Group-theory approach within the framework of the tight-binding model

Abstract

A new approach to the constructing of the model Hamiltonian within the framework of the general tight-binding formalism is proposed. Considerable simplification of the conventional procedure of matrix element determination is achieved taking advantages of the group theory. It is shown, that the overlapping of wave functions centered on the neighboring lattice sites in arbitrary low-symmetric lattice may be counted up through the coupling integrals between atom-like states, as though these atoms should be placed at the same distance along the z-axis. It is pointed out, that the self- consistent ab-initio calculation scheme based on the general assumptions of the tight-binding model appears to be possible.