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We show that an optimized projection functions method can automaticallyconstruct maximally localized Wannier functions even for bands with nontrivialtopology. We demonstrate this method on a tight-binding model of atwo-dimensional $\mathbb{Z}_2$ topological insulator, on a three-dimensionalstrong $\mathbb{Z}_2$ topological insulator, as well as on first-principlesdensity functional theory calculated valence states of Bi$_2$Se$_3$. In allcases, the resulting Wannier functions contain large imaginary components andare more extended than those in the topologically trivial phase.

Automated construction of maximally localized Wannier functions for bands with nontrivial topology