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

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