Wilson-loop characterization of inversion-symmetric topological insulators

A. Alexandradinata, Xi Dai, B. Andrei Bernevig

Research output: Contribution to journalArticle

78 Scopus citations


The ground state of translationally invariant insulators comprises bands which can assume topologically distinct structures. There are few known examples where this distinction is enforced by a point-group symmetry alone. In this paper we show that 1D and 2D insulators with the simplest point-group symmetry, inversion, have a Z≥ classification. In 2D, we identify a relative winding number that is solely protected by inversion symmetry. By analysis of Berry phases, we show that this invariant has similarities with the first Chern class (of time-reversal breaking insulators), but is more closely analogous to the Z2 invariant (of time-reversal invariant insulators). Implications of our work are discussed in holonomy, the geometric-phase theory of polarization, the theory of maximally localized Wannier functions, and in the entanglement spectrum.

Original languageEnglish (US)
Article number155114
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number15
StatePublished - Apr 11 2014

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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