The transition temperature of a superconductor with defects in the crystal structure: application to Cu - O layers and -type systems

Abstract

We have re-examined the electron - phonon interaction from the viewpoint of its dependence on the crystal structure, particularly on the positioning of atoms in the unit cell. It is found that the strength of the interaction depends on the number of Cu - O layers per unit cell only when there are defects. Accordingly the transition temperature depends on the variable number n of Cu - O layers per unit cell. The larger the number of layers, the larger the transition temperature. We find that the lattice waves can be treated using spherical Bessel functions, and that the electron - phonon interaction oscillates as a function of the number of Cu - O planar layers. The transition temperature of the superconductor then oscillates as a function of n, having a large value at n = 3 and smaller value at n = 4. We predict that the next maximum value of occurs at n = 7. The predicted variation of as a function of n is in reasonable agreement with the experimental values.