{
  "id": "2008.08231",
  "version": "v1",
  "published": "2020-08-19T02:52:47.000Z",
  "updated": "2020-08-19T02:52:47.000Z",
  "title": "Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices",
  "authors": [
    "Da-Shuai Ma",
    "Yuanfeng Xu",
    "Christie S. Chiu",
    "Nicolas Regnault",
    "Andrew A. Houck",
    "Zhida Song",
    "B. Andrei Bernevig"
  ],
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to construct two-dimensional (2D) topological quasi-flat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands. The flat band connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasi-flat and gapped from the dispersive bands. By studying a series of specific line graphs and split graphs of bipartite lattices, we find that (i) if the flat band (without SOC) has inversion or $C_2$ symmetry and is non-degenerate, then the resulting quasi-flat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists an SOC potential such that the resulting quasi-flat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasi-flat bands in 2D crystalline materials and meta-materials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-19T02:52:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "split graph",
      "bipartite lattice",
      "spin-orbit-induced topological flat bands",
      "line graph",
      "resulting quasi-flat band"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}