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 -