A non-perturbative relativistic tight-binding (TB) approximation method applicable to crystalline material immersed in a magnetic field was developed in 2015. To apply this method to any material in the magnetic field, the electronic structure of the material in absence of a magnetic field must be calculated. In this study, we present the relativistic TB approximation method for graphene in a zero magnetic field. The Hamiltonian and overlap matrix is constructed considering the nearest neighbouring atomic interactions between the s and p valence orbitals, where the relativistic hopping and overlap integrals are calculated using the relativistic version of the Slater-Koster table. The method of constructing the Hamiltonian and overlap matrix and the resulting energy-band structure of graphene in the first Brillouin zone is presented in this paper. It is found that there is an appearance of a small band-gap at the K points (also known as the spin-orbit gap) due to the relativistic effect, whose magnitude is 25μeV.
@article{arxiv.2204.06836,
title = {Relativistic Tight-Binding Model for Hexagonal Lattice: Application to Graphene},
author = {Rohin Sharma and Amit Shrestha and Masahiko Higuchi and Katsuhiko Higuchi and Dipendra B. Hamal},
journal= {arXiv preprint arXiv:2204.06836},
year = {2023}
}