Automated construction of maximally localized Wannier functions for bands with nontrivial topology

TL;DR

This paper introduces an optimized projection functions method that automatically constructs maximally localized Wannier functions for bands with nontrivial topology, demonstrated on models and real materials.

Contribution

It presents a novel automated approach for constructing Wannier functions in topologically nontrivial systems, overcoming previous limitations.

Findings

Wannier functions contain large imaginary components in topologically nontrivial phases.

The method works on tight-binding models, 3D topological insulators, and first-principles calculations.

Wannier functions are more extended in topologically nontrivial phases.

Abstract

We show that an optimized projection functions method can automatically construct maximally localized Wannier functions even for bands with nontrivial topology. We demonstrate this method on a tight-binding model of a two-dimensional $\mathbb{Z}_2$ topological insulator, on a three-dimensional strong $\mathbb{Z}_2$ topological insulator, as well as on first-principles density functional theory calculated valence states of Bi$_2$Se$_3$. In all cases, the resulting Wannier functions contain large imaginary components and are more extended than those in the topologically trivial phase.