Specifc Heat and Thermodynamic Critical Field for Calcium under the Pressure at 120 GPa

TL;DR

This study calculates the specific heat and thermodynamic critical field of calcium under 120 GPa pressure using Eliashberg theory, revealing deviations from BCS universal laws in its thermodynamic properties.

Contribution

It provides the first detailed numerical analysis of calcium's thermodynamic quantities under high pressure using the Eliashberg approach, highlighting non-BCS behavior.

Findings

The specific heat jump ratio ΔC(T_C)/C^N(T_C) is 2.48.

The ratio T_C C^N(T_C)/H_C^2(0) is 0.154.

Thermodynamic quantities do not follow BCS universal laws.

Abstract

The free energy difference between the superconducting and normal state for Calcium under the pressure at 120 GPa has been determined. The numerical calculations have been made in the framework of the imaginary axis Eliashberg approach. On the basis of the obtained results the specific heat in the superconducting C^{S}(T) and normal C^{N}(T) state, as well as, the thermodynamic critical field H_{C}(T) have been obtained. It has been shown that the characteristic values of the considered thermodynamic quantities do not obey the BCS universal laws. In particular, {\Delta}C(T_{C})/C^N(T_{C})=2.48 and T_{C}C^{N}(T_{C})/H_{C}^{2}(0)=0.154.