Specific heat and thermodynamic critical field for the molecular metallic hydrogen

TL;DR

This study uses the Eliashberg formalism to analyze the thermodynamic properties of molecular metallic hydrogen under high pressure, revealing significant deviations from BCS theory predictions.

Contribution

It provides detailed calculations of specific heat and critical field for metallic hydrogen at different pressures, highlighting pressure-dependent deviations from BCS behavior.

Findings

Specific heat jump increases with pressure

Thermodynamic critical field grows near zero Kelvin with pressure

Parameters significantly diverge from BCS model predictions

Abstract

In the framework of the Eliashberg formalism the free energy difference between the superconducting and normal state for the molecular metallic hydrogen was calculated. The pressure values $p_{1}=347$ GPa and $p_{2}=428$ GPa were taken into consideration. It has been shown, that together with the increase of the pressure, grows the value of the specific heat jump at the critical temperature and the value of the thermodynamic critical field near zero Kelvin: $[\Delta C(T_{C})]_{p2}/[\Delta C(T_{C})]_{p1}\simeq 2.33$ and $[H_{C}(0)]_{p2}/[H_{C}(0)]_{p1}\simeq 1.74$. Next, it has been stated, that the ratio $\Delta C(T_{C})/C^{N}(T_{C})$ also increases from 1.91 to 2.39; whereas $T_{C}C^{N}(T_{C})/H^{2}_{C}(0)$ decreases from 0.152 to 0.140. The last results prove that the considered parameters significantly diverge from the prediction based on the BCS model.