Accurate polarization within a unified Wannier function formalism

TL;DR

This paper introduces a simplified, invariant formalism for calculating maximally localized Wannier functions, improving convergence and enabling efficient, accurate polarization calculations in crystalline solids.

Contribution

A new, simple formalism for Wannier functions that is invariant under Brillouin zone folding and enhances convergence for polarization computations.

Findings

Formalism is exactly invariant under Brillouin zone folding.

Convergence of Wannier functions is significantly improved with a refinement step.

Method enables efficient and accurate polarization calculations.

Abstract

We present an alternative formalism for calculating the maximally localized Wannier functions in crystalline solids, obtaining an expression which is extremely simple and general. In particular, our scheme is exactly invariant under Brillouin zone folding, and therefore it extends trivially to the Gamma-point case. We study the convergence properties of the Wannier functions, their quadratic spread and centers as obtained by our simplified technique. We show how this convergence can be drastically improved by a simple and inexpensive ``refinement'' step, which allows for very efficient and accurate calculations of the polarization in zero external field.