Z2 topological invariant and topological insulators

We briefly review some of the equivalent ways of determining the Z2 invariant in 2D insulators. We introduce a new expression for this invariant in band insulators using non-Abelian Berry's connection. The new expression can be used to determine the topological nature of a general band insulator in a way that does not require any gauge fixing. By this means, we have recalculated the Z2 topological index for 2D graphene systems, and have obtained results consistent with previous studies.