Tight-binding theory of the electronic structures for rhombohedral semimetals

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Abstract
A semiempirical tight-binding theory of energy bands in rhombohedral A7-structure crystals is developed and applied to three group-V semimetals: arsenic, antimony, and bismuth. A general description of the method is explicitly given, including the matrix elements of the tight-binding Hamiltonian, and the treatment of the spin-orbit interaction which is noticeable in Bi. For each of these materials the theory uses 15 parameters, obtained in accord with a third-neighbor model which includes the spin-orbit coupling, to reproduce the major features of the band structures. The determination of these parameters is made by fitting the existing pseudopotential and ab initio data for the band structures at some high-symmetry points of the Brillouin zone. Comparison with first-principle calculations and experiments gives very good agreement throughout.