TIGHT-BINDING THEORY OF THE ELECTRONIC-STRUCTURES FOR RHOMBOHEDRAL SEMIMETALS

A semiempirical tight-binding theory of energy bands in rhombohedral A 7-structure crystals is developed and applied to three group-V semimet als: arsenic, antimony, and bismuth. A general description of the meth od is explicitly given, including the matrix elements of the tight-bin ding Hamiltonian, and the treatment of the spin-orbit interaction whic h is noticeable in Bi. For each of these materials the theory uses 15 parameters, obtained in accord with a third-neighbor model which inclu des the spin-orbit coupling, to reproduce the major features of the ba nd structures. The determination of these parameters is made by fittin g the existing pseudopotential and ab initio data for the band structu res at some high-symmetry points of the Brillouin zone. Comparison wit h first-principle calculations and experiments gives very good agreeme nt throughout.