{
  "id": "2204.12438",
  "version": "v1",
  "published": "2022-04-26T16:56:56.000Z",
  "updated": "2022-04-26T16:56:56.000Z",
  "title": "Brillouin Klein Bottle From Artificial Gauge Fields",
  "authors": [
    "Z. Y. Chen",
    "Shengyuan A. Yang",
    "Y. X. Zhao"
  ],
  "journal": "Nat Commun 13, 2215 (2022)",
  "doi": "10.1038/s41467-022-29953-7",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "A Brillouin zone is the unit for the momentum space of a crystal. It is topologically a torus, and distinguishing whether a set of wave functions over the Brillouin torus can be smoothly deformed to another leads to the classification of various topological states of matter. Here, we show that under $\\mathbb{Z}_2$ gauge fields, i.e., hopping amplitudes with phases $\\pm 1$, the fundamental domain of momentum space can assume the topology of a Klein bottle. This drastic change of the Brillouin zone theory is due to the projective symmetry algebra enforced by the gauge field. Remarkably, the non-orientability of the Brillouin Klein bottle corresponds to the topological classification by a $\\mathbb{Z}_2$ invariant, in contrast to the Chern number valued in $\\mathbb{Z}$ for the usual Brillouin torus. The result is a novel Klein-bottle insulator featuring topological modes at two edges related by a nonlocal twist, radically distinct from all previous topological insulators. Our prediction can be readily achieved in various artificial crystals, and the discovery opens a new direction to explore topological physics by gauge-field-modified fundamental structures of physics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-26T16:56:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "artificial gauge fields",
      "insulator featuring topological modes",
      "klein-bottle insulator featuring topological",
      "brillouin klein bottle corresponds",
      "brillouin zone"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Nature"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}