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

We introduce an expression for the 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.