{
  "id": "2004.05504",
  "version": "v1",
  "published": "2020-04-11T22:42:51.000Z",
  "updated": "2020-04-11T22:42:51.000Z",
  "title": "Topological insulators and higher-order topological insulators from gauge-invariant 1D lines",
  "authors": [
    "Heqiu Li",
    "Kai Sun"
  ],
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a two-fold-rotational symmetry or a mirror symmetry, a gauge-invariant quantity can be defined for arbitrary 1D lines in the Brillouin zone. Such 1D quantities provide a new pathway to compute the $Z_2$ index of topological insulators. In contrast to the generic setup, where the $Z_2$ index generally involves 2D planes in the Brillouin zone with a globally-defined smooth gauge, this 1D approach only involves some 1D lines in the Brillouin zone without requiring a global gauge. Such a simplified approach can be used in any time-reversal invariant insulators with a two-fold crystalline symmetry, which can be found in 30 of the 32 point groups. In addition, this 1D quantity can be further generalized to higher-order topological insulators to compute the magnetoelectric polarization $P_3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-11T22:42:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher-order topological insulators",
      "gauge-invariant 1d lines",
      "brillouin zone",
      "1d quantity",
      "two-fold crystalline symmetry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}