Superconductivity of calcium under the pressure at 120 GPa

TL;DR

This paper investigates the superconducting properties of calcium at 120 GPa, revealing a high Coulomb pseudopotential, deviations from standard formulas, and detailed electron interaction characteristics.

Contribution

It provides exact solutions of Eliashberg equations on the real axis for calcium under high pressure, highlighting the need for modified formulas and detailed electron interaction analysis.

Findings

Coulomb pseudopotential reaches 0.215

Critical temperature not accurately predicted by Allen-Dynes formula

Electron effective mass ratio reaches 2.36 at T_C

Abstract

The properties of the superconducting state in calcium under the pressure at 120 GPa were analyzed. By using the imaginary axis Eliashberg equations it has been shown, that the Coulomb pseudopotential reaches the high value equal to 0.215. In the considered case, the critical temperature is not properly described by the Allen-Dynes formula and it should be calculated with an use of the modified expression. In the paper the exact solutions of the Eliashberg equations on the real axis were also obtained. On this basis it was stated, that the effective potential of the electron-electron interaction is attractive for the frequencies lower or equal to the maximum phonon frequency. Then, the dimensionless parameter 2\Delta(0)/k_{B}T_{C}=4.10 was calculated. In the last step it has been proven, that the ratio of the electron effective mass to the bare electron mass is high and reaches its maximum equal to 2.36 for the critical temperature.