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

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.