Superconducting critical temperature under pressure

Abstract

The present record on the critical temperature of a superconductor is held by sulfur hydride (approx. 200 K) under very high pressure (approx. 56 GPa.). As a consequence, the dependence of the superconducting critical temperature on pressure became a subject of great interest and a high number of papers on of different aspects of this subject have been published in the scientific literature since. In this paper, we calculate the superconducting critical temperature as a function of pressure, Tc(P), by a simple method. Our method is based on the functional derivative of the critical temperature with the Eliashberg function, δTc(P)/δα2F(ω). We obtain the needed coulomb electron-electron repulsion parameter, μ*(P) at each pressure in a consistent way by fitting it to the corresponding Tc using the linearized Migdal–Eliashberg equation. This method requires as input the knowledge of Tc at the starting pressure only. It applies to superconductors for which the Migdal–Eliashberg equations hold. We study Al and β−Sn two weak-coupling low-Tc superconductors and Nb, the strong coupling element with the highest critical temperature. For Al, our results for Tc(P) show an excellent agreement with the calculations of Profeta et al. which are known to agree well with experiment. For β−Sn and Nb, we found a good agreement with the experimental measurements reported in several works. This method has also been applied successfully to PdH elsewhere. Our method is simple, computationally light and gives very accurate results.