Non-BCS thermodynamic properties of H2S superconductor

Abstract: The present paper determines the thermodynamic properties of the superconducting state in the ${\rm H_{2}S}$ compound. The values of the pressure from $130$ GPa to $180$ GPa were taken into consideration. The calculations were performed in the framework of the Eliashberg formalism. In the first step, the experimental course of the dependence of the critical temperature on the pressure was reproduced: $T_{C}\in\left<31,88\right>$ K, whereas the Coulomb pseudopotential equal to $0.15$ was adopted. Next, the following quantities were calculated: the order parameter at the temperature of zero Kelvin ($\Delta\left(0\right)$), the specific heat jump at the critical temperature ($\Delta C\left(T_{C}\right)\equiv C^{S}\left(T_{C}\right)-C^{N}\left(T_{C}\right)$), and the thermodynamic critical field ($H_{C}\left(0\right)$). It was found that the values of the dimensionless ratios: $R_{\Delta}\equiv 2\Delta(0)/k_{B}T_{C}$, $R_{C}\equiv{\Delta C\left(T_{C}\right)}/{C^{N}\left(T_{C}\right)}$, and $R_{H}\equiv{T_{C}C^{N}\left(T_{C}\right)}/{H_{C}^{2}\left(0\right)}$ deviate from the predictions of the BCS theory: $R_{\Delta}\in\left<3.64,4.16\right>$, $R_{C}\in\left<1.59,2.24\right>$, and $R_{H}\in\left<0.144, 0.163\right>$. Generalizing the results on the whole family of the ${\rm H_{n}S}$-type compounds, it was shown that the maximum value of the critical temperature can be equal to $\sim 290$ K, while $R_{\Delta}$, $R_{C}$ and $R_{H}$ adopt the following values: $6.53$, $3.99$, and $0.093$, respectively.