The higher superconducting transition temperatureT_cand the functional derivative ofT_cwithα²F(ω) for electron-phonon...

This work presents an analysis of the functional derivative of the superconducting transition temperatureT_cwith respect to the electron-phonon coupling functionα²F(ω) [δT_c/δα²F(ω)] andα²F(ω) spectrum of H₃S (Im3̄m), in the pressure range where the high-T_cwas 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 ofδT_c/δα²F(ω) andα²F(ω) with its higherT_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 highestT_c, and determining the optimal physical conditions (pressure, alloying or doping concentration) that lead to the superconductor reaching its highestT_cpossible.