Description of the thermodynamic properties of $\rm{BiH_{5}}$ and $\rm{BiH_{6}}$ superconductors beyond the mean-field approximation

TL;DR

This study investigates the thermodynamic properties of high-pressure superconducting BiH5 and BiH6 compounds beyond mean-field theory using Eliashberg equations, providing detailed insights into their critical parameters and thermodynamic ratios.

Contribution

The paper presents a detailed thermodynamic analysis of BiH5 and BiH6 superconductors beyond mean-field approximation, based on ab initio calculations and Eliashberg formalism, which is novel for these compounds.

Findings

Calculated order parameter and wave function renormalization with temperature.

Estimated free energy difference, critical field, and specific heat.

Determined dimensionless ratios indicating strong-coupling superconductivity.

Abstract

The ab initio calculations suggest (Y. Ma et al.), that the high-pressure ($p=200$~GPa) superconducting state in $\rm{BiH_{5}}$ and $\rm{BiH_{6}}$ compounds characterizes with a high value of the critical temperature ($T_{C}\sim 100$~K). Due to the large value of the electron-phonon coupling constant ($\lambda\sim 1.2$), the thermodynamic parameters of the superconducting phase in $\rm{BiH_{5}}$ and $\rm{BiH_{6}}$ have been determined beyond the mean-field approximation - in the framework of the Eliashberg equations formalism. We have calculated the dependence of the order parameter ($\Delta$) and the wave function renormalization factor on the temperature. Then we have estimated the free energy difference between the superconducting state and the normal state, the thermodynamic critical field ($H_{C}$) and the specific heat of the superconducting state ($C^{S}$) and the normal state ($C^{N}$). The values of the dimensionless ratios $R_{\Delta}=2\Delta\left(0\right)/k_{B}T_{C}$, $R_{C}=\Delta C\left(T_{C}\right)/C^{N}\left(T_{C}\right)$ and $R_{H}=T_{C}C^{N}\left(T_{C}\right)/H^{2}_{C}\left(0\right)$ are equal $R_{\Delta_{{\rm BiH_{5}}}}=4.17$ and $R_{\Delta_{{\rm BiH_{6}}}}=4.20$, $R_{C_{{\rm BiH_{5}}}}=2.54$ and $R_{C_{{\rm BiH_{6}}}}=2.58$, $R_{H_{{\rm BiH_{5}}}}=0.146$ and $R_{H_{{\rm BiH_{6}}}}=0.146$ respectively.