{
  "id": "cond-mat/0307534",
  "version": "v3",
  "published": "2003-07-22T10:42:03.000Z",
  "updated": "2004-06-12T10:07:56.000Z",
  "title": "Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals",
  "authors": [
    "V. Tripathi",
    "M. Turlakov",
    "Y. L. Loh"
  ],
  "comment": "11 pages REVTeX, 3 Figures. Appendix added, replaced with published version",
  "journal": "J. Phys.: Condens. Matter 16, 4867 (2004)",
  "doi": "10.1088/0953-8984/16/28/008",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "We study the effects of Coulomb interaction and inter-grain quantum tunnelling in an array of metallic grains using the phase-functional approach for temperatures $T$ well below the charging energy $E_{c}$ of individual grains yet large compared to the level spacing in the grains. When the inter-grain tunnelling conductance $g\\gg1$, the conductivity $\\sigma$ in $d$ dimensions decreases logarithmically with temperature ($\\sigma/\\sigma_{0}\\sim1-\\frac{1}{2\\pi gd}\\ln(gE_{c}/T)$), while for $g\\to0$, the conductivity shows simple activated behaviour ($\\sigma \\sim \\exp(-E_c/T)$). We show, for bare tunnelling conductance $g \\gtrsim 1$, that the parameter $\\gamma \\equiv g(1-2/(g\\pi)\\ln(gE_{c}/T))$ determines the competition between charging and tunnelling effects. At low enough temperatures in the regime $1\\gtrsim \\gamma \\gg 1/\\sqrt{\\beta E_{c}}$, a charge is shared among a finite number $N=\\sqrt{(E_{c}/T)/\\ln(\\pi/2\\gamma z)}$ of grains, and we find a soft activation behaviour of the conductivity, $\\sigma\\sim z^{-1}\\exp(-2\\sqrt{(E_{c}/T)\\ln(\\pi/2\\gamma z)})$, where $z$ is the effective coordination number of a grain.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-06-12T10:07:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coulomb blockade",
      "quantum tunnelling",
      "low-conductivity phase",
      "granular metals",
      "soft activation behaviour"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}