The existence of the physical elementary energy bands describing the Davydov splitting was demonstrated in the energy spectra of the layered orthorhombic 4 3In Se crystal. It was confirmed that the physical elementary energy bands are related to the exactly determined Wyckoff position in the unit cell, where the maximum of the valence electron density is localized. By means of ab initio calculations, the dispersion laws with the low-energy non-parabolicity were obtained for electrons and holes of the 4 3In Se crystal. The reasons for such a dispersion law to occur in 4 3In Se are discussed as well as its similarity to the dispersion law for holes in the β-InSe crystal under pressure.
One-electron states in a layered crystal with chaotically placed covalent bridges have been calculated using the group decomposition of the Green's function with respect to the concentration of interacting dopants. The calculations have been based on the Fivaz's dispersion law for conduction electrons. It has been shown that a rearrangement of the conduction band takes place at a certain concentration of the covalent bridges (c ) c 0 ; c ( 1, where c 0 is the characteristic concentration larger than that of an isotropic crystal). After this rearrangement an anisotropic dopant band is formed. All parameters of this rearrangement have been found as well as the effective mass tensor components for the rearranged conduction band and for the created dopant band. It has been demonstrated that the interaction process leading to the formation of the covalent bridges can be a reason of the change of the anisotropy of the electric conductivity in a layered crystal. The density and the number of the quasi-Bloch states have been calculated in the created energy band. The number of these states increases with the increase of the dopant concentration. The possibility of dielectric-metal transition in intercalated layered crystals was analyzed.
For three-dimensional charge carriers described by the dispersion ław with quartic terms of the wave vector, the density of states function similar as in the one-dimensional case was determined. This similarity allows the Pekar and Dejgen condenson states in the continuum approximation to exist. The calculated phonon spectrum reveals optical vibrations of a very low frequency, which favours the electron-phonon interaction and creation of the condenson states.
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