Charge carriers energy spectra in anisotropic and bounded structures

In this paper we shall study crystalline structures where translational symmetry of the atom (ion) distribution of the electron (or hole) system is broken by the sputtering and due to existence of two boundary surfaces. This is a model of high-temperature superconductors in which the observed symmetry breaking orthogonal to CuO planes was treated as a perturbation. The single-particle fermion wave functions and the possible energies of charge carriers were determined. The competitive existence of the superconductive and normal regions in such sample was shown in agreement with experimental data. The conditions for the formation of superconductive states and the limitations on current density values in the planes parallel to boundary surfaces (in CuO planes) were obtained and discussed. (authors)