Wilson-loop characterization of inversion-symmetric topological insulators

A. Alexandradinata, Xi Dai, B. Andrei Bernevig

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208 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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