M. S. Dresselhaus, MITMay 30, 2012
Graphene and Beyond:A Perspective
Europe and Korea are launching large graphene programs
The European Union together with other European countries like the UK are investing 1 billion Euros in graphene research.Korea is heavily investing in graphene, with an application emphasis.
2
This conference is lookingbeyond graphene
• Research presentations from the research community
• Breakout sessions• 2D Layered Materials for Electronics Applications• 2D Layered Materials for Structural and Energy
Applications• 2D Layered Materials for Photonic and Sensing
Applications 3
Outline: Graphene and Beyond
• Background
• Introducing Isotopes
• Introducing Dopants
• hBN and Carbon BN Superlattices
• Other Graphene-Like Materials
• Layered Materials Unlike Graphene4
Graphene and the field of carbon research
Number of physics-related publications on carbon
Early history
Fullerenes
Nanotubes
Graphene
Graphiteintercalation compounds
c-c3a a P.R. Wallace, Phys. Rev. 71, 622 (1947)
In 1957-1960 McClure extended the 2D graphene electronic structure to 3D graphite and included the magnetic field dependence
Near the K point
is the overlap integral between nearest neighbor -orbitals (0 values are from 2.9 to 3.1eV).
0
( ) v | |FE linear relation
03v2F
a
and
and
EF
where
J.W. McClure, Phys. Rev., 108:612 (1957); 119:606 (1960)
The Electronic Structure of Graphene
Thickness determined by TEM
“This means that the thinnest films consist of few carbon layers, maybe even just one layer”
Graphene
monolayerbilayer
bilayer
trilayerFirst Brillouin zone
Graphene
Electronic structure
Anomalous Quantum Hall Effect in 1-LG Graphene
• Half integer quantum Hall effect, • Factor of 4 in 4e2/h • Berry’s phase of π
• This work attracted great attention and interest in grapheneNovoselov, Geim et al., Nature 438(197) 2005
Three anomalies:
Thinnest material sheet imaginable…yet the strongest! (5 times stronger than steel and much lighter!)
Graphene is a zero band gap semiconductor: it conducts as well as the best metals, yet its electrical properties can be modulated (it can be switched “ON” and “OFF”)
Very high current densities (equivalent to ~109 Å/cm2)
Superb heat conductor (~5·103 W/m·K)
High mobility (100000 cm2/Vs @RT) Ballistic conduction for hundreds of nm
Bipolar materials (electrons and holes)
Low energy behavior described by Dirac equation
Truly 2D: pure surface with no bulk!
Band structure can be modified by application of electromagnetic fields
Band structure of graphene structures depends on geometry (stacking, size, and atomic structure)
Interesting electron spin dynamics (weak spin orbit, nearly absent hyperfine interaction, etc…)
Mono-layer
Bi-layer
Raman Spectrum for Graphene
Ferrari et al., 2006
Outline: Graphene and Beyond
• Background
• Introducing Isotopes
• Introducing Dopants
• hBN and Carbon BN Superlattices
• Other Graphene-Like Materials
• Layered Materials Unlike Graphene14
M. Kalbac, H. Farhat, J. Kong, P. Janda, L. Kavan, and M. S. Dresselhaus. Nanoletters 11(5):1957-1963 (2011).
Ram
an in
tens
ity, a
. u.
2800260024002200200018001600Raman shift, cm -1
13C 1-LG
12C 1-LG
Ram
an in
tens
ity, a
. u.
2800260024002200200018001600Raman shift, cm -1
13C 1-LG
12C 1-LG
13C/12C 2-LG
Ram
an in
tens
ity, a
. u.
2800260024002200200018001600Raman shift, cm -1
13C 1-LG
12C 1-LG
13C/12C 2-LG
13C/12C 2-LG on BN
Top
Bottom
Isotope labeling in 2-LG
Isotopes allow us to study the behavior of individual layers in bilayer graphene
Costa et al., Carbon 49:4719-4723, 2011
Effect of 13C isotope dopingon the optical phonon modes:
Raman spectroscopy and localization
Raman spectra of SWCNT at different 13C concentrations G band linewidth G as a function
of 13C density
• Phonon lifetimes and localization length affected by the presence of13C isotope impurities.
• Measurable effects in Raman spectroscopy
Phonon Lifetime:
Phonon lifetime due to 13C scattering:
13C density dependence of the lifetime.
Plot of Iqn for the different phonon modes and wavectors.
Decoupling of density dependence and
wavevector
Phonon Scattering Mechanisms: E-PH, PH-PH (T-controlled), PH-IMP
J Rodriguez-Nieva, unpublished
Comparison Theory vs. Experiment:
Spectral width of Costa et al. vs. theory model.
Typical values of lifetimes at G-band:
Natural C:
50% dopedGraphene:
Estimated broadening:
Natural C:
50% doped Graphene:
Comparison with other processes (G-band):Negligible
Comparable
Outline: Graphene and Beyond
• Background
• Introducing Isotopes
• Introducing Dopants
• hBN and Carbon BN Superlattices
• Other Graphene-Like Materials
• Layered Materials Unlike Graphene19
Doped Nanoribbons
F. Lopez-Urias, E. Gracias-Espino, M. S. Dresselhaus, M. Terrones, et al. Unpublished (2012) 20
Similar general behavior for each dopant, but the magnitudes of the bonding interactions differ
275027002650260025502500
x0.9
Ram
an in
tens
ity, a
.u.
1650160015501500
Raman shift, cm-1
Doping of 2-LG
21Electrochemical doping of graphene as observed in Raman scattering
M. Kalbac et al.
Outline: Graphene and Beyond
• Background
• Introducing Isotopes
• Introducing Dopants
• hBN and Carbon BN Superlattices
• Other Graphene-Like Materials
• Layered Materials Unlike Graphene22
Property Graphite/Graphene h-BNDensity 2.1 g/cm3 2.1 g/cm3
Stacking AB AA′C-C/B-N distance 1.421 Å 1.446 ÅBand gap 0 5-6 eVElectrical semimetal insulatorDielectric constant - 3-4
- Ultra-flat- Chemically inert
hexagonal-BN sheetsAtomic force microscope topography images of boron nitride vs SiO2
Root mean squared roughness of BN = 50pm! (50-100pm typical)
boron nitride SiO2
SiO2 rms = 250pm (200-300pm typical)
Ram
an in
tens
ity, a
.u.
2800260024002200200018001600Raman frequency, cm-1
2-LG on BN substrate
Ram
an in
tens
ity, a
.u.
2800260024002200200018001600Raman frequency, cm-1
2-LG on BN substrate
Enhancement is similar for the top and bottom layers
M. Kalbac, O. Frank, et al. J. Phys. Chem. Lett. 2012, DOI: 10.1021/jz300176a
Enhancement of the G mode in Raman spectra of 2-LG
25
Mobility= 110,000 cm2/Vs
Two orders of magnitude higher mobility than previous TLG on SiO2: Cracium et al. Nat. Nano. (2009); Zhu et al. PRB (2009)
ABA Trilayer Graphene
Koshino et al. PRB 81:115315 (2010)
BN substrates useful for studying layer stacking
Twisted Bilayer GrapheneVary twist angle Rich set of behaviors
θ
Low twist angles -low energy van Hove singularity-slowdown vF
Lopez et al. PRL 2007Li et al. Nature Physics 2010
Large twist anglesSingle-layer dispersion in both layers
Hass et al. PRL 2008
BN substrates useful for studying twisted layer stacking
Outline: Graphene and Beyond
• Background
• Introducing Isotopes
• Introducing Dopants
• hBN and Carbon BN Superlattices
• Other Graphene-Like Materials
• Layered Materials Unlike Graphene29
Graphene nanoribbons and flakes are special forms of graphene with edges
Single-layer graphene
Graphene flake
Graphene nanoribbon (GNR)
30
[Nakada, Phys. Rev. B (1996)]
Metallic
Metallic or SemiconductorArmchair ribbons
Zigzag ribbons
1 2 3 4 NN-1N-2
1
23 4 5 6 N-2 N-1
N
From tight binding calculations
Edges in graphene nanoribbonsSemiconductor
Spin-resolved band structure[Son, Nature (2006)]
16-zigzag GN
R
31
32
Dirac cones
Also: B. Lalmi et al. APL 97:223109 (2010)
Silicene
33
34
Nano Lett. 12, 1045 (2012)Also the Germanium-
based 2D-material
Outline: Graphene and Beyond
• Background
• Introducing Isotopes
• Introducing Dopants
• hBN and Carbon BN Superlattices
• Other Graphene-Like Materials
• Layered Materials Unlike Graphene35
36
Molybdenum Sulfide
Single-layer MoS2 is a direct gap semiconductor while multi-layer MoS2 is an indirect gap semiconductor
37
Titanium OxideCalcium Niobium
OxideDouble
Hydroxide
Adv. Mater. 22:5082 (2010)
Oxides and HydroxidesTransition metal dichalcogenidesare semiconductors
More complex layered structures including transition metal dichalcogenides are in this class
38
Topological Insulators: Bi2Se3, Bi2Te3 …
L. A. Wray et al. (2010)
SCIENCE 325, 278 (2009)
Nano Lett. 10:1209 (2010)
39
Nano Lett. 10, 5032 (2010)
Six varieties of Dirac cones in Bi1-xSbx
• Review of bulk bismuth, bulk Bi1-xSbx
• Construct various Dirac-cone-materials– Single-, bi-, and tri-Dirac-cone– Exact-, quasi-, and semi-Dirac-cone– Dirac cones with various anisotropies
• Different high-symmetry orientations of two-dimensional Bi1-xSbx
Crystal Structure of Bi1-xSbx
• Rhombohedral structure• 2 atoms in each unit cell (red
and green)• 2 FCC sub-lattices elongated
along the trigonal axis and inter-penetrating
• Trigonal axis has three-fold symmetry
• The bisectrix axis and the trigonal axis form a mirror plane.
Carrier-Pockets in the First Brillouin Zone of Bi1-xSbx
• The Brillouin Zone contains 1 T point, 3 three-fold symmetrical Lpoints and 6 H points with inversion symmetry and three-fold symmetry along the T axis
• The bottom of the conduction band is located at the L points• The top of the valence band is at the L point for bulk Bi and at the H
point for bulk Sb, and the exact location depends on x for Bi1-xSbx
Band Structure of Bi1-xSbx in 3D
x<0.07: Semimetalx=0.07~0.09: Indirect-Semiconductorx=0.09~0.15: Direct-Semiconductorx=0.15~0.22: Indirect-Semiconductorx>0.22: Semimetal
Band CrossingJPCS 57:89
• The L-point conduction band edge and valence band edge are close to each other and strongly coupled.
• The dispersion relation at the Lpoints is non-parabolic or linear
Different types of Dirac cones in Bi1-xSbx
• Dirac Point:• Dirac Cone: 2D projection of Dirac Point
– Single-Dirac-cone: Topological Insulator (Bi2Se3 surface states)
– Bi-Dirac-cone: Graphene– Tri-Dirac-cone—Bi1-xSbx
• Quasi-Dirac-cone• Semi-Dirac-cone: semi-classically dispersive
and semi-relativistically dispersive
( )E k v k
S. Tang & M. S. Dresselhaus, Nano Letters 12:2021(2012)
Anisotropic Single-Dirac-Cone in Bi1-xSbx Thin Film
Prediction only—no experiments
*Bisectrix-Oriented Growth—2D
Thermal smearing of ( )fE
, where f is the Fermi-Dirac Distribution. The effective range of smearing is ~kBT
Thermal shearing
3D Phase Diagram
Single-, Bi-, and Tri-Dirac-Cones in Bi1-xSbx
Single-Dirac-Cone Material:Bisectrix Oriented Growth
Bi-Dirac-Cone Material:Binary Oriented Growth
Tri-Dirac-Cone Material:Trigonal Oriented Growth
lz=100 nm
S. Tang & M. S. Dresselhaus, Constructing a Large Variety of Dirac-Cone Materials in the Bi1-xSbx Thin Film System, arXiv:1111.5525v1 (2011)
Group Velocity and Anisotropy
210Diracij lightv c
Bisectrix Growth Oriented lz=300nm
[6061] Growth Oriented lz=300nm
Anisotropy Coefficient
max
min
vv
velocity anisotropy for different in-film directions
Trigonal Growth
Bisectrix Growth
Binary Growth
Controlling the L-point Mini-Gap
Trigonal
Bisectrix
Binary
Eg vs. lz and growth orientation Eg vs. lz and x
Phase Diagrams forThin Film Bi1-xSx
SM: semi-metalISC: indirect-semiconductorDSC: direct-semiconductor
Antimony Composition x
S. Tang & M. S. Dresselhaus, Phase Diagrams of Bi1-xSbx Thin Films with Different Growth Orientations, to be submitted
Summary of Dirac Cone Types
• Predicted construction of different Dirac cones: – single-, bi-, and tri-Dirac-cone materials – exact-, quasi-, and semi-Dirac-cone materials– Dirac cones with different anisotropies
All are based on Bi1-xSbx thin films.
Europe and Korea are launching large graphene programs
The European Union together with other European countries like the UK are investing 1 billion Euros in graphene research.Korea is heavily investing in graphene, with an application emphasis.
52
This conference is lookingbeyond graphene
• Research presentations from the research community
• Breakout sessions• 2D Layered Materials for Electronics Applications• 2D Layered Materials for Structural and Energy
Applications• 2D Layered Materials for Photonic and Sensing
Applications 53