Compact Wannier Functions in One Dimension

Abstract

Wannier functions have widespread utility in condensed matter physics and beyond. Topological physics on the other hand has largely involved the related notion of compactly supported Wanniertype functions which arise naturally in flat bands. In this work, we establish a connection between these two notions, by finding the necessary and sufficient conditions under which compact Wannier functions exist in one dimension. We present an exhaustive construction of models with compact Wannier functions and show that the Wannier functions are unique and in general, distinct from the corresponding maximally localized Wannier functions.