Maximally-localized generalized Wannier functions for composite energy bands

TL;DR

This paper presents a practical method for computing maximally localized generalized Wannier functions directly from Bloch functions, useful for analyzing electronic structures in crystalline solids.

Contribution

It introduces a direct minimization approach for localized Wannier functions using unitary rotations, compatible with standard electronic-structure calculations.

Findings

Successfully applied to Si, GaAs, C2H4, and LiCl.

Provides total polarization and Wannier center locations.

Method is compatible with existing electronic-structure codes.

Abstract

We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread sum_n [ <r^2>_n - <r>_n^2 ] of the Wannier functions in real space, our method proceeds directly from the Bloch functions as represented on a mesh of k-points, and carries out the minimization in a space of unitary matrices U_mn^k describing the rotation among the Bloch bands at each k-point. The method is thus suitable for use in connection with conventional electronic-structure codes. The procedure also returns the total electric polarization as well as the location of each Wannier center. Sample results for Si, GaAs, molecular C2H4, and LiCl will be presented.