{
  "abstract": "The orbital Hall effect (OHE) underpins the emerging field of orbitronics. A complete quantum-mechanical evaluation of the usual orbital-current operator must retain all matrix elements of the position operator, including its band-diagonal differential part; intrinsic calculations based on this full evaluation can differ by orders of magnitude from the conventional truncation. A relaxation-time estimate of disorder effects on the full current has been reported, but a microscopic treatment of extrinsic scattering has remained unavailable because the position operator requires wavevector-off-diagonal density-matrix elements. Here we develop such a theory by solving the quantum kinetic equation for the wavevector-off-diagonal density matrix, including band-structure, field-corrected side-jump, and skew-scattering terms within the non-crossing approximation. We apply the theory to a massive Dirac cone and to the same model with a particle-hole-symmetry-breaking quadratic term. Disorder-generated contributions of order $τ^0$ are generically comparable to the intrinsic current in the metallic regime and cannot be separated from it by simple disorder-strength scaling. For the bare massive Dirac cone the surviving non-crossing extrinsic correction cancels the conventional intrinsic value and leaves a total current exactly twice the quantum correction, whereas particle-hole asymmetry activates conventional skew scattering for disorder with a non-zero third moment, which dominates in sufficiently clean samples. The wavevector-off-diagonal construction is independent of the two-band model and provides a general route to disorder corrections for position-dependent observables in multiband solids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28628",
  "author_total": 2,
  "authors": [
    {
      "name": "James H Cullen"
    },
    {
      "name": "Dimitrie Culcer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7z1tzfdgwxx35.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28628",
  "fulltext_url": null,
  "id": "7z1tzfdgwxx35",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28628",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7214296006",
  "pdf_url": "https://arxiv.org/pdf/2609.28628",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7z1tzfdgwxx35.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.28628",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28628"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Theory of extrinsic contributions to the full orbital current",
  "title_text": "Theory of extrinsic contributions to the full orbital current",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/7z1tzfdgwxx35",
  "venue": "arXiv",
  "versions": []
}