{
  "id": "1005.4883",
  "version": "v2",
  "published": "2010-05-26T17:17:16.000Z",
  "updated": "2010-12-28T22:59:42.000Z",
  "title": "Disordered Topological Insulators via $C^*$-Algebras",
  "authors": [
    "T. A. Loring",
    "M. B. Hastings"
  ],
  "comment": "Added detail regarding the mapping of almost commuting unitary matrices to almost commuting Hermitian matrices that form an approximate representation of the sphere. 6 pages, 6 figures",
  "journal": "Europhysics Letters 92, 67004 (2010)",
  "categories": [
    "cond-mat.mes-hall",
    "math-ph",
    "math.MP",
    "math.OA",
    "quant-ph"
  ],
  "abstract": "The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z_2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z_2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-28T22:59:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "disordered topological insulators",
      "time-reversal symmetry",
      "quantum hall effect",
      "quantum hall case",
      "numerical procedure"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1209/0295-5075/92/67004",
      "journal": "EPL (Europhysics Letters)",
      "year": 2010,
      "month": "Dec",
      "volume": 92,
      "number": 6,
      "pages": 67004
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010EL.....9267004L"
    }
  }
}