{
  "id": "2309.06416",
  "version": "v1",
  "published": "2023-09-12T17:29:56.000Z",
  "updated": "2023-09-12T17:29:56.000Z",
  "title": "Kubo formula for dc conductivity in the presence of spin-orbit coupling: a revision",
  "authors": [
    "I. A. Ado",
    "M. Titov",
    "Rembert A. Duine",
    "Arne Brataas"
  ],
  "comment": "5 pages",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "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 $\\partial H/\\partial \\boldsymbol p$, where $H$ is the Hamiltonian and $\\boldsymbol p$ 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-Streda formula. We show that the widely used Rashba model does in fact provide a finite anomalous Hall dc conductivity in the metallic regime (in the noncrossing approximation). In addition to the Kubo formula, the Berry-phase theory of the anomalous Hall effect should also be revised for systems where the velocity operator differs from $\\partial H/\\partial \\boldsymbol p$. While we focus on the Hall response of the charge current to the electric field, linear response theories of other SOC-related effects should be modified similarly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-12T17:29:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kubo formula",
      "spin-orbit coupling",
      "finite anomalous hall dc conductivity",
      "linear response theories",
      "velocity operator differs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}