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

A computationally inexpensive kp-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 computationally demanding to compute, for instance, in combination with hybrid functionals within the density functional theory (DFT) or with perturbative expansions beyond DFT such as the GW method. The scheme is based on solving the k$\cdot$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 that 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 test cases. We illustrate that d-electron and semi-core states, which are particular challenging for the k$\cdot$p method, can be handled with the correction scheme if the sparse grid is not too sparse.