Maximally localized Wannier functions for entangled energy bands

TLDR

The paper introduces a method to generate well‑localized Wannier functions for entangled energy bands. The method selects an energy window, disentangles the target bands by minimizing subspace dispersion, and then applies the Marzari–Vanderbilt localization algorithm as a post‑processing step on standard electronic‑structure outputs. The approach yields Wannier functions for copper’s low‑lying bands centered at tetrahedral interstitial sites, indicating a possible alternative tight‑binding model. Cited reference: Marzari & Vanderbilt, Phys.

Abstract

We present a method for obtaining well-localized Wannier-like functions (WF's) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally localized WF's method [N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12 847 (1997)] that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally localized WF's for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WF's which are centered at the tetrahedral-interstitial sites, suggesting an alternative tight-binding parametrization.