Practical Band Interpolation With A Generalized Luttinger-Kohn Method

Herein, an interpolation scheme for energy and wave functions of a crystal using a generalization of Luttinger-Kohn functions is presented. For each k-point where the interpolated bands are desired, a variational orthogonal basis is constructed using a singular value decomposition (SVD) where the Luttinger-Kohn functions are derived from reference k-points. A crucial step of the scheme is that before the SVD, the Luttinger-Kohn functions are multiplied by weights that depend on the distance between the reference k-points and the k-point to be interpolated. After the SVD, the less relevant orthogonal functions may be discarded. In contrast with some other methods, it is a true interpolation and it is continuous, it does not require a starting localized basis set or band disentanglement or any specific information from the user. The procedure should be straightforward to implement in most electronic-structure codes. Examples of the application of the scheme to density functional calculations of silicon, copper, and rhombohedral graphite are presented.