The higher superconducting transition temperature T c and the functional derivative of T c with α 2 F(ω) for electron–phonon superconductors

Abstract

This work presents an analysis of the functional derivative of the superconducting transition temperature T c with respect to the electron-phonon coupling function α 2 F(ω) [δT c/δα 2 F(ω)] and α 2 F(ω) spectrum of H3S (), in the pressure range where the high-T c was measured (155–225 GPa). The calculations are done in the framework of the Migdal–Eliashberg theory. We find for this electron–phonon superconductor, a correlation between the maximums of δT c/δα 2 F(ω) and α 2 F(ω) with its higher T c. We corroborate this behavior in other electron–phonon superconductors by analyzing data available in the literature, which suggests its validity in this type of superconductors. The correlation observed could be considered as a theoretical tool that in an electron–phonon superconductor, allows describing qualitatively the proximity to its highest T c, and determining the optimal physical conditions (pressure, alloying or doping concentration) that lead to the superconductor reaching its highest T c possible.