The higher superconducting transition temperature Tc and the functional derivative of Tc with α2F(ω) for electron-phonon superconductors

This work presents an analysis of the functional derivative of the superconducting transition temperature Tc with respect to the electron-phonon coupling function α2F(ω) [δTc/δα2F(ω)] and α2F(ω) spectrum of H3S (Im3̄m), in the pressure range where the high-Tc 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 δTc/δα2F(ω) and α2F(ω) with its higher Tc. 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 Tc, and determining the optimal physical conditions (pressure, alloying or doping concentration) that lead to the superconductor reaching its highest Tc possible.