{
  "id": "1407.2131",
  "version": "v2",
  "published": "2014-07-08T15:16:28.000Z",
  "updated": "2015-02-02T17:23:29.000Z",
  "title": "Random-matrix theory of Majorana fermions and topological superconductors",
  "authors": [
    "C. W. J. Beenakker"
  ],
  "comment": "V1: 18 pages, 16 figures; pre-submission version, for feedback; V2: 33 pages, 31 figures; greatly expanded in response to feedback, thank you!",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.supr-con"
  ],
  "abstract": "I. Introduction (What is new in RMT, Superconducting quasiparticles, Experimental platforms) II. Topological superconductivity (Kitaev chain, Majorana operators, Majorana zero-modes, Phase transition beyond mean-field) III. Fundamental symmetries (Particle-hole symmetry, Majorana representation, Time-reversal and chiral symmetry) IV. Hamiltonian ensembles (The ten-fold way, Midgap spectral peak, Energy level repulsion) V. Scattering matrix ensembles (Fundamental symmetries, Chaotic scattering, Circular ensembles, Topological quantum numbers) VI. Electrical conduction (Majorana nanowire, Counting Majorana zero-modes, Conductance distribution, Weak antilocalization, Andreev resonances, Shot noise of Majorana edge modes) VII. Thermal conduction (Topological phase transitions, Super-universality, Heat transport by Majorana edge modes, Thermopower and time-delay matrix, Andreev billiard with chiral symmetry) VIII. Josephson junctions (Fermion parity switches, 4{\\pi}-periodic Josephson effect, Discrete vortices) IX. Conclusion",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-08T15:16:28.000Z",
      "abstract": "The theory of random matrices originated half a century ago as a universal description of the spectral statistics of atoms and nuclei, dependent only on the presence or absence of fundamental symmetries. Applications to quantum dots (artifical atoms) followed, stimulated by developments in the field of quantum chaos, as well as applications to Andreev billiards -- quantum dots with induced superconductivity. Superconductors with topologically protected subgap states, Majorana zero-modes and Majorana edge modes, provide for a new arena of applications of random-matrix theory. We review these recent developments, with an emphasis on electrical and thermal transport properties that can probe the Majoranas.",
      "comment": "18 pages, 16 figures; pre-submission version, for feedback; let me know if your favorite RMT application is missing",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-02T17:23:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74.45.+c",
      "03.65.Nk",
      "74.78.Na",
      "71.10.Pm"
    ],
    "keywords": [
      "random-matrix theory",
      "majorana fermions",
      "topological superconductors",
      "quantum dots",
      "majorana edge modes"
    ],
    "publication": {
      "doi": "10.1103/RevModPhys.87.1037",
      "journal": "Reviews of Modern Physics",
      "year": 2015,
      "month": "Jul",
      "volume": 87,
      "number": 3,
      "pages": 1037
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1305355,
      "adsabs": "2015RvMP...87.1037B"
    }
  }
}