sample 2 is 27 plusmn3 meV which is slightly larger than the spacing

in sample 1 If we fit this spacing for sample 2 with our model calculation using the same 162

meV moireacute potential as for sample 1 we obtain a twist angle of 14o from the fit This value is

within our estimated uncertainty in determining the angle via the optical microscope image of the

heterostructure A larger twist angle causes the lowest energy transition in a TMD hBL to

become more indirect in momentum space20

leading to a longer recombination lifetime Indeed

we observe slower time-resolved PL dynamics for sample 2 shown in figure 67 Fitting the

time-resolved PL curves with a single exponential function yields time constants of 195 ns and

896 ns for samples 1 and 2 respectively

105

VIII Additional heterostructures with interlayer exciton splitting H-type samples

We fabricated an H-type hBL (ie 60o twist angle) that shows two IX peaks at 1356 meV

and 1395 meV (figure 68) The energy separation between peaks is 40 meV which is consistent

with previous reports of hBN encapsulated H-type MoSe2WSe2 hBLs3132

Our theoretical model

predicts that the moireacute potential is on the order of 10-20 meV for H-type hBLs which is too

small to lead to the observed splitting 40 meV In hBLs with -type stacking (near 60deg twist

angle) the observation of two IX resonances separated by 25-50 meV has been attributed to

momentum indirect transitions3132

which is consistent with the spectrum of our H-type sample

(figure 68)

Figure 67 (a) Steady state PL spectra from 1o sample (sample 1) and 2o sample (sample 2) (b) Time-resolved PL dynamics for IX emission at 1320 meV as indicated by the shaded area in (a)

a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)

Energy (meV) Time (ns)

sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106

IX Photoluminescence emission from Sz = 1 and Sz = 0 exciton transitions

A recent theoretical study has also proposed IX resonances arising from

transitions which are optically dark in monolayers but become bright in hBLs[68] Although we

cannot completely rule out states as a possible explanation for some of the observed

resonances we argue below that such an explanation is less likely for the higher-energy states

observed in our study which are less-stable states at a higher temperature and exhibit a shorter

lifetime compared to the lower-energy resonances In an -type heterostructure exciton

recombination is predicted to emit left- (right-) circularly polarized light at the (

) atomic

configurations Since the exciton at the K point consists of a spin-down conduction band

electron and spin-up valence band electron (see Fig 1b of the main text) it emits at an energy

higher than that of the states by the conduction band spin splitting of ~30 meV (see Ref

Figure 68 Comparison between IX resonances from H-type sample (upper panel) and R-type sample (lower panel)

R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

[154]) With increasing temperature thermalization of excitons might lead to enhanced emission

from states which is inconsistent with the temperature dependence of the excited states

shown in Fig 5a of the main text The states are expected to have longer recombination

lifetimes than the states due to a weaker transition dipole moment[68] which is contrary

to the trends in the measured lifetimes in Fig 5b of the main text We can also rule out the Sz = 0

z-polarized transition since our 50X objective has small NA number (042) compared to much

higher NA number (082) objective used to detect the z-polarized dark exciton in TMD

monolayer reported in the previous work[43] Therefore we suppress excitation and collection of

these states by an additional order of magnitude compared to the in-plane transitions as shown

experimentally in the supplemental material of Ref [43]

X Outlook and conclusion

To control moireacute excitons a natural choice would be to tune the moireacute period through the

twist angle Indeed in another hBL with a small twist angle of ~2deg we observe multiple IX

resonances spaced by 27plusmn3 meVmdashlarger than the spacing for the 1deg sample as expected (see

figure 63) While systematic studies of the twist angle dependence of IX in TMD hBLs have

been performed for large (~5deg) steps[1067] the broad inhomogeneous linewidth has precluded

the effect of the moireacute potential to be observed An applied electric field or magnetic field may

also allow one to tune the IX properties Previous experiments have reported IXs exhibit a Stark

shift as a function of the electric field[155] or a Zeeman splitting as a function of the magnetic

field[147155] Other recent experiments have also reported multiple interlayer exciton

resonances However these experiments were performed on samples either with different

stacking conditions[155156] (see figure 68)

or with significantly broader IX inhomogeneous

linewidths that mask any effects of the moireacute potential[1067] We also discuss the possible

108

contribution from transitions (see Methods) which are optically dark in monolayers but

become bright in hBLs

In summary we observed multiple interlayer exciton resonances in an hBN-encapsulated

MoSe2WSe2 heterobilayer The key spectroscopic features observed in our experimentsmdashfour

IX resonances with alternating circularly polarized PL systematic changes in the lifetime with

energy and the temperature dependencemdashare naturally explained by assuming the presence of

the moireacute superlattice expected to exist in a stacked hBL In multiple samples with slightly

different twist angles we have observed systematic changes in IX energy spacing and lifetimes

which is consistent with the effect of the moireacute potential Multiple IX resonances originating

from phonon replicas[157] momentum-space indirect transitions[156] or states are

possible in TMD bilayers however we consider them less likely explanations in the samples

investigated here based on the arguments discussed in the main text and Methods section Future

experiments capable of resolving individual IXs confined within a supercell using either near-

field optical probe or combined scanning tunneling spectroscopy and optical spectroscopy

studies will be most valuable to further establish the influence of the moireacute potential

109

Chapter 7 Conclusion and outlook

In this dissertation wersquove briefly discussed exciton properties of monolayer TMD

namely the strong binding energy giving rise to short lifetime due to the reduced dielectric

screening the extremely short valley coherence and valley polarization (less than 1ps) due to

electron-hole exchange interaction One way to extend those timescales up to 4 orders of

magnitude is to create TMD heterostructure with interlayer exciton We discussed in extension

the properties of the interlayer exciton in heterostructures with various twist angles Due to the

spatial indirect nature of the interlayer exciton its lifetime and valley polarization can be 10-100

nanoseconds

We further discuss our method for creating high-quality monolayer TMD and

heterostructure to the best of our knowledge in the appendix Since sample fabrication is an

empirical process our tips and tricks are accumulated over the years by many undergrads and

graduate students working on creating samples Admittedly our fabrication method is not

perfect More work needs to be done in order to further improve sample quality indicated by the

reduced low-temperature exciton linewidth Nevertheless our method should be a very good

starting point for new members of the group who wish to fabricate samples

With the improved sample quality we have successfully created TMD heterostructures

with interlayer Moireacute excitons in MoSe2WSe2 heterobilayer which possess extremely intriguing

optical properties Particularly different exciton excited states confined within the Moireacute

potential exhibit alternating polarization due to the spatial variation of optical selection rule It is

also this property that we can pinpoint the origin of our multiple interlayer exciton peaks

observed in low-temperature photoluminescence Our study of the Moireacute excitons is the first

110

experimental evidence of Moireacute effect on the optical properties of van der Waal heterostructure

It has changed peoples perspective on TMD heterostructure Since our paper is published on

Arxiv various research groups have claimed evidence for intralayer Moireacute excitons in

MoS2MoSe2[158] and WS2WSe2[74] heterobilayers Another group has claimed optical

signature for trapped interlayer Moireacute excitons in MoSe2WSe2[159] Another study reports the

hybridization between the interlayer and intralayer excitons due to moireacute potential in WS2MoSe2

heterobilayers[160] More importantly recent pump-probe study also reports multiple interlayer

excitons resonances in the WS2WSe2 heterobilayer [161]with either conserving or reversing

circular polarization

The fact that the Moireacute superlattice defines a regular array of quantum dot potentials and

localizes the quasiparticles offers exciting future studies of TMD heterostructures Because of

the unique optical selection rules associated with these quasiparticles photon spin and valleys

are naturally entangled making them an ideal platform to explore matter and photonic qubit

entanglement as an essential element for large-scale quantum information processing Yet there

are a lot of things we dont know about this system Thus we have proposed to invest

fundamental of properties of interlayer Moireacute excitons including quantum yield dipole moments

formation dynamics and dephasing mechanisms Interlayer excitons are stable at room

temperature and exhibit a long lifetime Their properties relevant to quantum information

applications remain mostly unknown These properties will be the focus of our group near future

studies Our next step would be to study the quantum dynamics of the valley index associated

with interlayer excitons As a binary quantum degree of freedom in TMDs this valley index can

represent a qubit with potentially long decoherence time due to large momentum mismatch and

the associated spin flip to the opposite valley[82162163] Demonstrating Rabi oscillations of

111

interlayer excitons is in our list for the next experiment Rabi oscillations refer to the reversal

control of electronic state occupancy by light This is a benchmark experiment in controlling a

qubit since it is equivalent to a single bit NOT gate[164-167] The confined and localized

nature of Moireacute excitons makes it more likely to realize this quantum control Lastly we will

explore spin-photon entanglement of Moireacute excitons They are excellent single photon emitters

due to the spatial confinement We will follow similar protocols[168-172] in neutral atoms

trapped ions and self-assembled quantum dots spin-photon entanglement associated with the

confined pseudospins in the Moireacute superlattice will be investigated

112

APPENDIX

Sample fabrication techniques

In this appendix we discuss the techniques of mechanical exfoliation to make monolayer

TMD and dry transfer method to stack these monolayers onto predefined pattern or onto TMD

heterostructure Well also talk about tips and tricks for making good samples and mistakes to

avoid The aim is to provide members of the Li group a reference for sample fabrication As we

constantly strive to make a better quality sample our techniques are constantly updating The

information discussed in this chapter is up to date as of November 2018

I Exfoliation

1 Materials and tools

a Tape

We use cleanroom blue tape UltraTape 1310TB100-P5D to exfoliate monolayer TMD

This tape has low adhesiveness and less residue than the common 3M Scotch tape

b PDMS (polydimethylsiloxane)

We find that exfoliating TMD directly onto the silicon substrate has a much low rate of

finding a monolayer than exfoliating onto PDMS Also a monolayer on PDMS is more

convenient for transferring and stacking heterostructure We use two types of PDMS

Commercial PMDS (figure A1b) can be purchased from GelPak The specific models are X0

and X4 PF films X4 film is stickier than X0 Home-made PDMS (see figure A1a) can be made

113

from the PDMS kit available for purchase from Amazon Search for Sylgard 184 silicone

elastomer kit How to make this type of PDMS will be discussed in the later part of this section

Type of

PDMS

Commercial Home-made

Pro Smoother surface -gt larger monolayer

size and more spatial uniformity

Thinner -gt easier for dry transfer

Stickier -gt may increase the amount

of monolayer exfoliated per hour

Con Thicker -gt more difficult for dry

transfer

Less even surface -gt monolayer tends

to have more cracks and wrinkles if

the tape is not lifted carefully

Table A1 Pros and cons of the two types of PDMS

Table V1 describes the pros and cons of the commercial and homemade PDMS Notice

that these pros and cons wont make or break the exfoliation and transfer The quality of the

fabricated sample depends more crucially on other factors For example wrinkles and cracks of

the monolayer can be minimized by lifting the blue tape carefully Monolayer size and yield rate

depend crucially on the quality of bulk TMD material

c Cell phone film

We use cell phone film to exfoliate hBN (hexagonal boron nitride) on to commercial

PDMS This type of film is commercially available on Amazon The band is Tech Armor High

Definition Clear PET film screen protector for iPhone 55C5S Exfoliating TMD using cell

phone film results in more cracks and wrinkles and smaller size monolayer than using blue tape

The procedure to exfoliate hBN on commercial PDMS will be discussed later in this chapter

114

d Materials

We have been purchasing bulk TMD from two companies 2D Semiconductor and HQ

Graphene Table V2 summarizes the pros and cons of each type

Company 2D semiconductor HQ graphene

Pro hBN encapsulated monolayer achieves

narrower linewidth at cryogenic temperature

~4 meV exciton linewidth for encapsulated

WSe2 ~3 meV exciton linewidth for

encapsulated MoSe2 (narrowest)

Very large size monolayers can be

exfoliated ~few hundred microns

(figure A1d)

Con More difficult to exfoliate than HQ graphene

bulk

Broader low-temperature exciton

PL linewidth

Table A2 Pros and cons of two commercial bulk TMDs

Narrow linewidth means that the material has less amount of impurity and defect leading

to inhomogeneous broadening Thus we mainly exfoliate 2D semiconductor bulk for optical

studies However if monolayer size becomes an important constraint andor the experiment

doesnt require narrow monolayer linewidth one may exfoliate from HQ graphene bulk

We exfoliate hBN grown by Taniguchi and Watanabe from national institute for material

science in Japan This hBN is of higher quality than the commercially available hBN

We havent worked much with graphene as a group However this will change as we

seek to add electrical contacts and an external electric field to the sample in the future Graphene

or few-layer graphite is ideal to apply vertical electric field because they are transparent

conductors Experience from our collaborator suggests that kish graphite yields the largest

115

graphene flake because it has a large grain size Kish graphite with various qualities can be

purchased from graphene-supermarketcom with grade 300 being the highest quality

2 Exfoliation Related Procedures

We find that exfoliating on PDMS provides acceptable monolayer yield rate while maintaining a

good quality sample We avoid another exfoliation methods such as gold-assisted

exfoliation[173] although produces larger size monolayer with a higher yield rate the optical

properties of the monolayer is severely degraded We also tried to exfoliated TMD on top heated

silicon[174] but we find that this method works best for graphene only Exfoliating TMD this

way still gives a lower yield rate than our PDMS method

a TMD exfoliation procedure

Thin down the bulk TMD onto the blue tape Kayleighs tip The flakes on blue tape should

be quite thin and flaky (figure A1c) so that when lifting fair amount number of flakes

remain on the PDMS If flakes on blue tape are too thick thin down them more by contact

the flakes with another empty blue tape and then separate

Cut a small square of PDMS 1 by 1 cm and lay it flat onto the middle of the microscope

slide

For commercial PDMS make sure that the PDMS surface is flat You can do this by lifting up

the PDMS and let it slowly on top of the slide Doing it this way will cause the PDMS to be

flattened

Make contact between the TMD flakes on blue tape and the PDMS Can use a finger to press

lightly on the tape Marshalls trick imagine petting the ant under the tape One should tap

lightly and uniformly without hurting the ant

116

Lift the tape up without knee-jerk motion Lift slowly enough so that a few flakes still

remain on the PDMS but not slower Marshalls trick lift the tape like you are waving a

magic wand

Examine the PDMS under the microscope Under transmission lighting look for a layer with

the least contrast with respect to the surrounding PMDS background This is monolayer

If overall a lot of flakes are still quite thick you can use another empty blue tape to make

contact with the flakes on PDMS Then lightly lift off and look again The process can be

repeated number of times usually no more than thrice If you still get no monolayer it is

better to move on exfoliating new flakes

b Preparation and storage of bulk material

Bulk material is stored inside containers within a plastic bag in the vacuum chamber


microscope slide respectively c) Bulk TMD thinned down on a piece of blue tape One can tell

the quality of the bulk TMD by looking at the flakes Good quality bulk usually appears with flat

cleaved surface In this case the bulk is not that good but still exfoliatable d) Huge monolayer

WSe2 exfoliated on home-made PDMS

100 mm

a) b) c) d)

117

Place the bulk between 2 pieces of blue tape - press lightly to ensure bulk adheres to both

pieces of blue tape

Slowly pull apart blue tape One side should have thinner exfoliated bulk material and the

other should have the majority of the bulk material Return the majority of the bulk to the

container

Using the thinner bulk material repeatedly thin the bulk between pieces of a blue tape Try to

create bulk patterns on the blue tape so that different flakes are close together ie efficient

exfoliation

You should have ~6-8 separate pieces of blue tape with bulk ready to exfoliate onto PDMS

Keep the majority of this bulk encapsulated between 2 pieces of blue tape Only separate the

blue tape when all bulk on exposed pieces is entirely exhausted DO NOT re-encapsulate the

bulk between the blue tape unless you are thinning the material This will cause the material

to become exhausted much more quickly

c How to make home-made PDMS

Mix the silicone and the curing agent together in 101 (10) weight ratio Using a clean stick

to stir for 5 minutes After that the mixture will be full of bubbles Avoid mixing PDMS in a

glass container because you cant remove it afterward Note more curing agent (gt10)

makes the PDMS softer and stickier We found that 10 is a good ratio to make firm and flat

PDMS

Pour the mixture into plastic Petri dishes The thickness of the PDMS should be about 2 mm

118

Put the Petri dishes into a vacuum container and pump down the pressure to eliminate

bubbles The time inside the vacuum container is varied from 1 to 2 hours Make sure that the

PDMS is free of any bubble before removing from the chamber

Put the Petri dishes inside the fume hood and let the PDMS cured (hardened) in ambient air

for 24 hours before it is ready to be used

II Transfer

1 Transfer microscope

We modified a microscope to transfer our monolayers to a pre-determined structure or

stack them on top of each other The schematic of the transfer microscope is described in figure

A2a The monolayer is transferred from the microscope slide held by the slide holder onto the

substrate held by the substrate holder

The relative position of the monolayer on the microscope slide with respect to the

substrate is controlled by numbers of stages First of all the translation of the monolayer is

control by x y and z micrometers The master XY translation stage moves both the microscope

slide and substrate with respect to the microscope objective The motion of the substrate is

further controlled by the rotation stage and the tilt stage The rotation stage rotates the substrate

with respect to the monolayer on the microscope slide The range of rotation is about 2 degrees

Larger rotation can be done by moving the substrate physically Tilt stage adjusts the tilt angle

between the substrate and the PDMS This is most crucial to ensure the successful dry transfer

discussed later on in this section The tilt stage has two knobs that can tilt the substrate either

back and forth or left and right

119

Other components of the transfer microscope include the vacuum pump the heater and

the multimeter for temperature monitoring During the transfer the substrate and the microscope

slide are held in place by air suction provided by a small pump through white plastic tubing (see

figure A2b) The substrate can be heated up by a high power ceramic heater that can go up to

500oC The heater is powered by a simple DC power supply and is insulated from the

surrounding by the substrate holder and four pillars underneath which are made out of macor -

one type of machinable ceramic (figure A2b) The heater also includes a thermal couple which

can provide temperature monitoring via multimeter (yellow casing next to the microscope in

figure A2b)

2 Transfer using PPC (polypropylene carbonate) coated PDMS dot

We follow the procedure previously described in the supplementary of [175] Here the PPC acts

as a glue with temperature dependent adhesiveness Thus one can pick up or drop off (release)

layer using different temperature The pickup temperature is lower than the drop off temp The


picture of the microscope

XYZ translation stage for slide holder

Master XY translation stage

Tilt stage

Rotation stage

Heat insulated pillars

Substrate holder with heater

Microscope objective

Slide holder

a) b)

120

PDMS dot acts as a probe that can pick up a selected layer while leaving the surrounding flakes

intact

a How to make PDMS dot

First we need to make the PDMS mixture using the PDMS kit The procedure is previously

described in section I2c

Use a mechanical pipette draw a small amount of PDMS mixture and drop it onto a piece of

flat home-made PDMS that is previously hardened The size of the PDMS dot depends on

how large the drop is Usually the dot is about 1 to 2 mm in diameter but can be made

smaller (figure A3b)

Leave the PDMS to cure inside the fume hood for 24 hours

b How to make PPC (polypropylene carbonate)

The polypropylene carbonate in solid form can be purchased online from Sigma Aldrich

Mix PPC and anisole according to 12100 to 15100 weight ratio in a glass vial

Slowly shake the mixture for a few hours This step can be done by putting the vial on top of

a shaking plate The specific shaking speed does not matter too much We usually set the

speed to about 100 rpm (round per minute) After this step the PPC mixture becomes viscous

clear liquid (figure A3a) and is ready to be spin coated onto the PDMS dot

121

c How to spin coat PPC onto PDMS dot

Use a mechanical pipette draw a small amount of PPC inside the vial apply the PPC evenly

onto the PDMS dot Make sure that the PPC mixture is thoroughly stirred before this step

Avoid creating bubbles when dropping PPC

Put the PDMS dot into a spin coater Set the spinning speed to 3000 rpm in 60 seconds The

acceleration doesnt matter too much After this step the PPC is spread out on the surface of

the PDMS dot

Bake the PPC coated PDMS dot on a hot plate under 130oC for 5 to 10 minutes to evaporate

most of the anisole in the PPC

Let the PDMS cool down to room temperature We now ready for transfer

d Transfer procedure

i Pick up

Figure A3 a) 12 PPC liquid inside the glass vial ready to be spin coated b) PMDS dot

a) b)

122

The layers can be picked up from the home-made or commercial PDMS using PPC coated

PDMS dot

Heat the substrate to ~50oC

Slowly lower the PDMS dot by using the z micrometer in the XYZ translation stage

Approach the monolayer slowly and carefully Crashing the dot to the monolayer will

cause the layer to crack andor shatter

After the dot contact the monolayer fully lift the PDMS dot slowly while keeping the

temperature at 50oC

Alternatively you can turn off the heater after the dot and the monolayer are in full

contact Temperature decreasing will retract the contact region and pick up the monolayer

slowly

ii Drop off release

The layer on the PDMS dot can be dropped off on a substrate by using high temperature to

partially melt the PPC releasing the layer


Slowly make a full contact between monolayer on PDMS dot and the substrate

Wait for a few minutes The hot substrate partially melts the PPC

Keep the temperature high ~80oC ie dont turn off the heater Slowly lift up the PDMS

Note the substrate should be cleaned to ensure successful transferring If the monolayer is still

sticking to the dot use slightly higher temperature ie 90 o

C or 100 oC during drop off Be careful

not to let the PPC completely melt on the substrate

123

The optimal pickup and drop-off temperatures seem to strongly depend on the substrate

type When using different substrate other than sapphire or silicon practice transferring with

various drop-off and pick-up temperature to get an idea of exact temperature to use

3 All-dry transfer method - no chemical

This transfer method is first described in ref [145]

o After locating the position of the monolayer on the commercial PMDS observe the

monolayer under the microscope with the lowest magnification objective (5x) Next use

a razor blade carefully making horizontal and vertical line cuts removing extra PDMS

around the monolayer If you transfer home-made PDMS skip this step

o Fit the microscope slide (with the monolayer on PDMS) upside down on to the slide

holder of the transfer microscope

o Carefully lower the PMDS until the monolayer contact the substrate If the monolayer

cannot make contact the PDMS is probably not parallel with the substrate You need to

watch for the contact region which might be outside the objective field of vision Move

the master stage so that you can identify where the PDMS and the substrate make contact

If the contact region is to the right(left) of the monolayer rotate the tilt stage so that the

substrate is moving to the right(left) when observed on the screen to compensate for the

tilt For example if the contact region is as depicted in figure A4 you would have to

rotate the tilt stage up and to the right The amount of rotation is dependent on the tilt

angle Since we dont know this value we can rotate some amount and make the

approach again

124

o Make contact again to see how close is the contact region to the monolayer Then repeat

the previous step The point is to avoid pressing the monolayer onto the substrate If you

force the monolayer to contact the substrate you will probably break the monolayer

o After successfully make contact between the monolayer and the substrate wait for a few

minutes then slowly lift the microscope slide The slower the lifting the better the end

result is What I usually do is that I rotate the z micrometer on the XYZ translation stage

a few degrees and watch if the contact region receding Then repeat rotating and

watching

o When dry transferring monolayer make sure you dont use any heating If the substrate is

hot when the monolayer approaching it will break the monolayer

o When dry transferring hBN in order to facilitate the transfer you can heat up the

substrate AFTER making contact between the hBN and the substrate The heat will

soften the PDMS make it easier to release the hBN Heating can also be applied when

transferring the top hBN to cover the heterostructure

125

Overall all-dry transfer method gives narrower monolayer PL linewidth compared to the

PPC transfer due to no chemical involved Thus it is the preferred method in our group for

making a sample for the optical study This method is trickier to carry out than the PPC assisted

transfer because the PDMS and the substrate surface need to be relatively parallel As we have

seen this involves a bit of tilting adjustment before contact between monolayer and the substrate

can be successfully made

III Encapsulated heterostructure fabrication


PDMS) is at the lower left corner outside the field of view

126

We present detailed fabrication steps for making hBN encapsulated hetero-bilayer The

fabrication of encapsulated monolayer is similar except the number of steps is reduced

Currently we use two methods to prepare the heterostructure sample as indicated in figure A5

1 PPC fabrication (figure A5a)

This technique has been described in ref [176]

Step 1 The PDMS dot picks up the top hBN exfoliated on top of a commercial PDMS

Step 2 The PDMS dot then picks up the MoSe2 monolayer exfoliated on commercialhome-

made PDMS The van der Waal force between hBN and monolayer is stronger than the force

between the monolayer and the PDMS Therefore the monolayer will be easily picked up by the

hBN

Step 3 The PMDS dot then picks up the WSe2 monolayer This step is crucial because one needs

to ensure that the 2 monolayers are rotationally aligned and sufficiently overlapped with respect

to each other The angle between the two monolayers is determined by each monolayers straight

edge which is confirmed by polarization-resolved andor phase-resolved second harmonic

measurement

Step 4 The stacks of layers are dropped on to a bottom hBN that is pre-transferred and annealed

on top of the substrate (The reason that the bottom hBN is not picked up together with the stack

then dropped off to the substrate is that the bottom hBN is usually thick so picking it up is

difficult not to mention it may damage the whole stack if fail)

For the method on how to pick up and drop off layer using PPC coated PDMS dot please see

section II2d

127

2 All dry fabrication (figure A5b)

Step 1 The bottom hBN pre-exfoliated on PDMS is transferred on to a clean substrate The

sample is annealed afterward

Step 2 The monolayer MoSe2 pre-exfoliated on PDMS is then transferred on top of the bottom

hBN The sample is annealed afterward

Step 3 The monolayer WSe2 pre-exfoliated on PDMS is then transferred on top of the

monolayer MoSe2 The angle between the two monolayers is determined by each monolayers

straight edge which is confirmed by polarization-resolved andor phase-resolved second

harmonic measurement This step is crucial because one needs to ensure that the 2 monolayers

are rotationally aligned and sufficiently overlapped with respect to each other The sample is

then annealed afterward

Step 4 The top hBN pre-exfoliated on PDMS is transferred on top of the whole stack covering

the heterostructure The sample is then annealed afterward


a) b)

128

3 Important notes

During the fabrication process the monolayers are kept from contact of any chemical as

this is detrimental to the sample quality which shows up as very broad PL linewidth and low PL

peak energy at low temperature For example in the case of PDMS dot picks up monolayer

directly PPC will be in contact with the monolayer After transfer PPC is cleansed using

acetone The PL spectrum of the monolayer MoSe2 at low temperature after acetone cleaning is

shown in figure A6 Keep monolayer from contact with any chemical during the transfer

process

Using all dry transfer technique we were able to observe interlayer exciton splitting

which is attributed to localization in Moire potential[61] We think that the dry transfer

technique is better for the optical quality of the sample than the PPC fabrication Each time the

sample is annealed the residue coagulates into blob leaving some clean regions In a big enough

sample chances are youll find some region that is atomically clean providing narrow PL

linewidth such that the effect of Moire potential can be observed

129

4 Anneal process

We anneal sample under high vacuum pressure ~10-5

mbarr in the furnace with the

temperature following the chart below The time at which the sample stay at 200 oC can be

varied

Figure A6 PL spectra from monolayer MoSe2 at 10 K excited using 660 nm CW laser with 30

W power The exciton (X) and trion (T) peaks are labeled Keep monolayer from contact with

any chemical during transfer process

X

X

X

T

T

130

IV Atomic Force Microscope (AFM) images of the fabricated samples

In this section we show some AFM images of the sample to give an idea of how flatness

of the substrate determines the sample qualityPL linewidth


semiconductor dry transferred on top of an annealed hBN b) Zoom-in region from a showing

super flat surface c) Lateral force image shows atomic resolution of the region d) Sample

schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000

RMS Roughness 0076nm

120 nm 4 8

00

1 V

Div

Sample Schematic

Topography image Topography image Lateral Force image

a) b) c)

d)

Figure A7 Temperature chart for annealing TMD sample

131

Figure A8 shows AFM images of a monolayer MoSe2 sample from 2D semiconductor

prepared using all dry fabrication Topography image shows a very smooth surface with the root

means square roughness of 0076 nm The lateral force measurement reveals the atomic

resolution of the sample On the other hand the surface roughness of monolayer MoSe2 sample

from HQ graphene prepared with identical method shows multiple patches of triangle shapes

We think that this is the result of growth Monolayer MoSe2 from HQ graphene also gives

broader PL linewidth at low temperature than monolayer MoSe2 from the 2D semiconductor

company

Finally we do AFM scan on the bare monolayer MoSe2 on the silicon substrate As

expected the monolayer surface is a lot rougher than monolayer transferred on hBN

Figure A9 a) and b) Topography image showing the roughness of monolayer MoSe2 from HQ

graphene on top of an annealed hBN

04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000

Topography image Topography image

a) b)

200

132


semiconductor dry transferred on silicon b) Line cut showing various peaks and troughs c)

Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

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The Dissertation Committee for Kha Xuan Tran Certifies that this is the approved version

of the following disseration


Heterostructures

Committee

Xiaoqin Li Supervisor

Chih-Kang Shih

Ananth Dodabalapur

Keji Lai

Nanshu Lu


Heterostructures

by

Kha Xuan Tran

Dissertation




of the Requirements

for the Degree of



May 2019

Dedication


v

Acknowledgements





















vi


to continue his PhD







vii


Heterostructures

Kha Xuan Tran PhD















viii









spectroscopy













ix

Table of Contents

List of tables xi

List of figures xii









monolayer 12

III Excitons13


V Dark excitons 20


VII Trions28








x






I Motivation 89





heterostructure101




IX Conclusion 108



I Exfoliation 113

II Transfer 119



References 134

xi

List of tables



samples 71



xii

List of Figures


2


wikipedia 3











( panel b) 9









xiii
















band gap value 18














respectively 25






xiv




X- negative trion X

+ positive trion X























denoting the









xv





probe setup 47


modulator) 48








to 56




near twist angle 58





xvi



















and half Gauss 72











xvii







also illustrated 80





























xviii








transition 96




















o sample (sample 2)



xix








made PDMS 117







128









xx






1



Wolfgang Pauli 1931



















theory of solids

2












3









world war II[18]










Source wikipedia

4








to mass produced
















5














a) b)

6















7











from ref [2]

8

















9







Ge)[26]




gEgE

k k

0 0

a) b)

10


(TMDs)





















11














temperature[39]

12


monolayer













Top

vie

wSi

de

vie

w

13










III Excitons








G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14













of mass motion




where aB is the





15











16
















gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17
















18






[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15


(c)

19















25b

20

V Dark excitons







an exciton dark








a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21
























22








K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23



















shown that[12]

24













25

2 Valley coherence











co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26









27






28

VII Trions






















29






30







Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31
















a) b) c)



32







33























34








35















WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36




















IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37













33de)[9]

38







25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)


12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39






















40








exciton peaks






41











42






1 Working principle







detector

43













the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44























45





a Pulse shaper









46















47














probe setup

48
















modulator)

49

















50












51


is proportional to
















52













53


















o

twist angle


54















the


55


contained in



has only 4 non


components are








Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

















perpendicular to

b)a)

57



















o) twist angle

58







only contain one

term for both

and

ie




twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59













are zeros which


we obtain




60








OX is

61


TMD













theoretical studies

1 Motivation






62
























63












2 Background


|Kgt

|Krsquogt

b)

K Krsquo

a)

64











(1)












65

(2)


polarization














66


1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67












localized excitons











68











[107108]











sample

69









1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)


a

5a

a

4a

a

3a

Sample E2

Sample E3

70











5 Conclusion












71



6 Extended Data












CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83


72











73










74







75




76












1 Motivation











77


















2 Background






78





















resonances [5493]


79




















80















81
























82












83





(a) and (c)

84






















85

4 Summary





86
























87









applications





88



















I Motivation




89























90





















respectively where




91







site (








92









a

b


σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50


-1 0 1


93
























94


























95




a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL


PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96









97








oscillator



where are non-









98











vanishes at site (














99










figure 66)

100








a

hf g

101























102


meV)











PBE-D2 PBE-D3

Stacking


Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking



b

c

a

103







quantum dots[153]


a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450


25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104



o twist













105











(figure 68)


a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)


sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106









) atomic





R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

























108
















109









nanoseconds














110
























111









112

APPENDIX








I Exfoliation


a Tape









113



Type of

PDMS








transfer










c Cell phone film






114

d Materials











(figure A1d)


bulk


PL linewidth












115
















slide



flattened




116



magic wand














100 mm

a) b) c) d)

117


pieces of blue tape



container



exfoliation











PDMS


118






II Transfer
















119









figure A2b)









Tilt stage

Rotation stage




Slide holder

a) b)

120


intact
















121







the PDMS dot





i Pick up


a) b)

122


PDMS dot






temperature at 50oC



slowly

ii Drop off release











123





















approach again

124








watching







125










126










hBN





measurement






section II2d

127















a) b)

128

3 Important notes







process







129

4 Anneal process




varied




X

X

X

T

T

130







schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000


120 nm 4 8

00

1 V

Div

Sample Schematic


a) b) c)

d)


131








company





04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000


a) b)

200

132



Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

References


























4041 (2017)









6242 (2015)









Vol 1

134




Rev B 96 085302 (2017)






1922) 2nd edn p^pp 433-439


231 (1945)


Review 74 230 (1948)






















10421 (2015)



13 3664 (2013)





041302 (2017)

135



887 (2012)



125407 125407 (2002)






(2017)









047401 (2017)








Nat Phys 11 830 (2015)



Nat Phys 12 677 (2016)



71 1752 (1993)



Applied Physics 101 014507 014507 (2007)






041401(R) (2016)

136



4 011034 (2014)



(2014)




























682 (2014)






(2016)



187002 (2015)



137


Nat Phys 14 801 (2018)








(2013)




(2013)






6 8315 (2015)






201401 (2013)








2467 (1995)











138








Phys Rev Lett 117 187401 (2016)














26 (2017)



Lett 115 117401 (2015)



Nano DOI 101038nnano2016282 (2017)








Nat Nano 10 497 (2015)









Pigments 32 229 (1996)

139


16 2204 (1998)







4670 (1998)




(2005)










Reports 5 9218 (2015)



89 205436 (2014)








(2015)







WSe2 Phys Rev B 90 075413 (2014)



221907 (2012)

140



(2014)



Nano Lett 14 202 (2014)






ACS Nano 7 11087 (2013)








(2005)






well arXiv160501771 (2016)












(2015)






(B) 252 2349 (2015)



141





43 (2018)
















Mater 13 1135 (2014)







2D Mater 1 011002 (2014)







1551 (2017)



Rev B 72 195341 (2005)








142






17 740 (2017)



(2018)








(2018)



567 66 (2019)





(2019)




arXiv190205887 (2019)















133603 (2001)



143



434 (2016)



















Appl Phys Lett 105 013101 (2014)


Heterostructures

by

Kha Xuan Tran

Dissertation




of the Requirements

for the Degree of



May 2019

Dedication


v

Acknowledgements





















vi


to continue his PhD







vii


Heterostructures

Kha Xuan Tran PhD















viii









spectroscopy













ix

Table of Contents

List of tables xi

List of figures xii









monolayer 12

III Excitons13


V Dark excitons 20


VII Trions28








x






I Motivation 89





heterostructure101




IX Conclusion 108



I Exfoliation 113

II Transfer 119



References 134

xi

List of tables



samples 71



xii

List of Figures


2


wikipedia 3











( panel b) 9









xiii
















band gap value 18














respectively 25






xiv




X- negative trion X

+ positive trion X























denoting the









xv





probe setup 47


modulator) 48








to 56




near twist angle 58





xvi



















and half Gauss 72











xvii







also illustrated 80





























xviii








transition 96




















o sample (sample 2)



xix








made PDMS 117







128









xx






1



Wolfgang Pauli 1931



















theory of solids

2












3









world war II[18]










Source wikipedia

4








to mass produced
















5














a) b)

6















7











from ref [2]

8

















9







Ge)[26]




gEgE

k k

0 0

a) b)

10


(TMDs)





















11














temperature[39]

12


monolayer













Top

vie

wSi

de

vie

w

13










III Excitons








G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14













of mass motion




where aB is the





15











16
















gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17
















18






[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15


(c)

19















25b

20

V Dark excitons







an exciton dark








a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21
























22








K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23



















shown that[12]

24













25

2 Valley coherence











co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26









27






28

VII Trions






















29






30







Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31
















a) b) c)



32







33























34








35















WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36




















IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37













33de)[9]

38







25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)


12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39






















40








exciton peaks






41











42






1 Working principle







detector

43













the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44























45





a Pulse shaper









46















47














probe setup

48
















modulator)

49

















50












51


is proportional to
















52













53


















o

twist angle


54















the


55


contained in



has only 4 non


components are








Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

















perpendicular to

b)a)

57



















o) twist angle

58







only contain one

term for both

and

ie




twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59













are zeros which


we obtain




60








OX is

61


TMD













theoretical studies

1 Motivation






62
























63












2 Background


|Kgt

|Krsquogt

b)

K Krsquo

a)

64











(1)












65

(2)


polarization














66


1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67












localized excitons











68











[107108]











sample

69









1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)


a

5a

a

4a

a

3a

Sample E2

Sample E3

70











5 Conclusion












71



6 Extended Data












CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83


72











73










74







75




76












1 Motivation











77


















2 Background






78





















resonances [5493]


79




















80















81
























82












83





(a) and (c)

84






















85

4 Summary





86
























87









applications





88



















I Motivation




89























90





















respectively where




91







site (








92









a

b


σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50


-1 0 1


93
























94


























95




a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL


PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96









97








oscillator



where are non-









98











vanishes at site (














99










figure 66)

100








a

hf g

101























102


meV)











PBE-D2 PBE-D3

Stacking


Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking



b

c

a

103







quantum dots[153]


a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450


25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104



o twist













105











(figure 68)


a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)


sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106









) atomic





R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

























108
















109









nanoseconds














110
























111









112

APPENDIX








I Exfoliation


a Tape









113



Type of

PDMS








transfer










c Cell phone film






114

d Materials











(figure A1d)


bulk


PL linewidth












115
















slide



flattened




116



magic wand














100 mm

a) b) c) d)

117


pieces of blue tape



container



exfoliation











PDMS


118






II Transfer
















119









figure A2b)









Tilt stage

Rotation stage




Slide holder

a) b)

120


intact
















121







the PDMS dot





i Pick up


a) b)

122


PDMS dot






temperature at 50oC



slowly

ii Drop off release











123





















approach again

124








watching







125










126










hBN





measurement






section II2d

127















a) b)

128

3 Important notes







process







129

4 Anneal process




varied




X

X

X

T

T

130







schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000


120 nm 4 8

00

1 V

Div

Sample Schematic


a) b) c)

d)


131








company





04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000


a) b)

200

132



Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

References


























4041 (2017)









6242 (2015)









Vol 1

134




Rev B 96 085302 (2017)






1922) 2nd edn p^pp 433-439


231 (1945)


Review 74 230 (1948)






















10421 (2015)



13 3664 (2013)





041302 (2017)

135



887 (2012)



125407 125407 (2002)






(2017)









047401 (2017)








Nat Phys 11 830 (2015)



Nat Phys 12 677 (2016)



71 1752 (1993)



Applied Physics 101 014507 014507 (2007)






041401(R) (2016)

136



4 011034 (2014)



(2014)




























682 (2014)






(2016)



187002 (2015)



137


Nat Phys 14 801 (2018)








(2013)




(2013)






6 8315 (2015)






201401 (2013)








2467 (1995)











138








Phys Rev Lett 117 187401 (2016)














26 (2017)



Lett 115 117401 (2015)



Nano DOI 101038nnano2016282 (2017)








Nat Nano 10 497 (2015)









Pigments 32 229 (1996)

139


16 2204 (1998)







4670 (1998)




(2005)










Reports 5 9218 (2015)



89 205436 (2014)








(2015)







WSe2 Phys Rev B 90 075413 (2014)



221907 (2012)

140



(2014)



Nano Lett 14 202 (2014)






ACS Nano 7 11087 (2013)








(2005)






well arXiv160501771 (2016)












(2015)






(B) 252 2349 (2015)



141





43 (2018)
















Mater 13 1135 (2014)







2D Mater 1 011002 (2014)







1551 (2017)



Rev B 72 195341 (2005)








142






17 740 (2017)



(2018)








(2018)



567 66 (2019)





(2019)




arXiv190205887 (2019)















133603 (2001)



143



434 (2016)



















Appl Phys Lett 105 013101 (2014)

Dedication


v

Acknowledgements





















vi


to continue his PhD







vii


Heterostructures

Kha Xuan Tran PhD















viii









spectroscopy













ix

Table of Contents

List of tables xi

List of figures xii









monolayer 12

III Excitons13


V Dark excitons 20


VII Trions28








x






I Motivation 89





heterostructure101




IX Conclusion 108



I Exfoliation 113

II Transfer 119



References 134

xi

List of tables



samples 71



xii

List of Figures


2


wikipedia 3











( panel b) 9









xiii
















band gap value 18














respectively 25






xiv




X- negative trion X

+ positive trion X























denoting the









xv





probe setup 47


modulator) 48








to 56




near twist angle 58





xvi



















and half Gauss 72











xvii







also illustrated 80





























xviii








transition 96




















o sample (sample 2)



xix








made PDMS 117







128









xx






1



Wolfgang Pauli 1931



















theory of solids

2












3









world war II[18]










Source wikipedia

4








to mass produced
















5














a) b)

6















7











from ref [2]

8

















9







Ge)[26]




gEgE

k k

0 0

a) b)

10


(TMDs)





















11














temperature[39]

12


monolayer













Top

vie

wSi

de

vie

w

13










III Excitons








G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14













of mass motion




where aB is the





15











16
















gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17
















18






[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15


(c)

19















25b

20

V Dark excitons







an exciton dark








a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21
























22








K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23



















shown that[12]

24













25

2 Valley coherence











co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26









27






28

VII Trions






















29






30







Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31
















a) b) c)



32







33























34








35















WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36




















IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37













33de)[9]

38







25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)


12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39






















40








exciton peaks






41











42






1 Working principle







detector

43













the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44























45





a Pulse shaper









46















47














probe setup

48
















modulator)

49

















50












51


is proportional to
















52













53


















o

twist angle


54















the


55


contained in



has only 4 non


components are








Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

















perpendicular to

b)a)

57



















o) twist angle

58







only contain one

term for both

and

ie




twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59













are zeros which


we obtain




60








OX is

61


TMD













theoretical studies

1 Motivation






62
























63












2 Background


|Kgt

|Krsquogt

b)

K Krsquo

a)

64











(1)












65

(2)


polarization














66


1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67












localized excitons











68











[107108]











sample

69









1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)


a

5a

a

4a

a

3a

Sample E2

Sample E3

70











5 Conclusion












71



6 Extended Data












CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83


72











73










74







75




76












1 Motivation











77


















2 Background






78





















resonances [5493]


79




















80















81
























82












83





(a) and (c)

84






















85

4 Summary





86
























87









applications





88



















I Motivation




89























90





















respectively where




91







site (








92









a

b


σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50


-1 0 1


93
























94


























95




a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL


PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96









97








oscillator



where are non-









98











vanishes at site (














99










figure 66)

100








a

hf g

101























102


meV)











PBE-D2 PBE-D3

Stacking


Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking



b

c

a

103







quantum dots[153]


a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450


25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104



o twist













105











(figure 68)


a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)


sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106









) atomic





R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

























108
















109









nanoseconds














110
























111









112

APPENDIX








I Exfoliation


a Tape









113



Type of

PDMS








transfer










c Cell phone film






114

d Materials











(figure A1d)


bulk


PL linewidth












115
















slide



flattened




116



magic wand














100 mm

a) b) c) d)

117


pieces of blue tape



container



exfoliation











PDMS


118






II Transfer
















119









figure A2b)









Tilt stage

Rotation stage




Slide holder

a) b)

120


intact
















121







the PDMS dot





i Pick up


a) b)

122


PDMS dot






temperature at 50oC



slowly

ii Drop off release











123





















approach again

124








watching







125










126










hBN





measurement






section II2d

127















a) b)

128

3 Important notes







process







129

4 Anneal process




varied




X

X

X

T

T

130







schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000


120 nm 4 8

00

1 V

Div

Sample Schematic


a) b) c)

d)


131








company





04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000


a) b)

200

132



Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

References


























4041 (2017)









6242 (2015)









Vol 1

134




Rev B 96 085302 (2017)






1922) 2nd edn p^pp 433-439


231 (1945)


Review 74 230 (1948)






















10421 (2015)



13 3664 (2013)





041302 (2017)

135



887 (2012)



125407 125407 (2002)






(2017)









047401 (2017)








Nat Phys 11 830 (2015)



Nat Phys 12 677 (2016)



71 1752 (1993)



Applied Physics 101 014507 014507 (2007)






041401(R) (2016)

136



4 011034 (2014)



(2014)




























682 (2014)






(2016)



187002 (2015)



137


Nat Phys 14 801 (2018)








(2013)




(2013)






6 8315 (2015)






201401 (2013)








2467 (1995)











138








Phys Rev Lett 117 187401 (2016)














26 (2017)



Lett 115 117401 (2015)



Nano DOI 101038nnano2016282 (2017)








Nat Nano 10 497 (2015)









Pigments 32 229 (1996)

139


16 2204 (1998)







4670 (1998)




(2005)










Reports 5 9218 (2015)



89 205436 (2014)








(2015)







WSe2 Phys Rev B 90 075413 (2014)



221907 (2012)

140



(2014)



Nano Lett 14 202 (2014)






ACS Nano 7 11087 (2013)








(2005)






well arXiv160501771 (2016)












(2015)






(B) 252 2349 (2015)



141





43 (2018)
















Mater 13 1135 (2014)







2D Mater 1 011002 (2014)







1551 (2017)



Rev B 72 195341 (2005)








142






17 740 (2017)



(2018)








(2018)



567 66 (2019)





(2019)




arXiv190205887 (2019)















133603 (2001)



143



434 (2016)



















Appl Phys Lett 105 013101 (2014)

v

Acknowledgements





















vi


to continue his PhD







vii


Heterostructures

Kha Xuan Tran PhD















viii









spectroscopy













ix

Table of Contents

List of tables xi

List of figures xii









monolayer 12

III Excitons13


V Dark excitons 20


VII Trions28








x






I Motivation 89





heterostructure101




IX Conclusion 108



I Exfoliation 113

II Transfer 119



References 134

xi

List of tables



samples 71



xii

List of Figures


2


wikipedia 3











( panel b) 9









xiii
















band gap value 18














respectively 25






xiv




X- negative trion X

+ positive trion X























denoting the









xv





probe setup 47


modulator) 48








to 56




near twist angle 58





xvi



















and half Gauss 72











xvii







also illustrated 80





























xviii








transition 96




















o sample (sample 2)



xix








made PDMS 117







128









xx






1



Wolfgang Pauli 1931



















theory of solids

2












3









world war II[18]










Source wikipedia

4








to mass produced
















5














a) b)

6















7











from ref [2]

8

















9







Ge)[26]




gEgE

k k

0 0

a) b)

10


(TMDs)





















11














temperature[39]

12


monolayer













Top

vie

wSi

de

vie

w

13










III Excitons








G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14













of mass motion




where aB is the





15











16
















gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17
















18






[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15


(c)

19















25b

20

V Dark excitons







an exciton dark








a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21
























22








K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23



















shown that[12]

24













25

2 Valley coherence











co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26









27






28

VII Trions






















29






30







Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31
















a) b) c)



32







33























34








35















WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36




















IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37













33de)[9]

38







25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)


12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39






















40








exciton peaks






41











42






1 Working principle







detector

43













the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44























45





a Pulse shaper









46















47














probe setup

48
















modulator)

49

















50












51


is proportional to
















52













53


















o

twist angle


54















the


55


contained in



has only 4 non


components are








Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

















perpendicular to

b)a)

57



















o) twist angle

58







only contain one

term for both

and

ie




twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59













are zeros which


we obtain




60








OX is

61


TMD













theoretical studies

1 Motivation






62
























63












2 Background


|Kgt

|Krsquogt

b)

K Krsquo

a)

64











(1)












65

(2)


polarization














66


1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67












localized excitons











68











[107108]











sample

69









1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)


a

5a

a

4a

a

3a

Sample E2

Sample E3

70











5 Conclusion












71



6 Extended Data












CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83


72











73










74







75




76












1 Motivation











77


















2 Background






78





















resonances [5493]


79




















80















81
























82












83





(a) and (c)

84






















85

4 Summary





86
























87









applications





88



















I Motivation




89























90





















respectively where




91







site (








92









a

b


σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50


-1 0 1


93
























94


























95




a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL


PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96









97








oscillator



where are non-









98











vanishes at site (














99










figure 66)

100








a

hf g

101























102


meV)











PBE-D2 PBE-D3

Stacking


Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking



b

c

a

103







quantum dots[153]


a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450


25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104



o twist













105











(figure 68)


a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)


sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106









) atomic





R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

























108
















109









nanoseconds














110
























111









112

APPENDIX








I Exfoliation


a Tape









113



Type of

PDMS








transfer










c Cell phone film






114

d Materials











(figure A1d)


bulk


PL linewidth












115
















slide



flattened




116



magic wand














100 mm

a) b) c) d)

117


pieces of blue tape



container



exfoliation











PDMS


118






II Transfer
















119









figure A2b)









Tilt stage

Rotation stage




Slide holder

a) b)

120


intact
















121







the PDMS dot





i Pick up


a) b)

122


PDMS dot






temperature at 50oC



slowly

ii Drop off release











123





















approach again

124








watching







125










126










hBN





measurement






section II2d

127















a) b)

128

3 Important notes







process







129

4 Anneal process




varied




X

X

X

T

T

130







schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000


120 nm 4 8

00

1 V

Div

Sample Schematic


a) b) c)

d)


131








company





04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000


a) b)

200

132



Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

References


























4041 (2017)









6242 (2015)









Vol 1

134




Rev B 96 085302 (2017)






1922) 2nd edn p^pp 433-439


231 (1945)


Review 74 230 (1948)






















10421 (2015)



13 3664 (2013)





041302 (2017)

135



887 (2012)



125407 125407 (2002)






(2017)









047401 (2017)








Nat Phys 11 830 (2015)



Nat Phys 12 677 (2016)



71 1752 (1993)



Applied Physics 101 014507 014507 (2007)






041401(R) (2016)

136



4 011034 (2014)



(2014)




























682 (2014)






(2016)



187002 (2015)



137


Nat Phys 14 801 (2018)








(2013)




(2013)






6 8315 (2015)






201401 (2013)








2467 (1995)











138








Phys Rev Lett 117 187401 (2016)














26 (2017)



Lett 115 117401 (2015)



Nano DOI 101038nnano2016282 (2017)








Nat Nano 10 497 (2015)









Pigments 32 229 (1996)

139


16 2204 (1998)







4670 (1998)




(2005)










Reports 5 9218 (2015)



89 205436 (2014)








(2015)







WSe2 Phys Rev B 90 075413 (2014)



221907 (2012)

140



(2014)



Nano Lett 14 202 (2014)






ACS Nano 7 11087 (2013)








(2005)






well arXiv160501771 (2016)












(2015)






(B) 252 2349 (2015)



141





43 (2018)
















Mater 13 1135 (2014)







2D Mater 1 011002 (2014)







1551 (2017)



Rev B 72 195341 (2005)








142






17 740 (2017)



(2018)








(2018)



567 66 (2019)





(2019)




arXiv190205887 (2019)















133603 (2001)



143



434 (2016)



















Appl Phys Lett 105 013101 (2014)

vi


to continue his PhD







vii


Heterostructures

Kha Xuan Tran PhD















viii









spectroscopy













ix

Table of Contents

List of tables xi

List of figures xii









monolayer 12

III Excitons13


V Dark excitons 20


VII Trions28








x






I Motivation 89





heterostructure101




IX Conclusion 108



I Exfoliation 113

II Transfer 119



References 134

xi

List of tables



samples 71



xii

List of Figures


2


wikipedia 3











( panel b) 9









xiii
















band gap value 18














respectively 25






xiv




X- negative trion X

+ positive trion X























denoting the









xv





probe setup 47


modulator) 48








to 56




near twist angle 58





xvi



















and half Gauss 72











xvii







also illustrated 80





























xviii








transition 96




















o sample (sample 2)



xix








made PDMS 117







128









xx






1



Wolfgang Pauli 1931



















theory of solids

2












3









world war II[18]










Source wikipedia

4








to mass produced
















5














a) b)

6















7











from ref [2]

8

















9







Ge)[26]




gEgE

k k

0 0

a) b)

10


(TMDs)





















11














temperature[39]

12


monolayer













Top

vie

wSi

de

vie

w

13










III Excitons








G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14













of mass motion




where aB is the





15











16
















gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17
















18






[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15


(c)

19















25b

20

V Dark excitons







an exciton dark








a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21
























22








K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23



















shown that[12]

24













25

2 Valley coherence











co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26









27






28

VII Trions






















29






30







Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31
















a) b) c)



32







33























34








35















WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36




















IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37













33de)[9]

38







25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)


12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39






















40








exciton peaks






41











42






1 Working principle







detector

43













the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44























45





a Pulse shaper









46















47














probe setup

48
















modulator)

49

















50












51


is proportional to
















52













53


















o

twist angle


54















the


55


contained in



has only 4 non


components are








Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

















perpendicular to

b)a)

57



















o) twist angle

58







only contain one

term for both

and

ie




twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59













are zeros which


we obtain




60








OX is

61


TMD













theoretical studies

1 Motivation






62
























63












2 Background


|Kgt

|Krsquogt

b)

K Krsquo

a)

64











(1)












65

(2)


polarization














66


1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67












localized excitons











68











[107108]











sample

69









1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)


a

5a

a

4a

a

3a

Sample E2

Sample E3

70











5 Conclusion












71



6 Extended Data












CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83


72











73










74







75




76












1 Motivation











77


















2 Background






78





















resonances [5493]


79




















80















81
























82












83





(a) and (c)

84






















85

4 Summary





86
























87









applications





88



















I Motivation




89























90





















respectively where




91







site (








92









a

b


σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50


-1 0 1


93
























94


























95




a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL


PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96









97








oscillator



where are non-









98











vanishes at site (














99










figure 66)

100








a

hf g

101























102


meV)











PBE-D2 PBE-D3

Stacking


Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking



b

c

a

103







quantum dots[153]


a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450


25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104



o twist













105











(figure 68)


a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)


sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106









) atomic





R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

























108
















109









nanoseconds














110
























111









112

APPENDIX








I Exfoliation


a Tape









113



Type of

PDMS








transfer










c Cell phone film






114

d Materials











(figure A1d)


bulk


PL linewidth












115
















slide



flattened




116



magic wand














100 mm

a) b) c) d)

117


pieces of blue tape



container



exfoliation











PDMS


118






II Transfer
















119









figure A2b)









Tilt stage

Rotation stage




Slide holder

a) b)

120


intact
















121







the PDMS dot





i Pick up


a) b)

122


PDMS dot






temperature at 50oC



slowly

ii Drop off release











123





















approach again

124








watching







125










126










hBN





measurement






section II2d

127















a) b)

128

3 Important notes







process







129

4 Anneal process




varied




X

X

X

T

T

130







schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000


120 nm 4 8

00

1 V

Div

Sample Schematic


a) b) c)

d)


131








company





04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000


a) b)

200

132



Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

References


























4041 (2017)









6242 (2015)









Vol 1

134




Rev B 96 085302 (2017)






1922) 2nd edn p^pp 433-439


231 (1945)


Review 74 230 (1948)






















10421 (2015)



13 3664 (2013)





041302 (2017)

135



887 (2012)



125407 125407 (2002)






(2017)









047401 (2017)








Nat Phys 11 830 (2015)



Nat Phys 12 677 (2016)



71 1752 (1993)



Applied Physics 101 014507 014507 (2007)






041401(R) (2016)

136



4 011034 (2014)



(2014)




























682 (2014)






(2016)



187002 (2015)



137


Nat Phys 14 801 (2018)








(2013)




(2013)






6 8315 (2015)






201401 (2013)








2467 (1995)











138








Phys Rev Lett 117 187401 (2016)














26 (2017)



Lett 115 117401 (2015)



Nano DOI 101038nnano2016282 (2017)








Nat Nano 10 497 (2015)









Pigments 32 229 (1996)

139


16 2204 (1998)







4670 (1998)




(2005)










Reports 5 9218 (2015)



89 205436 (2014)








(2015)







WSe2 Phys Rev B 90 075413 (2014)



221907 (2012)

140



(2014)



Nano Lett 14 202 (2014)






ACS Nano 7 11087 (2013)








(2005)






well arXiv160501771 (2016)












(2015)






(B) 252 2349 (2015)



141





43 (2018)
















Mater 13 1135 (2014)







2D Mater 1 011002 (2014)







1551 (2017)



Rev B 72 195341 (2005)








142






17 740 (2017)



(2018)








(2018)



567 66 (2019)





(2019)




arXiv190205887 (2019)















133603 (2001)



143



434 (2016)



















Appl Phys Lett 105 013101 (2014)

vii


Heterostructures

Kha Xuan Tran PhD















viii









spectroscopy













ix

Table of Contents

List of tables xi

List of figures xii









monolayer 12

III Excitons13


V Dark excitons 20


VII Trions28








x






I Motivation 89





heterostructure101




IX Conclusion 108



I Exfoliation 113

II Transfer 119



References 134

xi

List of tables



samples 71



xii

List of Figures


2


wikipedia 3











( panel b) 9









xiii
















band gap value 18














respectively 25






xiv




X- negative trion X

+ positive trion X























denoting the









xv





probe setup 47


modulator) 48








to 56




near twist angle 58





xvi



















and half Gauss 72











xvii







also illustrated 80





























xviii








transition 96




















o sample (sample 2)



xix








made PDMS 117







128









xx






1



Wolfgang Pauli 1931



















theory of solids

2












3









world war II[18]










Source wikipedia

4








to mass produced
















5














a) b)

6















7











from ref [2]

8

















9







Ge)[26]




gEgE

k k

0 0

a) b)

10


(TMDs)





















11














temperature[39]

12


monolayer













Top

vie

wSi

de

vie

w

13










III Excitons








G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14













of mass motion




where aB is the





15











16
















gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17
















18






[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15


(c)

19















25b

20

V Dark excitons







an exciton dark








a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21
























22








K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23



















shown that[12]

24













25

2 Valley coherence











co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26









27






28

VII Trions






















29






30







Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31
















a) b) c)



32







33























34








35















WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36




















IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37













33de)[9]

38







25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)


12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39






















40








exciton peaks






41











42






1 Working principle







detector

43













the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44























45





a Pulse shaper









46















47














probe setup

48
















modulator)

49

















50












51


is proportional to
















52













53


















o

twist angle


54















the


55


contained in



has only 4 non


components are








Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

















perpendicular to

b)a)

57



















o) twist angle

58







only contain one

term for both

and

ie




twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59













are zeros which


we obtain




60








OX is

61


TMD













theoretical studies

1 Motivation






62
























63












2 Background


|Kgt

|Krsquogt

b)

K Krsquo

a)

64











(1)












65

(2)


polarization














66


1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67












localized excitons











68











[107108]











sample

69









1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)


a

5a

a

4a

a

3a

Sample E2

Sample E3

70











5 Conclusion












71



6 Extended Data












CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83


72











73










74







75




76












1 Motivation











77


















2 Background






78





















resonances [5493]


79




















80















81
























82












83





(a) and (c)

84






















85

4 Summary





86
























87









applications





88



















I Motivation




89























90





















respectively where




91







site (








92









a

b


σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50


-1 0 1


93
























94


























95




a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL


PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96









97








oscillator



where are non-









98











vanishes at site (














99










figure 66)

100








a

hf g

101























102


meV)











PBE-D2 PBE-D3

Stacking


Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking



b

c

a

103







quantum dots[153]


a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450


25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104



o twist













105











(figure 68)


a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)


sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106









) atomic





R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

























108
















109









nanoseconds














110
























111









112

APPENDIX








I Exfoliation


a Tape









113



Type of

PDMS








transfer










c Cell phone film






114

d Materials











(figure A1d)


bulk


PL linewidth












115
















slide



flattened




116



magic wand














100 mm

a) b) c) d)

117


pieces of blue tape



container



exfoliation











PDMS


118






II Transfer
















119









figure A2b)









Tilt stage

Rotation stage




Slide holder

a) b)

120


intact
















121







the PDMS dot





i Pick up


a) b)

122


PDMS dot






temperature at 50oC



slowly

ii Drop off release











123





















approach again

124








watching







125










126










hBN





measurement






section II2d

127















a) b)

128

3 Important notes







process







129

4 Anneal process




varied




X

X

X

T

T

130







schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000


120 nm 4 8

00

1 V

Div

Sample Schematic


a) b) c)

d)


131








company





04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000


a) b)

200

132



Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

References


























4041 (2017)









6242 (2015)









Vol 1

134




Rev B 96 085302 (2017)






1922) 2nd edn p^pp 433-439


231 (1945)


Review 74 230 (1948)






















10421 (2015)



13 3664 (2013)





041302 (2017)

135



887 (2012)



125407 125407 (2002)






(2017)









047401 (2017)








Nat Phys 11 830 (2015)



Nat Phys 12 677 (2016)



71 1752 (1993)



Applied Physics 101 014507 014507 (2007)






041401(R) (2016)

136



4 011034 (2014)



(2014)




























682 (2014)






(2016)



187002 (2015)



137


Nat Phys 14 801 (2018)








(2013)




(2013)






6 8315 (2015)






201401 (2013)








2467 (1995)











138








Phys Rev Lett 117 187401 (2016)














26 (2017)



Lett 115 117401 (2015)



Nano DOI 101038nnano2016282 (2017)








Nat Nano 10 497 (2015)









Pigments 32 229 (1996)

139


16 2204 (1998)







4670 (1998)




(2005)










Reports 5 9218 (2015)



89 205436 (2014)








(2015)







WSe2 Phys Rev B 90 075413 (2014)



221907 (2012)

140



(2014)



Nano Lett 14 202 (2014)






ACS Nano 7 11087 (2013)








(2005)






well arXiv160501771 (2016)












(2015)






(B) 252 2349 (2015)



141





43 (2018)
















Mater 13 1135 (2014)







2D Mater 1 011002 (2014)







1551 (2017)



Rev B 72 195341 (2005)








142






17 740 (2017)



(2018)








(2018)



567 66 (2019)





(2019)




arXiv190205887 (2019)















133603 (2001)



143



434 (2016)



















Appl Phys Lett 105 013101 (2014)

viii









spectroscopy













ix

Table of Contents

List of tables xi

List of figures xii









monolayer 12

III Excitons13


V Dark excitons 20


VII Trions28








x






I Motivation 89





heterostructure101




IX Conclusion 108



I Exfoliation 113

II Transfer 119



References 134

xi

List of tables



samples 71



xii

List of Figures


2


wikipedia 3











( panel b) 9









xiii
















band gap value 18














respectively 25






xiv




X- negative trion X

+ positive trion X























denoting the









xv





probe setup 47


modulator) 48








to 56




near twist angle 58





xvi



















and half Gauss 72











xvii







also illustrated 80





























xviii








transition 96




















o sample (sample 2)



xix








made PDMS 117







128









xx






1



Wolfgang Pauli 1931



















theory of solids

2












3









world war II[18]










Source wikipedia

4








to mass produced
















5














a) b)

6















7











from ref [2]

8

















9







Ge)[26]




gEgE

k k

0 0

a) b)

10


(TMDs)





















11














temperature[39]

12


monolayer













Top

vie

wSi

de

vie

w

13










III Excitons








G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14













of mass motion




where aB is the





15











16
















gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17
















18






[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15


(c)

19















25b

20

V Dark excitons







an exciton dark








a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21
























22








K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23



















shown that[12]

24













25

2 Valley coherence











co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26









27






28

VII Trions






















29






30







Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31
















a) b) c)



32







33























34








35















WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36




















IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37













33de)[9]

38







25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)


12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39






















40








exciton peaks






41











42






1 Working principle







detector

43













the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44























45





a Pulse shaper









46















47














probe setup

48
















modulator)

49

















50












51


is proportional to
















52













53


















o

twist angle


54















the


55


contained in



has only 4 non


components are








Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

















perpendicular to

b)a)

57



















o) twist angle

58







only contain one

term for both

and

ie




twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59













are zeros which


we obtain




60








OX is

61


TMD













theoretical studies

1 Motivation






62
























63












2 Background


|Kgt

|Krsquogt

b)

K Krsquo

a)

64











(1)












65

(2)


polarization














66


1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67












localized excitons











68











[107108]











sample

69









1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)


a

5a

a

4a

a

3a

Sample E2

Sample E3

70











5 Conclusion












71



6 Extended Data












CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83


72











73










74







75




76












1 Motivation











77


















2 Background






78





















resonances [5493]


79




















80















81
























82












83





(a) and (c)

84






















85

4 Summary





86
























87









applications





88



















I Motivation




89























90





















respectively where




91







site (








92









a

b


σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50


-1 0 1


93
























94


























95




a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL


PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96









97








oscillator



where are non-









98











vanishes at site (














99










figure 66)

100








a

hf g

101























102


meV)











PBE-D2 PBE-D3

Stacking


Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking



b

c

a

103







quantum dots[153]


a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450


25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104



o twist













105











(figure 68)


a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)


sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106









) atomic





R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

























108
















109









nanoseconds














110
























111









112

APPENDIX








I Exfoliation


a Tape









113



Type of

PDMS








transfer










c Cell phone film






114

d Materials











(figure A1d)


bulk


PL linewidth












115
















slide



flattened




116



magic wand














100 mm

a) b) c) d)

117


pieces of blue tape



container



exfoliation











PDMS


118






II Transfer
















119









figure A2b)









Tilt stage

Rotation stage




Slide holder

a) b)

120


intact
















121







the PDMS dot





i Pick up


a) b)

122


PDMS dot






temperature at 50oC



slowly

ii Drop off release











123





















approach again

124








watching







125










126










hBN





measurement






section II2d

127















a) b)

128

3 Important notes







process







129

4 Anneal process




varied




X

X

X

T

T

130







schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000


120 nm 4 8

00

1 V

Div

Sample Schematic


a) b) c)

d)


131








company





04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000


a) b)

200

132



Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

References


























4041 (2017)









6242 (2015)









Vol 1

134




Rev B 96 085302 (2017)






1922) 2nd edn p^pp 433-439


231 (1945)


Review 74 230 (1948)






















10421 (2015)



13 3664 (2013)





041302 (2017)

135



887 (2012)



125407 125407 (2002)






(2017)









047401 (2017)








Nat Phys 11 830 (2015)



Nat Phys 12 677 (2016)



71 1752 (1993)



Applied Physics 101 014507 014507 (2007)






041401(R) (2016)

136



4 011034 (2014)



(2014)




























682 (2014)






(2016)



187002 (2015)



137


Nat Phys 14 801 (2018)








(2013)




(2013)






6 8315 (2015)






201401 (2013)








2467 (1995)











138








Phys Rev Lett 117 187401 (2016)














26 (2017)



Lett 115 117401 (2015)



Nano DOI 101038nnano2016282 (2017)








Nat Nano 10 497 (2015)









Pigments 32 229 (1996)

139


16 2204 (1998)







4670 (1998)




(2005)










Reports 5 9218 (2015)



89 205436 (2014)








(2015)







WSe2 Phys Rev B 90 075413 (2014)



221907 (2012)

140



(2014)



Nano Lett 14 202 (2014)






ACS Nano 7 11087 (2013)








(2005)






well arXiv160501771 (2016)












(2015)






(B) 252 2349 (2015)



141





43 (2018)
















Mater 13 1135 (2014)







2D Mater 1 011002 (2014)







1551 (2017)



Rev B 72 195341 (2005)








142






17 740 (2017)



(2018)








(2018)



567 66 (2019)





(2019)




arXiv190205887 (2019)















133603 (2001)



143



434 (2016)



















Appl Phys Lett 105 013101 (2014)

ix

Table of Contents

List of tables xi

List of figures xii









monolayer 12

III Excitons13


V Dark excitons 20


VII Trions28








x






I Motivation 89





heterostructure101




IX Conclusion 108



I Exfoliation 113

II Transfer 119



References 134

xi

List of tables



samples 71



xii

List of Figures


2


wikipedia 3











( panel b) 9









xiii
















band gap value 18














respectively 25






xiv




X- negative trion X

+ positive trion X























denoting the









xv





probe setup 47


modulator) 48








to 56




near twist angle 58





xvi



















and half Gauss 72











xvii







also illustrated 80





























xviii








transition 96




















o sample (sample 2)



xix








made PDMS 117







128









xx






1



Wolfgang Pauli 1931



















theory of solids

2












3









world war II[18]










Source wikipedia

4








to mass produced
















5














a) b)

6















7











from ref [2]

8

















9







Ge)[26]




gEgE

k k

0 0

a) b)

10


(TMDs)





















11














temperature[39]

12


monolayer













Top

vie

wSi

de

vie

w

13










III Excitons








G M

K

a) b) c)

Bulk Monolayer

Q

Q

Q

14













of mass motion




where aB is the





15











16
















gE

k

0

1Bn

2Bn

3Bn

Bn

BE

2035 2010 1985 1960

5

75

10

Energy (meV)

Per

cen

tage

Tra

nsm

issi

on

1s

2s3s

4s5s

d) e) f)

a) b) c)

17
















18






[15]

Bulk 3D

Monolayer 2D

Log

(dI

dV

) (d

ecad

ed

iv)

-35 -30 -25 -20 -15 -10 -05 00 05 10 15


(c)

19















25b

20

V Dark excitons







an exciton dark








a)

K

K

K

Krsquo

KrsquoKrsquo

ky

kx

b1

b2

K Krsquo

_

+

σ+

_

+

σ-

b)

21
























22








K Krsquo

_

+

a)

b)

brightdark

K Krsquo

+

_

brightdark

c)

WX2 MoX2

23



















shown that[12]

24













25

2 Valley coherence











co circular

cross circular

17 18 19 20 21 22 23

1800

1500

1200

900

600

300

0

PL

inte

nsi

ty (

au

)

Photon energy (eV)

co circular

cross circular

160 165 170 175

Photon energy (eV)

PL

inte

nsi

ty (

au

)

120

240

360

a)

b)

0

X0

X0X-

26









27






28

VII Trions






















29






30







Vg

Ene

rgy

(eV

) PL

inte

nsi

ty (

au

)

Exciton

Trion

a)

b)

c)

d)

31
















a) b) c)



32







33























34








35















WSe2

MoSe2- -

-

+++

IX

~10 fs

~10 fs

~1 ps ~1 ps~10 ns

K Krsquo

_

+

K Krsquo

0o stacking

IX

13 14 15 16 17 18

Energy (eV)

Inte

nsity (

au

)a) b)

c)IX

36




















IX in

ten

sity

(a

u)

IX in

ten

sity

(a

u)

100

10-1

10-2

0 10 20 30 40 50 60Time (ns)

2o sample1o sample

35o sample

a) b) c)

37













33de)[9]

38







25

20

15

10

05

000 5 10 15 20 25

Hei

ght

(Å)


12

10

08

06

04

Ban

d g

ap (

eV

)

a)

b)

c) d)

e)

39






















40








exciton peaks






41











42






1 Working principle







detector

43













the detector

Sample

in

cryostat

PumpProbeTime

Delay

50-X

QWP

Filter Probe

Ti-Sapph

Laser

Detector

44























45





a Pulse shaper









46















47














probe setup

48
















modulator)

49

















50












51


is proportional to
















52













53


















o

twist angle


54















the


55


contained in



has only 4 non


components are








Xrsquo

Yrsquo

Chalcogen atom

Metal atom

a) b)

56

















perpendicular to

b)a)

57



















o) twist angle

58







only contain one

term for both

and

ie




twist angle

a)

c)B

BO

cry

stal

sam

ple

Tisapphire

sho

rt-p

ass

filt

er

spectrometer

2ω

ref

Co

llim

atin

g le

ns

2ω

sam

ple

ω

10

X o

bje

ctiv

e

t

b)

59













are zeros which


we obtain




60








OX is

61


TMD













theoretical studies

1 Motivation






62
























63












2 Background


|Kgt

|Krsquogt

b)

K Krsquo

a)

64











(1)












65

(2)


polarization














66


1660 1680 1700 1720 1740 1760Energy (meV)

1

a08

a06

a04

a02

a0

PL

In

tensity

(au

)a)

1730 1740 1750 1760

025

a020

a015

a010

a005

a0

1

a08

a06

a04

a02

a0

Energy (meV)

PL In

tensity

(au

)

Va

lley

Co

here

nce

co linear

cross linear

VC

b)

1

a08

a06

a04

a02

a0

Va

lley

Po

lariza

tio

n

PL

In

tensity

(au

)

co circular

cross circular

VP

Energy (meV)

025

a020

a015

a010

a005

a0

1730 1740 1750 1760

c)

67












localized excitons











68











[107108]











sample

69









1 3 5 7 9

06

a055

a050

a045

a040

040

a035

a030

a025

a020

Va

lley

Co

here

nce

Va

lley

Po

lariza

tio

n

Stokes Shift (meV)

VC

VP

b)

1

a08

a06

a04

a02

a0

02

a015

a010

a005

a0

SS

1720 1740 1760 1780

Energy (meV)

PL

In

tensity

(au

)

Abso

rption

a)

X

SS

(m

eV

)


a

5a

a

4a

a

3a

Sample E2

Sample E3

70











5 Conclusion












71



6 Extended Data












CVD1 17435 1744 17437 231 207 237 16 21 18

E2 17558 17558 17557 176 149 136 41 41 40

E3 17572 17573 17572 181 159 128 47 48 47

E4 17537 17537 17536 208 161 154 65 65 65

E5 17557 17566 17566 447 368 250 75 84 83

E6 17575 17575 17571 211 170 155 86 86 83


72











73










74







75




76












1 Motivation











77


















2 Background






78





















resonances [5493]


79




















80















81
























82












83





(a) and (c)

84






















85

4 Summary





86
























87









applications





88



















I Motivation




89























90





















respectively where




91







site (








92









a

b


σ+

K

K

σ-

K

K

K

K

c

-100 -50 0 50


-1 0 1


93
























94


























95




a c

b

WSe2

MoSe2

- --

+++

IX

10 microm

1L WSe2

1L MoSe2

hBL


PL Inte

nsity (

arb

units)

1

08

06

04

02

0

IX

hBN encapsulated

uncapped

X0

X-

X0

WSe2MoSe2

96









97








oscillator



where are non-









98











vanishes at site (














99










figure 66)

100








a

hf g

101























102


meV)











PBE-D2 PBE-D3

Stacking


Gap at K (eV) 105 093 1047 1082 1032 1144

Stacking



b

c

a

103







quantum dots[153]


a

b

PL

Inte

nsi

ty (

arb

un

its)

10aa

08

a

06

a

04

a

02

a

01250 1300 1350 1400 1450


25 K 70 K

0 5 10 15 20 25Time (ns)

100

10-1

10-2

PL

Inte

nsi

ty (

arb

un

its)

Life

tim

e (n

s) 101

100

Energy (meV)1300 1350 1400

104



o twist













105











(figure 68)


a b

sample 1 (1o)

sample 2 (2o)P

L inte

nsity (

norm

aliz

ed)

PL inte

nsity (

norm

aliz

ed)


sample 1 (1o)

sample 2 (2o)

1250 1300 1350 1400 1450 -10 0 10 20 30 40 50 60

100

10-1

10-2

106









) atomic





R type (1o)

H type (60o)P

L Inte

nsity

(norm

aliz

ed)

1250 1300 1350 1400 1450


107

























108
















109









nanoseconds














110
























111









112

APPENDIX








I Exfoliation


a Tape









113



Type of

PDMS








transfer










c Cell phone film






114

d Materials











(figure A1d)


bulk


PL linewidth












115
















slide



flattened




116



magic wand














100 mm

a) b) c) d)

117


pieces of blue tape



container



exfoliation











PDMS


118






II Transfer
















119









figure A2b)









Tilt stage

Rotation stage




Slide holder

a) b)

120


intact
















121







the PDMS dot





i Pick up


a) b)

122


PDMS dot






temperature at 50oC



slowly

ii Drop off release











123





















approach again

124








watching







125










126










hBN





measurement






section II2d

127















a) b)

128

3 Important notes







process







129

4 Anneal process




varied




X

X

X

T

T

130







schematic

1 n

mD

iv

MoSe2

Annealed hBN

Silicon 300nm SiO2

000 200 400 m

40

nm

Div

800 nm4000


120 nm 4 8

00

1 V

Div

Sample Schematic


a) b) c)

d)


131








company





04

nm

Div

000 200 400 m

10

nm

Div

600 nm4000


a) b)

200

132



Sample schematics

400 nm2000

20

nm

Div

400 nm2000

22

14

06

nmb)a)

MoSe2

Silicon substrate

c)

133

References


























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6242 (2015)









Vol 1

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Rev B 96 085302 (2017)






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WSe2 Phys Rev B 90 075413 (2014)



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Nano Lett 14 202 (2014)






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well arXiv160501771 (2016)












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Rev B 72 195341 (2005)








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