Construction of Wannier Functions in Disordered Systems

TL;DR

This paper introduces a new method for constructing Wannier functions in disordered systems directly from energy eigenstates, involving phase transformation and energy-based mixing, with demonstrated implementation in one-dimensional systems.

Contribution

The paper presents a novel, practical approach to constructing Wannier functions in disordered systems, extending the methodology to higher dimensions.

Findings

Effective construction of Wannier functions in 1D disordered systems

Method simplifies calculations by approximating operations with band matrices

Framework can be generalized to higher-dimensional systems

Abstract

We propose a general method of constructing Wannier functions in disordered systems directly out of energy eigenstates. This method consists of two successive operations: (i) a phase transformation setting the proper localization center; (ii) the mixing of adjacent states in energy to sufficiently minimize the spread of the Wannier functions. The latter operation can be well approximated by a band matrix, further facilitating the calculation. Detailed implementation of our method is illustrated with one dimensional systems; the generalization to higher dimensions is straightforward.