{
  "id": "2012.05308",
  "version": "v2",
  "published": "2020-12-09T20:40:04.000Z",
  "updated": "2021-01-29T14:29:37.000Z",
  "title": "Tutorial: Dirac Equation Perspective on Higher-Order Topological Insulators",
  "authors": [
    "Frank Schindler"
  ],
  "comment": "24 pages, 7 figures",
  "journal": "Journal of Applied Physics 128, 221102 (2020)",
  "doi": "10.1063/5.0035850",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "In this tutorial, we pedagogically review recent developments in the field of non-interacting fermionic phases of matter, focussing on the low energy description of higher-order topological insulators in terms of the Dirac equation. Our aim is to give a mostly self-contained treatment. After introducing the Dirac approximation of topological crystalline band structures, we use it to derive the anomalous end and corner states of first- and higher-order topological insulators in one and two spatial dimensions. In particular, we recast the classical derivation of domain wall bound states of the Su-Schrieffer-Heeger (SSH) chain in terms of crystalline symmetry. The edge of a two-dimensional higher-order topological insulators can then be viewed as a single crystalline symmetry-protected SSH chain, whose domain wall bound states become the corner states. We never explicitly solve for the full symmetric boundary of the two-dimensional system, but instead argue by adiabatic continuity. Our approach captures all salient features of higher-order topology while remaining analytically tractable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-01-29T14:29:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher-order topological insulators",
      "dirac equation perspective",
      "domain wall bound states",
      "corner states",
      "single crystalline symmetry-protected ssh chain"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Appl. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}