{
  "id": "1808.07469",
  "version": "v1",
  "published": "2018-08-21T19:34:11.000Z",
  "updated": "2018-08-21T19:34:11.000Z",
  "title": "Non-Abelian Statistics in Momentum Space",
  "authors": [
    "QuanSheng Wu",
    "Alexey A. Soluyanov",
    "Tomáš Bzdušek"
  ],
  "comment": "Main text: 5 pages with 4 figures. Supplemental Material attached as ancillary file: 26 pages with 17 figures. Submitted on 27 July 2018",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "We introduce non-Abelian statistics in momentum space of crystalline solids with weak spin-orbit coupling. We show that nodal lines and nodal chains of $\\mathcal{P}\\mathcal{T}$-symmetric metals host non-Abelian quaternion charges, similar to vortices of biaxial nematics. Starting from two-band considerations, we develop a complete many-band description of nodes in the presence of $\\mathcal{P}\\mathcal{T}$ and mirror symmetries, which explains possible topological phase transitions between different arrangements of nodal lines. Our arguments are illustrated with ${\\boldsymbol{k}}\\cdot{\\boldsymbol{p}}$ models as well as with real materials. We find and explain novel topological invariants that correspond to the quaternion charges. We show that these invariants characterize 1D topological insulator phases not described before. This work introduces a fundamentally novel approach to nodal topological excitations in metals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-21T19:34:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "momentum space",
      "non-abelian statistics",
      "1d topological insulator phases",
      "characterize 1d topological insulator",
      "metals host non-abelian quaternion charges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}