{
  "id": "2307.08754",
  "version": "v1",
  "published": "2023-07-17T18:00:47.000Z",
  "updated": "2023-07-17T18:00:47.000Z",
  "title": "Topological properties of a non-Hermitian quasi-one-dimensional chain with a flat band",
  "authors": [
    "C. Martínez-Strasser",
    "M. A. J. Herrera",
    "G. Palumbo",
    "F. K. Kunst",
    "D. Bercioux"
  ],
  "comment": "14 pages, 9 figures",
  "categories": [
    "cond-mat.mes-hall",
    "physics.optics",
    "quant-ph"
  ],
  "abstract": "We investigate the spectral properties of a non-Hermitian quasi-one-dimensional lattice in two possible dimerization configurations. Specifically, we focus on a non-Hermitian diamond chain that presents a zero-energy flat band. The flat band originates from wave interference and results in eigenstates with a finite contribution only on two sites of the unit cell. To achieve the non-Hermitian characteristics, we introduce non-reciprocal intrasite hopping terms in the chain. This leads to the accumulation of eigenstates on the boundary of the system, known as the non-Hermitian skin effect. Despite this accumulation of eigenstates, for one of the two possible configurations, we can characterize the presence of non-trivial edge states at zero energy by a real-space topological invariant known as the biorthogonal polarization. We show that this invariant, evaluated using the destructive interference method, characterizes the non-trivial phase of the non-Hermitian diamond chain. For the other possible non-Hermitian configuration, we find that there is a finite quantum metric associated with the flat band. Additionally, we observe the skin effect despite having the system a purely real or imaginary spectrum. For both configurations, we show that two non- Hermitian diamond chains can be mapped into two models of the Su-Schrieffer-Heeger chains, either non-Hermitian and Hermitian, in the presence of a flat band. This mapping allows us to draw valuable insights into the behavior and properties of these systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-17T18:00:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flat band",
      "non-hermitian quasi-one-dimensional chain",
      "topological properties",
      "non-hermitian diamond chain",
      "configuration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}