Equivalent expression of Z2 topological invariant for band insulators using the non-Abelian Berry connection

Rui Yu, Xiao Liang Qi, Andrei Bernevig, Zhong Fang, Xi Dai

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432 Scopus citations


We introduce an expression for the Z2 topological invariant of band insulators using the non-Abelian Berry connection. Our expression can identify the topological nature of a general band insulator without any of the gauge-fixing problems that plague the concrete implementation of previous invariants. This expression can be derived from the "partner switching" of the Wannier function center during time-reversal pumping and is thus equivalent to the Z2 topological invariant proposed by Kane and Mele. Using our expression, we have recalculated the Z2 topological index for several topological insulator material systems and obtained consistent results with the previous studies.

Original languageEnglish (US)
Article number075119
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number7
StatePublished - Aug 8 2011

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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