Universality of the Empty-Lattice Approximation to Predict the Topology of Energy Spectra of High-Symmetry Crystals and Superlattices Based upon Them

Abstract

h symmetry crystals were discussed to demonstrate universality of the empty-lattice approximation to obtain the topology and symmetry of the elementary energy bands creating the valence band of those crystals and to predict a localization of the maximum of valence electron density distribution in the unit cell. The elaborated concept of the elementary energy bands was applied to the (GaAs)5/(AlAs)5 superlattice and ordered solid solution Pb 0.5 Sn 0.5 S.

Elementary energy bands concept, band structure, and peculiarities of bonding in β-InSe crystal

“…The obtained sets of states (4) and (5) allow us, after comparison with the band representations, which are induced from the irreducible representations of the site symmetry groups of all Wyckoff positions of the $D_{6h}^4$ space group 30, to determine the so‐called actual Wyckoff positions 17, 24, 26.…”

“…The main idea of the concept is that even the simplest approximation of the solid state physics – the empty lattice approximation, based on the most general information of the crystal, such as its space symmetry group, parameters of the crystal lattice and existence of the forbidden gap, allows us to find the symmetry and topology of the closed elements of the band structure – elementary energy bands 20, 23. Obtained in such a way a certain band representation describing the elementary energy bands allows to choose the so‐called actual Wyckoff position 17, 22, 24–26 from all the possible ones for the given crystal structure. The largest valence electron density in the unit cell is concentrated in these actual positions as was shown in Refs.…”