The toy model for the high-Tc superconductivity

Abstract

The simple microscopic model for the high-T_{C} superconductors based on the electron-phonon (EPH) and electron-electron-phonon (EEPH) interactions has been presented. On the {\it fold} mean-field level, it has been shown, that the obtained model supplements the predictions based on the BCS van Hove scenario. In particular: (i) For strong EEPH coupling and T<T_{C} the energy gap (\Delta_{tot}) is very weak temperature dependent; up to the critical temperature \Delta_{tot} extends into the anomalous normal state to the Nernst temperature. (ii) The model explains well the experimental dependence of the ratio R_{1}\equiv 2\Delta_{tot}^{(0)}/k_{B}T_{C} on doping for the reported superconductors in the terms of the few fundamental parameters.