Wannier Function Perturbation Theory: Localized Representation and Interpolation of Wavefunction Perturbation

TL;DR

This paper introduces Wannier function perturbation theory, enabling efficient and accurate calculations of wavefunction perturbations and related properties in condensed matter systems, overcoming limitations of traditional Wannier approaches.

Contribution

The paper develops a new Wannier function perturbation theory that accurately handles wavefunction changes due to perturbations, extending the applicability of Wannier functions to infinite-band sums.

Findings

Calculated temperature-dependent optical absorption spectra of silicon.

Established a theory for shift spin conductivity without band-truncation errors.

Computed spin Hall conductivity of monolayer WTe2 accurately.

Abstract

Thanks to the nearsightedness principle, the low-energy electronic structure of solids can be represented by localized states such as the Wannier functions. Wannier functions are actively being applied to a wide range of phenomena in condensed matter systems. However, the Wannier-functionbased representation is limited to a small number of bands and thus cannot describe the change of wavefunctions due to various kinds of perturbations, which require sums over an infinite number of bands. Here, we introduce the concept of the Wannier function perturbation, which provides a localized representation of wavefunction perturbations. Wannier function perturbation theory allows efficient calculation of numerous quantities involving wavefunction perturbation, among which we provide three applications. First, we calculate the temperature-dependent indirect optical absorption spectra of silicon near the absorption edge nonadiabatically, i.e., differentiating phonon-absorption and phonon-emission processes, and without arbitrary temperature-dependent shifts in energy. Second, we establish a theory to calculate the shift spin conductivity without any band-truncation error. Unlike the shift charge conductivity, an exact calculation of the shift spin conductivity is not possible within the conventional Wannier function methods because it cannot be obtained from geometric quantities for low-energy bands. We apply the theory to monolayer WTe$_2$. Third, we calculate the spin Hall conductivity of the same material again without any band-truncation error. Wannier function perturbation theory is a versatile method that can be readily applied to calculate a wide range of quantities related to various kinds of perturbations.