QLunch: Construction of Wannier functions for insulators and metals

Abstract: I will review a research effort to designn umerical methods to automatically construct Wannier functions, a localized representation of spectral subspaces of periodic Schrödinger operators. In the classical case of insulators, this is challenging because of possible topological effects; we present a numerical method based on homotopies of unitary matrices that manages to build Wannier functions even in challenging cases such as the Kane-Mele model. In the case of metals, this is complicated by eigenvalue crossings; we show that it is nevertheless possible to construct Wannier functions representing the bands of interest.