Nonlocal resistance in graphene
Origins of Nonlocal Resistance in Multiterminal Graphene: Spin Hall and Valley
Hall vs. Other Competing Mechanisms
Branislav K. NikolićDepartment of Physics & Astronomy, University of Delaware, Newark, DE 19716, U.S.A.
1638–1655
RPGR 2017, Singapore
https://wiki.physics.udel.edu/qttg
Nonlocal resistance in grapheneRPGR 2017, Singapore
Collaborators
Dr. Jose H. García
Juan M. Marmolejo-Tejada Dr. Chien-Liang Chen
Dr. Alessandro Cresti Prof. Stephan Roche Prof. Ching-Ray Chang
Dr. Po-Hao Chang Dr. Xian-Lei Sheng
Dr. Xavier Waintal
Nonlocal resistance in grapheneRPGR 2017, Singapore
“Ancient” History: Nonlocal Resistance in Quantum Hall Systems
Landauer-Büttiker formula for quantum transport gains traction
Nonlocal resistance in grapheneRPGR 2017, Singapore
Nonlocal Resistance in Graphene with Adatoms due to Direct and Inverse Spin Hall Effect (SHE)Nature Phys. 9, 284 (2013) and Nat. Commun. 5, 4748 (2015)
Nature 511, 449 (2014)
PRB 79, 035304 (2009)
CONTROVERSYPRB 91, 165412 (2015)PRB 92, 161411 (2015)
LB quantum transport theory
removed in favor of semiclassical theory
connecting RNL to bulk conductivities based on PRB 79, 035304 (2009)
Nonlocal resistance in grapheneRPGR 2017, Singapore
Nonlocal Resistance in Graphene due to (?) Direct and Inverse Valley Hall Effect
Science 346, 448 (2014)
CONTROVERSYNat. Commun. 8, 14552 (2017)
PRL 114, 256601 (2015)
arXiv:1706.09361
Nonlocal resistance in graphene
Physical Mechanisms of SHE: Extrinsic vs. Intrinsic
RPGR 2017, Singapore
strong SOC with the nuclei of the
periodically arranged atoms is hidden behind the vacuum-like form
skew-scattering (SS)
side-jump (SJ)
SOC in band structure
PRB 72, 075335 (2005)
Nonlocal resistance in graphene
Landauer-Büttiker (LB) Quantum Transport Theory for Charge and Spin Currents in Mulititerminal Circuits
RPGR 2017, Singapore
PRL 117, 176602 (2016)
PRL 57, 1761 (1986)
PRB 82, 081414(R) (2010)
LB theory puts limits on the usage of Boltzmann equation for graphene
PRB 72, 075361 (2005); PRB 89, 195418 (2014)
https://kwant-project.org
Nonlocal resistance in graphene
Kubo vs. LB Computed SH Angle of Graphene with SOC due to Adatoms
RPGR 2017, Singapore
Real-space Kubo formula via
kernel polynomial method makes possible
numerically exact calculations on
~500 nm x 500 nm square containing ≤ 10 million atoms
PRL 117, 176602 (2016) Paper-pencil calculations: Which diagrams to consider?
EPL 111, 37004 (2015)
PRB 94, 201402(R) (2016)
SS
SJ
Q
Nonlocal resistance in graphene
LB Theory of Nonlocal Resistance in Multiterminal Graphene with Adatoms
PRL 117, 176602 (2016)
RPGR 2017, Singapore
Nonlocal resistance in graphene
How to Get Nonlocal Resistance Due to Purely Direct and Inverse SHE in Graphene with Adatoms
RPGR 2017, Singapore
PRL 117, 176602 (2016)
Nonlocal resistance in grapheneRPGR 2017, Singapore
First-Principles Bandstructure and Quantum Transport in Zigzag Nanowires of G/hBN vs. G
arXiv:1706.09361
Nonlocal resistance in grapheneRPGR 2017, Singapore
Ab Initio Tight-Binding Hamiltonian for Graphene-on-hBN Nanowires with Zigzag Edges
Edge
cur
rets
for
TBH
arXiv:1706.09361
Nonlocal resistance in grapheneRPGR 2017, Singapore
Landauer-Büttiker Theory of Nonlocal Resistance and ρxx in Multiterminal Graphene/hBN
arXiv:1706.09361
RNL peak is seen in aligned G/hBNzigzag wires, never in nonaligned ones despite edge states being present
ρxx peak value is metallic-like ρxx peak is wider than RNL peak RNL peak centroid is slightly shifted to
the left of the DP
COMPARE TO EXPERIMENT
Nonlocal resistance in grapheneRPGR 2017, Singapore
Kubo Theory of Valley Hall Conductivity in Graphene/hBN
nonlocal resistance obtained indirectly from σvxy +
semiclassical diffusion
arXiv:1706.09361real-space numerically exact Kubo formula
Science 346, 448 (2014); PNAS 122, 10879 (2015)
PRB
94, 1
2140
8(R)
(201
6)
PRL 99, 236809 (2007)
JPSJ
84,
114
705
(201
5)PRL 114, 256601 (2015)
Nonlocal resistance in graphene
Conclusions in Pictures
RPGR 2017, Singapore
SHE
VHE(?)
Origins of Nonlocal Resistance in Multiterminal Graphene: Spin Hall and Valley Hall vs. Other Competing MechanismsCollaborators “Ancient” History: Nonlocal Resistance �in Quantum Hall SystemsNonlocal Resistance in Graphene with Adatoms due to Direct and Inverse Spin Hall Effect (SHE)Nonlocal Resistance in Graphene due to (?) �Direct and Inverse Valley Hall Effect Physical Mechanisms of SHE: �Extrinsic vs. IntrinsicLandauer-Büttiker (LB) Quantum Transport Theory for Charge and Spin Currents in Mulititerminal Circuits Kubo vs. LB Computed SH Angle of �Graphene with SOC due to Adatoms��LB Theory of Nonlocal Resistance in �Multiterminal Graphene with Adatoms��How to Get Nonlocal Resistance Due to Purely Direct and Inverse SHE in Graphene with Adatoms ��First-Principles Bandstructure and Quantum Transport in Zigzag Nanowires of G/hBN vs. G Ab Initio Tight-Binding Hamiltonian for Graphene-on-hBN Nanowires with Zigzag EdgesLandauer-Büttiker Theory of Nonlocal Resistance and ρxx in Multiterminal Graphene/hBNKubo Theory of �Valley Hall Conductivity in Graphene/hBNConclusions in Pictures ��
