Equivalent expression of Z 2 topological invariant for band insulators using the non-Abelian Berry connection

We introduce an expression for the ${\mathbb{Z}}_{2}$ 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 ${Z}_{2}$ topological invariant proposed by Kane and Mele. Using our expression, we have recalculated the ${Z}_{2}$ topological index for several topological insulator material systems and obtained consistent results with the previous studies.

• NS
  National Science Foundation