Kubo formula for dc conductivity: Generalization to systems with spin-orbit coupling
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 t...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-03-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.L012057 |
| _version_ | 1797210241973092352 |
|---|---|
| author | I. A. Ado M. Titov Rembert A. Duine Arne Brataas |
| author_facet | I. A. Ado M. Titov Rembert A. Duine Arne Brataas |
| author_sort | I. A. Ado |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:07:28Z |
| format | Article |
| id | doaj.art-82df2d21aff342bcbdb13d50803811da |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:07:28Z |
| publishDate | 2024-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-82df2d21aff342bcbdb13d50803811da2024-04-12T17:40:17ZengAmerican Physical SocietyPhysical Review Research2643-15642024-03-0161L01205710.1103/PhysRevResearch.6.L012057Kubo formula for dc conductivity: Generalization to systems with spin-orbit couplingI. A. AdoM. TitovRembert A. DuineArne BrataasWe 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.http://doi.org/10.1103/PhysRevResearch.6.L012057 |
| spellingShingle | I. A. Ado M. Titov Rembert A. Duine Arne Brataas Kubo formula for dc conductivity: Generalization to systems with spin-orbit coupling Physical Review Research |
| title | Kubo formula for dc conductivity: Generalization to systems with spin-orbit coupling |
| title_full | Kubo formula for dc conductivity: Generalization to systems with spin-orbit coupling |
| title_fullStr | Kubo formula for dc conductivity: Generalization to systems with spin-orbit coupling |
| title_full_unstemmed | Kubo formula for dc conductivity: Generalization to systems with spin-orbit coupling |
| title_short | Kubo formula for dc conductivity: Generalization to systems with spin-orbit coupling |
| title_sort | kubo formula for dc conductivity generalization to systems with spin orbit coupling |
| url | http://doi.org/10.1103/PhysRevResearch.6.L012057 |
| work_keys_str_mv | AT iaado kuboformulafordcconductivitygeneralizationtosystemswithspinorbitcoupling AT mtitov kuboformulafordcconductivitygeneralizationtosystemswithspinorbitcoupling AT rembertaduine kuboformulafordcconductivitygeneralizationtosystemswithspinorbitcoupling AT arnebrataas kuboformulafordcconductivitygeneralizationtosystemswithspinorbitcoupling |