The toy model for the high-Tc superconductivity

TL;DR

This paper introduces a simple microscopic model combining electron-phonon and electron-electron-phonon interactions to explain high-temperature superconductivity, extending BCS theory and aligning with experimental data.

Contribution

It presents a novel microscopic model that incorporates EPH and EEPH interactions, providing insights into the energy gap behavior and doping dependence in high-Tc superconductors.

Findings

Energy gap remains weakly temperature-dependent below T_C.

Model explains doping dependence of the gap ratio R_1.

Extends BCS van Hove scenario to 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.