Superconductivity under pressure: application of the functional derivative

TL;DR

This paper presents a method to calculate how the superconducting critical temperature varies with pressure using the functional derivative of Tc with respect to the Eliashberg function, validated on aluminum.

Contribution

The paper introduces a pressure-dependent Tc calculation method based on the functional derivative, requiring only initial Tc data, applicable to Migdal-Eliashberg superconductors.

Findings

Accurately predicts Tc(P) for aluminum under pressure

Method aligns well with experimental data and previous calculations

Requires minimal input, only initial Tc at starting pressure

Abstract

In this paper, we calculate the superconducting critical temperature as a function of pressure, Tc(P ), using a method based on the functional derivative of the critical temperature with the Eliashberg function, dTc/dA2F. The coulomb electron-electron repulsion parameter, mu*(p) at each pressure is obtained in a consistent way by solving the linearized Migdal-Eliashberg equation. This method requires as the starting input only the knowledge of Tc(P ) at the starting pressure. It applies to superconductors for which the Migdal-Eliashberg equations hold. We study Al, a typical BCS weak coupling superconductor with a low Tc . Our results of Tc(P ) as a function of pressure for Al show an excellent agreement with the calculations of Profeta et al. (Phys. Rev. Lett.96, 047003 (2006)) which agree well with experiment.