Analysis of the superconductivity in perovskite oxides using three-square-well BCS formalism

Abstract

Superconductivity in perovskite, BaKBiO, is studied in the Bardeen–Cooper–Schrieffer (BCS) model, with three-square-well potentials. Components of the new coupling are: the attractive acoustic phonon–electron, optical phonon–electron and repulsive Coulomb interactions. With these in the BCS pairing Hamiltonian, expressions for the superconducting transition temperature and isotope effect exponent are obtained. Results of our analysis are consistent with experiments. Contributions of interactions to system properties are exhibited and analysed. Acoustic phonon–electron and optical phonon–electron interactions have near-identical elevation of transition temperature, holding out possible explanations for high- Tc. Contrastingly, optical phonon–electron and Coulomb couplings cause debilitation of isotope exponent, a possible explanation for low isotope exponent in the cuprates and other high- Tc systems. It is found that BCS electron–phonon coupling appears synonymous with acoustic phonon–electron coupling.