Unit cell consistency of maximally localized Wannier functions

Abstract

Unit cell consistency (UCC) means that the physical properties or quantities of solids resulted from electronic structure calculations should not depend on the specific choice of the unit cell. The UCC of maximally localized wannier functions (MLWFs), a family of localized orbitals that are very useful in the theoretical characterization of solids, has scarcely been studied. In this work, we explore both analytically and numerically the UCC of MLWFs, and propose an explicit symmetry constraint on the unitary transformation matrices to ensure the UCC is rigorously preserved. Numerical calculations also demonstrate that without the symmetry constraint the MLWFs constructed in a supercell model may violate the UCC. This work thus provides useful guidance for the use of MLWFs in sophisticated solid-state systems and applications.