Description of the thermodynamic properties of $\mathrm{Bi}{\mathrm{H}}_5$ and $\mathrm{Bi}{\mathrm{H}}_6$ superconductors beyond the mean-field approximation

Abstract

The ab initio calculations suggest (Y. Ma et al.), that the high-pressure ($p=200$~GPa) superconducting state in $\mathrm{Bi}{\mathrm{H}}_5$ and $\mathrm{Bi}{\mathrm{H}}_6$ 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 $\mathrm{Bi}{\mathrm{H}}_5$ and $\mathrm{Bi}{\mathrm{H}}_6$ 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 $R_H=T_C{C}^N\left(T_C\right)/H_C^2\left(0\right)$ are equal $R_{{\Delta }_{\mathrm{Bi}{\mathrm{H}}_5}}=4.17$ and $R_{{\Delta }_{\mathrm{Bi}{\mathrm{H}}_6}}=4.20$, $R_{C_{\mathrm{Bi}{\mathrm{H}}_5}}=2.54$ and $R_{C_{\mathrm{Bi}{\mathrm{H}}_6}}=2.58$, $R_{H_{\mathrm{Bi}{\mathrm{H}}_5}}=0.146$ and $R_{H_{\mathrm{Bi}{\mathrm{H}}_6}}=0.146$ respectively.

4 pages, 4 figures