SHE in graphene
Computational Modeling of Spin Hall Effects
in Multiterminal Graphene Devices
Branislav K. NikolićDepartment of Physics & Astronomy, University of Delaware, Newark, DE 19716, U.S.A.
https://wiki.physics.udel.edu/qttg
1638–1655
KWANT Workshop, Villard-de-Lans 2015
SHE in grapheneKWANT Workshop, Villard-de-Lans 2015
Collaborators Theory & Computation:
Po-Hao Chang
Experiment:
Prof. John Q. Xiao
Dr. Farzad MahfouziProf. Ching-Ray Chang Prof. Son-Hsien ChenProf. Jian-Ping Wang
Juan Manuel Marmolejo-Tejada Dr. Chien-Liang Chen
SHE in grapheneKWANT Workshop, Villard-de-Lans 2015
The Family of Six Hall Effects
+ QHE +QAHE +QSHE
SHE in grapheneKWANT Workshop, Villard-de-Lans 2015
Experimental Detection of SHESc
ienc
e 30
6, 1
910
(200
4)
Optical detection in semiconductors Postmodern experiments on topological insulators
arX
iv:1
407.
7940
All-electrical detection in metals
PRL98
, 156
601
(200
7)
PRB
85, 0
5440
6 (2
012)
.
SHE in grapheneKWANT Workshop, Villard-de-Lans 2015
Experimental Detection of SHE in Graphene: Nonlocal Transport in Double Hall Bars
Nature Phys. 9, 284 (2013) and Nature Comm. 5, 4748 (2015)
Science 332, 328 (2013)
SHE in grapheneKWANT Workshop, Villard-de-Lans 2015
Theoretical Challenges for Description Nonlocal Transport in Graphene Hall Bars
Semiclassical transport theory does not work close to the Dirac
point
Phase-coherent quantum transport theory does not work at room temperature
PRB
79, 2
0140
4(R)
(200
9) PRB 85, 155414 (2012)
SHE in graphene
Crash Course on Spin-Orbit Coupling (SOC)
SO deflection force:x
yz
KWANT Workshop, Villard-de-Lans 2015
SHE in graphene
Rashba SOC in Inversion Asymmetric Heterostructures Hosting 2DEG
1D:
2D:
Spin configuration at the Ferm
i energy
KWANT Workshop, Villard-de-Lans 2015
SHE in graphene
Physical Mechanisms of SHE: Extrinsic vs. Intrinsic
KWANT Workshop, Villard-de-Lans 2015
skew-scattering
side-jump
SOC in bands
strong SOC with the nuclei of the
periodically arranged atoms is hidden behind the vacuum-like form
SHE in graphene
How to Calculate Spin Hall Angle: Conductivities via Kubo Formula
PRB 73, 113305 (2006)
PRL 96, 076604 (2006)
KWANT Workshop, Villard-de-Lans 2015
dc regime
SHE in graphene
How to Calculate Spin Hall Angle: Multiterminal Conductances via LB Approach
KWANT Workshop, Villard-de-Lans 2015
PRB 89, 195418 (2014)
SHE in graphene
SHE Conductance in 2DEG with Rashba SOC
-4.0 -3.8 -3.6 -3.4 -3.2 -3.0-0.1
0.0
0.1
0.2
0.3
0
20
40
60Gz s
H(e/4
π)
Number of Open Channels
Fermi Energy
100x100
PRB 72, 075361 (2005)
0 100 200 300 400 500 6000.0
0.1
0.2
LSO
Gz sH (
e/4π)
2DEG Size (a)KWANT Workshop, Villard-de-Lans 2015
SHE in graphene
All-Electrical Detection of Quantum Interference Controlled SHE in Double Aharonov-Casher Rings
1V 4V
3V
1cI 4
cI
sI 3 0cI =
RashbaE
( )RashbaB k k
5V 6V
2V
5 0cI = 6 0
cI =
RashbaE
( )RashbaB k k
sI2 0cI =
0 2 4 6 8 10
-0.10.00.1
0.450.500.55
-0.2
0.0
0.2
Rashba SO coupling QAR
V5 V6
NA=NB=100, NC=5
(V5-V
6)/V 1
V 5,6/V
1
Gz sH=
Is 2/V 1
(e/8π)
EF=-0.05, QBR=4.3
V
PRL 94, 106602 (2005)
KWANT Workshop, Villard-de-Lans 2015
SHE in graphene
Local Spin Hall Fluxes: Equilibrium vs. Nonequilibrium
x
y
z
PRB 73, 075303 (2006)
KWANT Workshop, Villard-de-Lans 2015
SHE in graphene
Fermi Sea vs. Fermi Surface Determined Local Spin Fluxes
PRB 73, 075303 (2006)
KWANT Workshop, Villard-de-Lans 2015
SHE in graphene
Quantum SHE in Graphene Decorated With Heavy In Adatoms
Nano Lett. 14, 3779 (2014)2-terminal
4-terminal
KWANT Workshop, Villard-de-Lans 2015
parameters fitted to DFT
SHE in graphene
SHE in Graphene Decorated with Clusters of Gold Atoms via KWANT
KWANT Workshop, Villard-de-Lans 2015
unpublished
parameters fitted to DFT
283701 atoms
PLA 373, 2091 (2009)
SHE in graphene
Improving KWANT Performance to Reach Experimental Cluster Sizes
KWANT Workshop, Villard-de-Lans 2015
SHE in graphene
Inelastic Effects in Quantum Transport via Keldysh Diagrammatics
KWANT Workshop, Villard-de-Lans 2015
PRB 90, 045115 (2014)
Diagrams for electron-boson (magnon below):
SHE in graphene
Dephasing via Momentum-Conserving and Momentum-Relaxing Simplified Self-Energies
PRB 75, 081301(R) (2007)
PRB 85, 155414 (2012)
momentum-conserving
momentum-relaxing
KWANT Workshop, Villard-de-Lans 2015
SHE in graphene
Conclusions in Pictures
KWANT Workshop, Villard-de-Lans 2015
Computational Modeling �of Spin Hall Effects �in Multiterminal Graphene DevicesCollaborators The Family of Six Hall EffectsExperimental Detection of SHEExperimental Detection of SHE in Graphene: �Nonlocal Transport in Double Hall BarsTheoretical Challenges for Description �Nonlocal Transport in Graphene Hall BarsCrash Course on Spin-Orbit Coupling (SOC)Rashba SOC in Inversion Asymmetric Heterostructures Hosting 2DEGPhysical Mechanisms of SHE: �Extrinsic vs. IntrinsicHow to Calculate Spin Hall Angle: Conductivities via Kubo FormulaHow to Calculate Spin Hall Angle: �Multiterminal Conductances via LB ApproachSHE Conductance in 2DEG with Rashba SOC��All-Electrical Detection of Quantum Interference Controlled SHE in Double Aharonov-Casher RingsLocal Spin Hall Fluxes: �Equilibrium vs. NonequilibriumFermi Sea vs. Fermi Surface Determined �Local Spin FluxesQuantum SHE in �Graphene Decorated With Heavy In Adatoms ��SHE in Graphene Decorated with �Clusters of Gold Atoms via KWANT�Improving KWANT Performance �to Reach Experimental Cluster Sizes�Inelastic Effects in Quantum Transport �via Keldysh Diagrammatics��Dephasing via Momentum-Conserving and Momentum-Relaxing Simplified Self-Energies ��Conclusions in Pictures ��
