{
  "abstract": "We develop a complete Boltzmann transport theory for the in-plane ($σ_{xx}$) and out-of-plane ($σ_{zz}$) conductivities of an electronic superlattice consisting of a periodic stack of two-dimensional (2D) parabolic-band layers coupled along the superlattice axis by nearest-neighbor tunneling $t$, in the physically relevant regime $t\\ll E_F$ where the Fermi surface is an open, corrugated cylinder. Within the relaxation-time approximation with a power-law energy-dependent scattering time $τ(E)\\propto E^{p}$, we study the seven models $p=0,\\pm1,\\pm3/2,\\pm2$ as functions of the 2D electron density $n$ per layer and temperature $T$. For $p=-2$ (in plane) and $p\\le -1$ (out of plane), long-lived carriers at the miniband bottom can dominate transport at finite temperature. For $p=-2$, these carriers produce a pronounced peak in $σ_{zz}(T)$ at $T\\sim E_F$. We find that the temperature dependence of the anisotropic metallic dc conductivity can be highly counterintuitive depending on $t$, $T$, and $p$, with no generic increase or decrease with temperature. The Lorenz ratio is determined by the energy variance of the current-carrying electrons; the Wiedemann-Franz (WF) law is exact as $T\\to0$ for all models at fixed $t$, with anisotropic corrections at finite temperature. Band-edge carriers first enhance the interlayer Lorenz ratio up to several times its low-temperature value through thermal occupation of separated energy ranges within the same electron band and then suppress it at high temperature by energy filtering. Strong violations of the Wiedemann-Franz law can therefore arise from miniband structure and energy-dependent elastic scattering alone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41101",
  "author_total": 2,
  "authors": [
    {
      "name": "Sankar Das Sarma"
    },
    {
      "name": "Yuqing Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18e8137jqexkv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41101",
  "fulltext_url": null,
  "id": "18e8137jqexkv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41101",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41101",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18e8137jqexkv.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.41101",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41101"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Anisotropic Boltzmann transport in a tight-binding superlattice: Exact results for power-law energy-dependent scattering",
  "title_text": "Anisotropic Boltzmann transport in a tight-binding superlattice: Exact results for power-law energy-dependent scattering",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/18e8137jqexkv",
  "venue": "arXiv",
  "versions": []
}