{
  "id": "1810.00426",
  "version": "v1",
  "published": "2018-09-30T17:19:56.000Z",
  "updated": "2018-09-30T17:19:56.000Z",
  "title": "Non-Born effects in scattering of electrons in a clean conducting tube",
  "authors": [
    "A. S. Ioselevich",
    "N. S. Peshcherenko"
  ],
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "Quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states $\\nu_F$ and the resistivity $\\rho$, occurring when the Fermi level $E$ crosses a bottom $E_N$ of some subband of transverse quantization. We demonstrate that the character of smearing of the singularities crucially depends on the concentration of impurities. There is a crossover concentration $n_c\\propto |\\lambda|$, $\\lambda\\ll 1$ being the dimensionless amplitude of scattering. For $n\\gg n_c$ the singularities are simply rounded at $\\varepsilon\\equiv E-E_N\\sim \\tau^{-1}$ -- the Born scattering rate. For $n\\ll n_c$ the non-Born effects in scattering become essential despite $\\lambda\\ll 1$. The peak of the resistivity is asymmetrically split in a Fano-resonance manner (however with a more complex structure). Namely, for $\\varepsilon>0$ there is a broad maximum at $\\varepsilon\\propto \\lambda^2$ while for $\\varepsilon<0$ there is a deep minimum at $|\\varepsilon|\\propto n^2\\ll \\lambda^2$. The behaviour of $\\rho$ below the minimum depends on the sign of $\\lambda$. In case of repulsion $\\rho$ monotonically grows with $|\\varepsilon|$ and saturates for $|\\varepsilon|\\gg \\lambda^2$. In case of attraction $\\rho$ has sharp maximum at $|\\varepsilon|\\propto \\lambda^2$. The latter feature is due to resonant scattering by quasistationary bound states that inevitably arise just below the bottom of each subband for any attracting impurity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-30T17:19:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "clean conducting tube",
      "non-born effects",
      "scattering",
      "systems demonstrate van hove singularities",
      "quasi-one-dimensional systems demonstrate van hove"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}