The superconducting phase of Calcium under the pressure at 200 GPa: the strong-coupling description

TL;DR

This paper investigates the superconducting properties of Calcium at 200 GPa using Eliashberg theory, revealing how critical temperature, energy gap, and effective mass vary with Coulomb pseudopotential, highlighting strong-coupling effects.

Contribution

It provides a detailed strong-coupling analysis of Calcium's superconducting state at high pressure using Eliashberg equations, including thermodynamic parameters and their dependence on Coulomb pseudopotential.

Findings

Critical temperature decreases from 36.15 K to 20.79 K with increasing pseudopotential.

The energy gap ratio $2igtriangleup(0)/k_{B}T_{C}$ decreases from 4.25 to 3.90.

Effective electron mass ratio reaches up to 2.23 at $T_{C}$.

Abstract

The thermodynamic parameters of the superconducting state in Calcium under the pressure at 200 GPa have been determined. The numerical analysis by using the Eliashberg equations in the mixed representation has been conducted. It has been stated, that the critical temperature ($T_{C}$) decreases from 36.15 K to 20.79 K dependently on the assumed value of the Coulomb pseudopotential ($\mu^{*}\in<0.1,0.3>$). Next, the order parameter near the temperature of zero Kelvin ($\Delta(0)$) has been obtained. It has been proven, that the dimensionless ratio $2\Delta(0)/k_{B}T_{C}$ decreases from 4.25 to 3.90 together with the growth of $\mu^{*}$. Finally, the ratio of the electron effective mass to the electron bare mass ($m^{*}_{e}/m_{e}$) has been calculated. It has been shown, that $m^{*}_{e}/m_{e}$ takes the high value in the whole range of the superconducting phase's existence, and its maximum is equal to 2.23 for T=T_{C}.