Practical Band Interpolation with a Generalized Luttinger–Kohn Method

• Published in: physica status solidi (b) 2021-03, Vol.258 (3), p.n/a
• Main Authors: Reis, Carlos L., Martins, José Luís
• Format: Article
• Language: English
• Subjects: band interpolation; density of states; electronic band structure; k·p method; Luttinger–Kohn method
• ISSN: 0370-1972; 1521-3951
• DOI: 10.1002/pssb.202000260

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. An interpolating scheme related to the k⋅p method that is both accurate and simple to implement is presented. The method is agnostic to the type of constituent atoms and to the localization of the wave functions in the material, and it has been applied to diverse materials ranging from semiconductors to metals.