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 ��