Bulk topological invariants in noninteracting point group symmetric insulators

Chen Fang, Matthew J. Gilbert, B. Andrei Bernevig

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223 Scopus citations

Abstract

We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that (i) the Chern number of a C n-invariant insulator can be determined, up to a multiple of n, by evaluating the eigenvalues of symmetry operators at high-symmetry points in the Brillouin zone; (ii) the Chern number of a C n-invariant insulator is also determined, up to a multiple of n, by the C n eigenvalue of the Slater determinant of a noninteracting many-body system; and (iii) the Chern number vanishes in insulators with dihedral point groups D n, and the quantized electric polarization is a topological invariant for these insulators. In three-dimensional insulators, we show that (i) only insulators with point groups C n, C nh, and S n PGS can have nonzero 3D quantum Hall coefficient and (ii) only insulators with improper rotation symmetries can have quantized magnetoelectric polarization P 3 in the term P 3E•B, the axion term in the electrodynamics of the insulator (medium).

Original languageEnglish (US)
Article number115112
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume86
Issue number11
DOIs
StatePublished - Sep 10 2012

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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