Spectral and Fermi surface properties from Wannier interpolation

TL;DR

This paper introduces an efficient first-principles method using Wannier functions for calculating Fermi surface and spectral properties, enabling accurate and low-cost k-space integrals for solids.

Contribution

It develops a Wannier-based interpolation technique that improves the accuracy and efficiency of computing electronic properties from first-principles calculations.

Findings

Accurate calculation of Fermi surface averages and spectral properties.

Efficient evaluation of transport and optical coefficients.

Successful application to cubic metals and iron.

Abstract

We present an efficient first-principles approach for calculating Fermi surface averages and spectral properties of solids, and use it to compute the low-field Hall coefficient of several cubic metals and the magnetic circular dichroism of iron. The first step is to perform a conventional first-principles calculation and store the low-lying Bloch functions evaluated on a uniform grid of k-points in the Brillouin zone. We then map those states onto a set of maximally-localized Wannier functions, and evaluate the matrix elements of the Hamiltonian and the other needed operators between the Wannier orbitals, thus setting up an ``exact tight-binding model.'' In this compact representation the k-space quantities are evaluated inexpensively using a generalized Slater-Koster interpolation. Because of the strong localization of the Wannier orbitals in real space, the smoothness and accuracy of the k-space interpolation increases rapidly with the number of grid points originally used to construct the Wannier functions. This allows k-space integrals to be performed with ab-initio accuracy at low cost. In the Wannier representation, band gradients, effective masses, and other k-derivatives needed for transport and optical coefficients can be evaluated analytically, producing numerically stable results even at band crossings and near weak avoided crossings.