{
  "id": "2305.16113",
  "version": "v1",
  "published": "2023-05-25T14:47:56.000Z",
  "updated": "2023-05-25T14:47:56.000Z",
  "title": "Euler--Chern Correspondence via Topological Superconductivity",
  "authors": [
    "Fan Yang",
    "Xingyu Li",
    "Chengshu Li"
  ],
  "comment": "4 pages, 3 figure",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.supr-con"
  ],
  "abstract": "The Fermi sea topology is characterized by the Euler characteristics $\\chi_F$. In this Letter, we examine how $\\chi_F$ of the metallic state is inhereted by the topological invariant of the superconducting state. We establish a correspondence between the Euler characteristic and the Chern number $C$ of $p$-wave topological superconductors without time-reversal symmetry in two dimensions. By rewriting the pairing potential $\\Delta_{\\bf k}=\\Delta_1-i\\Delta_2$ as a vector field ${\\bf u}=(\\Delta_1,\\Delta_2)$, we found that $\\chi_F=C$ when ${\\bf u}$ and fermion velocity ${\\bf v}$ can be smoothly deformed to be parallel or antiparallel on each Fermi surface. We also discuss a similar correspondence between Euler characteristic and 3D winding number of time-reversal-invariant $p$-wave topological superconductors in three dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-25T14:47:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological superconductivity",
      "euler-chern correspondence",
      "euler characteristic",
      "wave topological superconductors",
      "fermi sea topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}