The higher superconducting transition temperature T${}_c$ and the functional derivative of T${}_c$ with ${\alpha }^{2}F(\omega )$ 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 ${\alpha }^{2}F(\omega )$ [$\delta T_c/\delta {\alpha }^2$F($\omega$)] and ${\alpha }^{2}F(\omega )$ spectrum of H${}_3$S ($Im\bar{3}m$), 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 $\delta T_c/\delta {\alpha }^2$F($\omega$) and ${\alpha }^{2}F(\omega )$ 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.

arXiv comment9 pages, 2 figures, 1 table

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