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We introduce a new expression for the Z2 topological invariant of bandinsulators using non- Abelian Berry's connection. Our expression can identifythe topological nature of a general band insulator without any of the gaugefixing problems that plague the concrete implementation of previous invariants.The new expression can be derived from the "partner switching" of the Wannierfunction center during time reversal pumping and is thus equivalent to the Z2topological invariant proposed by Kane and Mele.

An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection