{
  "id": "1901.04467",
  "version": "v1",
  "published": "2019-01-14T18:59:51.000Z",
  "updated": "2019-01-14T18:59:51.000Z",
  "title": "Symmetry and Quantum Kinetics of the Non-linear Hall Effect",
  "authors": [
    "Snehasish Nandy",
    "Inti Sodemann"
  ],
  "comment": "5 pages, 1 figure",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We argue that the static non-linear Hall conductivity can always be represented as a vector in two-dimensions and as a pseudo-tensor in three-dimensions independent of its microscopic origin. In a single band model with a constant relaxation rate this vector or tensor is proportional to the Berry curvature dipole \\cite{Sodemann_2015}. Here, we develop a quantum Boltzmann formalism to second order in electric fields. We find that in addition to the Berry Curvature Dipole term, there exist additional disorder mediated corrections to the non-linear Hall tensor that have the same scaling in impurity scattering rate. These can be thought of as the non-linear counterparts to the side-jump and skew-scattering corrections to the Hall conductivity in the linear regime. We illustrate our formalism by computing the different contributions to the non-linear Hall conductivity of two-dimensional tilted Dirac fermions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-14T18:59:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-linear hall effect",
      "quantum kinetics",
      "berry curvature dipole term",
      "static non-linear hall conductivity",
      "additional disorder mediated corrections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}