{
  "id": "1607.03346",
  "version": "v1",
  "published": "2016-07-12T13:17:40.000Z",
  "updated": "2016-07-12T13:17:40.000Z",
  "title": "Numerical study of the quantum valley Hall effect",
  "authors": [
    "S. K. Wang",
    "Jun Wang",
    "Jun-Feng Liu"
  ],
  "comment": "5 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "Recently, the topological valley current flowing in the gapped graphene was observed in a four-terminal Hall-bar device by measuring the nonlocal resistivity signal [{{Gorbachev \\emph{et al.}, Science {\\bf{346}}, 448 (2014)}}]. In this work, we study numerically the quantum valley Hall effect in the same Hall bar geometry based on a lattice model and the multiple-terminal Landauer-B\\\"{u}ttiker formula. It is found that in the clean limit, the nonlocal resistivity $R_{NL}$ is quantized, $R_{NL}={h}/{e^2}$, as long as the Hall-bar width exceeds its length $w>l$ and in the opposite case $l>w$, it decreases exponentially, $R_{NL}{\\sim}e^{-l/w}$. The quantization of $R_{NL}$ originates from the quantized valley Hall conductivity of the gapped graphene, while its requirement of $w>l$ relates to the fact that the valley degree of freedom is defined in the reciprocal space and sensitive to the device profile. The quantization of $R_{NL}$ is also shown robust against both the rough edges of graphene and static disorders. Our findings may shed light on the fabrication of valley-based devices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-12T13:17:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum valley hall effect",
      "numerical study",
      "four-terminal hall-bar device",
      "nonlocal resistivity signal",
      "hall bar geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}