Analytic solution to the BCS equation for the superconducting transition temperature

Abstract

An analytic solution to the BCS equation for the superconducting transition temperature has been obtained. Instead of the electron- phonon interaction being assumed to be a constant in a certain range as was done in BCS theory, it has been considered varying with energy, a case more physical in nature. The resulting equation for the superconducting transition temperature Tc reduces to the standard BCS form when Tc is small but this equation does not put any higher limit on Tc. The gap parameter at the absolute zero has also been analytically obtained. These equations have been successfully applied to the high temperature superconductors. © 1992.