{
  "id": "1510.03834",
  "version": "v1",
  "published": "2015-10-13T19:37:07.000Z",
  "updated": "2015-10-13T19:37:07.000Z",
  "title": "Josephson current between topological and conventional superconductors",
  "authors": [
    "P. A. Ioselevich",
    "P. M. Ostrovsky",
    "M. V. Feigelman"
  ],
  "comment": "7 pages, 2 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We study the stationary Josephson current in a junction between a topological and an ordinary (topologically trivial) superconductor. Such an S-TS junction hosts a Majorana zero mode that significantly influences the current-phase relation. The presence of the Majorana state is intimately related with the breaking of the time-reversal symmetry in the system. We derive a general expression for the supercurrent for a class of short topological junctions in terms of the normal state scattering matrix. The result is strongly asymmetric with respect to the superconducting gaps in the ordinary ($\\Delta_0$) and topological ($\\Delta_{\\mathrm{top}}$) leads. We apply the general result to a simple model of a nanowire setup with strong spin-orbit coupling in an external magnetic field and proximity-induced superconductivity. The system shows parametrically strong suppression of the critical current $I_c \\propto \\Delta_{\\mathrm{top}}/R_N^2$ in the tunneling limit ($R_N$ is the normal state resistance). This is in strong contrast with the Ambegaokar-Baratoff relation applicable to junctions with preserved time-reversal symmetry. We also consider the case of a generic junction with a random scattering matrix and obtain a more conventional scaling law $I_c \\propto \\Delta_{\\mathrm{top}}/R_N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-13T19:37:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conventional superconductors",
      "topological",
      "time-reversal symmetry",
      "normal state resistance",
      "normal state scattering matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}