TY - JOUR
T1 - Kubo formula for dc conductivity
T2 - Generalization to systems with spin-orbit coupling
AU - Ado, IA
AU - Titov, M
AU - Duine, RA
AU - Brataas, A
N1 - Publisher Copyright:
© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
PY - 2024/3/11
Y1 - 2024/3/11
N2 - We revise the Kubo formula for the electric dc conductivity in the presence of spin-orbit coupling (SOC). We discover that each velocity operator that enters this formula differs from ∂H/∂p, where H is the Hamiltonian and p is the canonical momentum. Moreover, we find an additional contribution to the Hall dc conductivity from noncommuting coordinates that is missing in the conventional Kubo-Středa formula. This contribution originates from the "electron-positron"matrix elements of the velocity and position operators. We argue that the widely used Rashba model does in fact provide a finite anomalous Hall dc conductivity in the metallic regime (in the noncrossing approximation) if SOC-corrections to the velocity and position operators are properly taken into account. While we focus on the response of the charge current to the electric field, linear response theories of other SOC-related effects should be modified similarly.
AB - We revise the Kubo formula for the electric dc conductivity in the presence of spin-orbit coupling (SOC). We discover that each velocity operator that enters this formula differs from ∂H/∂p, where H is the Hamiltonian and p is the canonical momentum. Moreover, we find an additional contribution to the Hall dc conductivity from noncommuting coordinates that is missing in the conventional Kubo-Středa formula. This contribution originates from the "electron-positron"matrix elements of the velocity and position operators. We argue that the widely used Rashba model does in fact provide a finite anomalous Hall dc conductivity in the metallic regime (in the noncrossing approximation) if SOC-corrections to the velocity and position operators are properly taken into account. While we focus on the response of the charge current to the electric field, linear response theories of other SOC-related effects should be modified similarly.
UR - http://www.scopus.com/inward/record.url?scp=85187543787&partnerID=8YFLogxK
U2 - 10.1103/PhysRevResearch.6.L012057
DO - 10.1103/PhysRevResearch.6.L012057
M3 - Article
SN - 2643-1564
VL - 6
JO - Physical Review Research
JF - Physical Review Research
IS - 1
M1 - L012057
ER -