{
  "id": "1902.11101",
  "version": "v1",
  "published": "2019-01-17T05:42:25.000Z",
  "updated": "2019-01-17T05:42:25.000Z",
  "title": "Scaling Theory of Quantum Ratchet",
  "authors": [
    "Keita Hamamoto",
    "Takamori Park",
    "Hiroaki Ishizuka",
    "Naoto Nagaosa"
  ],
  "comment": "29 pages, 5 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "The asymmetric responses of the system between the external force of right and left directions are called \"nonreciprocal\". There are many examples of nonreciprocal responses such as the rectification by p-n junction. However, the quantum mechanical wave does not distinguish between the right and left directions as long as the time-reversal symmetry is intact, and it is a highly nontrivial issue how the nonreciprocal nature originates in quantum systems. Here we demonstrate by the quantum ratchet model, i.e., a quantum particle in an asymmetric periodic potential, that the dissipation characterized by a dimensionless coupling constant $\\alpha$ plays an essential role for nonlinear nonreciprocal response. The temperature ($T$) dependence of the second order nonlinear mobility $\\mu_2$ is found to be $\\mu_2 \\sim T^{6/\\alpha -4 }$ for $\\alpha<1$, and $\\mu_2 \\sim T^{2(\\alpha -1)}$ for $\\alpha>1$, respectively, where $\\alpha_c=1$ is the critical point of the localization-delocalization transition, i.e., Schmid transition. On the other hand, $\\mu_2$ shows the behavior $\\mu_2 \\sim T^{-11/4}$ in the high temperature limit. Therefore, $\\mu_2$ shows the nonmonotonous temperature dependence corresponding to the classical-quantum crossover. The generic scaling form of the velocity $v$ as a function of the external field $F$ and temperature $T$ is also discussed. These findings are relevant to the heavy atoms in metals, resistive superconductors with vortices and Josephson junction system, and will pave a way to control the nonreciprocal responses.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-17T05:42:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scaling theory",
      "left directions",
      "second order nonlinear mobility",
      "quantum ratchet model",
      "asymmetric periodic potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}