{
  "id": "2002.05590",
  "version": "v1",
  "published": "2020-02-13T16:07:44.000Z",
  "updated": "2020-02-13T16:07:44.000Z",
  "title": "Weak localization corrections to the thermal conductivity in $s$-wave superconductors",
  "authors": [
    "Lucia Gonzalez Rosado",
    "Fabian Hassler",
    "Gianluigi Catelani"
  ],
  "comment": "15 pages, 6 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.dis-nn",
    "cond-mat.supr-con"
  ],
  "abstract": "We study the thermal conductivity in disordered $s$-wave superconductors. Expanding on previous works for normal metals, we develop a formalism that tackles particle diffusion as well as the weak localization (WL) and weak anti-localization (WAL) effects. Using a Green's functions diagrammatic technique, which takes into account the superconducting nature of the system by working in Nambu space, we identify the system's low-energy modes, the diffuson and the Cooperon. The time scales that characterize the diffusive regime are energy dependent; this is in contrast with the the normal state, where the relevant time scale is the mean free time $\\tau_e$, independent of energy. The energy dependence introduces a novel energy scale $\\varepsilon_*$, which in disordered superconductors ($\\tau_e \\Delta\\ll 1$, with $\\Delta$ the gap) is given by $\\varepsilon_* = \\sqrt{\\Delta/\\tau_e}$. From the diffusive behavior of the low-energy modes, we obtain the WL correction to the thermal conductivity. We give explicitly expressions in two dimensions. We determine the regimes in which the correction depends explicitly on $\\varepsilon_*$ and propose an optimal regime to verify our results in an experiment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-13T16:07:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thermal conductivity",
      "weak localization corrections",
      "wave superconductors",
      "greens functions diagrammatic technique",
      "relevant time scale"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}