Enabling accurate first-principle calculations of electronic properties with a corrected k.p scheme

TL;DR

This paper introduces a computationally efficient k.p-based interpolation scheme that accurately extends electronic eigenvalues and properties from sparse to dense k-point grids, improving calculations of transport and optical properties.

Contribution

The paper presents a novel corrected k.p interpolation scheme that reduces computational cost and improves accuracy for dense sampling in electronic structure calculations.

Findings

Accurately generates dense band structures from sparse data.

Reduces the number of empty bands needed for calculations.

Handles challenging d-electron and semi-core states effectively.

Abstract

A computationally inexpensive k.p-based interpolation scheme is developed that can extend the eigenvalues and momentum matrix elements of a sparsely sampled k-point grid into a densely sampled one. Dense sampling, often required to accurately describe transport and optical properties of bulk materials, can be demanding to compute, for instance, in combination with hybrid functionals in density functional theory (DFT) or with perturbative expansions beyond DFT such as the $GW$ method. The scheme is based on solving the k.p method and extrapolating from multiple reference k-points. It includes a correction term that reduces the number of empty bands needed and ameliorates band discontinuities. We show how the scheme can be used to generate accurate band structures, density of states, and dielectric functions. Several examples are given, using traditional and hybrid functionals, with Si, TiNiSn, and Cu as model materials. We illustrate that d-electron and semi-core states, which are particular challenging for the k.p method, can be handled with the correction scheme if the sparse grid is not too sparse.