Automated mixing of maximally localized Wannier functions into target manifolds

TL;DR

This paper introduces a simple, robust algorithm to selectively mix and localize Wannier functions into specific energy-separated target manifolds, improving the construction of accurate tight-binding models for complex materials.

Contribution

It presents a novel method combining parallel transport and maximal localization to generate targeted Wannier functions from full sets, enhancing material modeling capabilities.

Findings

Successfully applied to silicon, MoS₂, SrVO₃, and 77 insulators.

Enables precise targeting of specific electronic manifolds.

Improves the accuracy of tight-binding models.

Abstract

Maximally localized Wannier functions (MLWFs) are widely used to construct first-principles tight-binding models that accurately reproduce the electronic structure of materials. Recently, robust and automated approaches to generate these MLWFs have emerged, leading to natural sets of atomic-like orbitals that describe both the occupied states and the lowest-lying unoccupied ones (when the latter can be meaningfully described by bonding/anti-bonding combinations of localized orbitals). For many applications, it is important to instead have MLWFs that describe only certain target manifolds separated in energy between them -- the occupied states, the empty states, or certain groups of bands. Here, we start from the full set of MLWFs describing simultaneously all the target manifolds, and then mix them using a combination of parallel transport and maximal localization to construct orthogonal sets of MLWFs that fully and only span the desired target submanifolds. The algorithm is simple and robust, and it is applied to some paradigmatic but non-trivial cases (the valence and conduction bands of silicon, the top valence band of MoS$_2$, the $3d$ and $t_{2g}$/$e_g$ bands of SrVO$_3$) and to a mid-throughput study of 77 insulators.