{
  "id": "2407.21098",
  "version": "v1",
  "published": "2024-07-30T18:00:01.000Z",
  "updated": "2024-07-30T18:00:01.000Z",
  "title": "Topological transition as a percolation of the Berry curvature",
  "authors": [
    "Han-Byul Kim",
    "Taewon Yuk",
    "Sang-Jin Sin"
  ],
  "comment": "9pages, 9 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We first study the importance of the sign of the Berry curvature in the Euler characteristic of the two-dimensional topological material with two bands. Then we report an observation of a character of the topological transition as a percolation of the sign of the Berry curvature. The Berry curvature F has peaks at the Dirac points, enabling us to divide the Brillouin zone into two regions depending on the sign of the F: one with the same sign with a peak and the other with the opposite sign. We observed that when the Chern number is non-zero, the oppositely signed regions are localized. In contrast, in the case of a trivial topology, the oppositely signed regions are delocalized dominantly. Therefore, the oppositely signed region will percolate under the topological phase transition from non-trivial to trivial. We checked this for several models including the Haldane model, the extended Haldane model, and the QWZ model. Our observation may serve as a novel feature of the topological phase transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-30T18:00:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "berry curvature",
      "topological transition",
      "oppositely signed region",
      "topological phase transition",
      "percolation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}