Study of layered superconductors in the framework of electron-phonon coupling theory

In this review we summarize a number of recent developments in the study of layered superconductors using e-phonon Eliashberg theory. Critical temperature of layered superconductors is calculated using Eliashberg theory. Influence of nonadiabacity effects on the critical temperature in layered superconductors is considered. Influence of Coulomb repulsion on the critical temperature is investigated taking into account the arbitrary thicknesses of conducting layers. Bardeen–Cooper–Schrieffer (BCS) equations for layered superconductors are applied for the calculation of a specific heat jump, which is smaller than in the case of isotropic BCS theory. The plasmon spectrum of layered superconductors with arbitrary thicknesses of conducting layers is calculated. Influence of fluctuations in the phase of the order parameter on the critical temperature of layered superconductors is studied using Ginzburg–Landau functional for free energy. The results are shown to be in qualitative agreement with some experimental data for cuprate superconductors and recently discovered MgB$_2$.