Academy of Sciences and Arts of the Republic of Srpska , Bosnia and Herzegovina
Faculty of Sciences and Mathematics, University of Banja Luka, Banja Luka, Bosnia and Herzegovina
The translational symmetry of the distribution of atoms (ions) of the charge carriers (electrons or holes) system is broken by sputtering (doping) due to the existence of two boundary surfaces. This is a model of high-temperature superconductors in which the observed symmetry breaking orthogonal to the CuO plane is treated as a perturbation. Single-particle fermion wave functions and possible charge carrier energies were determined. The competing existence of superconducting and normal regions in such a sample is shown in agreement with experimental data. The conditions for the formation of superconducting states and the limits of the current density values in the planes parallel to the boundary surfaces (in the CuO planes) were obtained and discussed.
The research presented in this paper was financially supported by the Ministry of Scientific and Technological Development, Higher Education and Information Society of the Republic of Srpska (Projects No. 19.032/961 36/19 and 19.032/961-42/19).
Authors retain copyright. This work is licensed under a Creative Commons Attribution 4.0 International License. 
The statements, opinions and data contained in the journal are solely those of the individual authors and contributors and not of the publisher and the editor(s). We stay neutral with regard to jurisdictional claims in published maps and institutional affiliations.