{
  "id": "2304.10699",
  "version": "v1",
  "published": "2023-04-21T02:01:02.000Z",
  "updated": "2023-04-21T02:01:02.000Z",
  "title": "Confined states and topological phases in two-dimensional quasicrystalline $π$-flux model",
  "authors": [
    "Rasoul Ghadimi",
    "Masahiro Hori",
    "Takanori Sugimoto",
    "Takami Tohyama"
  ],
  "comment": "5+20 pages, 4+19 figures, 1+11 tables",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.other",
    "cond-mat.quant-gas"
  ],
  "abstract": "Motivated by topological equivalence between an extended Haldane model and a chiral-$\\pi$-flux model on a square lattice, we apply $\\pi$-flux models to two-dimensional bipartite quasicrystals with rhombus tiles in order to investigate topological properties in aperiodic systems. Topologically trivial $\\pi$-flux models in the Ammann-Beenker tiling lead to massively degenerate confined states whose energies and fractions differ from the zero-flux model. This is different from the $\\pi$-flux models in the Penrose tiling, where confined states only appear at the center of the bands as is the case of a zero-flux model. Additionally, Dirac cones appear in a certain $\\pi$-flux model of the Ammann-Beenker approximant, which remains even if the size of the approximant increases. Nontrivial topological states with nonzero Bott index are found when staggered tile-dependent hoppings are introduced in the $\\pi$-flux models. This finding suggests a new direction in realizing nontrivial topological states without a uniform magnetic field in aperiodic systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-21T02:01:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "confined states",
      "two-dimensional quasicrystalline",
      "topological phases",
      "nontrivial topological states",
      "zero-flux model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}