{
  "id": "2007.13499",
  "version": "v1",
  "published": "2020-07-27T12:44:58.000Z",
  "updated": "2020-07-27T12:44:58.000Z",
  "title": "Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System",
  "authors": [
    "Yang Cao",
    "Yang Li",
    "Xiaosen Yang"
  ],
  "comment": "8 pages, 4 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper, we construct one-dimensional non-Hermitian Su-Schrieffer-Heeger model with periodic driving that exhibits non-Hermitian skin effects: all the eigenstates are localized at the boundary of the systems, whether the bulk states or the zero and the $\\pi$ modes. To capture the topological properties, the non-Bloch winding numbers are defined by the non-Bloch periodized evolution operators based on the generalized Brillouin zone. Furthermore, the non-Hermitian bulk-boundary correspondence is established: the non-Bloch winding numbers ($W_{0,\\pi}$) characterize the edge states with quasienergies $\\epsilon=0, \\pi$. In our non-Hermitian system, a novel phenomenon can emerge that the robust edge states can appear even when the Floquet bands are topological trivial with zero non-Bloch Chern number. We also show that the relation between the non-Bloch winding numbers and the Chern number of the Floquet bands: $C= W_{0}-W_{\\pi}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-27T12:44:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-hermitian bulk-boundary correspondence",
      "periodically driven system",
      "non-bloch winding numbers",
      "edge states",
      "construct one-dimensional non-hermitian su-schrieffer-heeger model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}