On the critical temperature and the energy gap in dense SiH4(H2)2 at 250 GPa

Abstract

The critical temperature ($T_{C}$) and the energy gap ($2\Delta(T)$) for the superconductor SiH$_4$(H$_2$)$_2$ at 250 GPa have been calculated. The wide range of the Coulomb pseudopotential's values has been considered: $\mu^{\star}\in<0.1,0.3>$. It has been stated that $T_{C}$ decreases together with the increase of $\mu^{\star}$ from 129.83 K to 81.40 K. The low-temperature energy gap ($T\sim 0$ K) decreases together with the increase of the Coulomb pseudopotential from 50.96 meV to 30.12 meV. The high values of $2\Delta(0)$ mean that the dimensionless ratio $R_{\Delta}\equiv 2\Delta(0)/k_{B}T_{C}$ significantly exceeds the value predicted by the classical BCS theory. In the considered case: $R_{\Delta}\in<4.55,4.29>$. Due to the unusual dependence of the critical temperature and the energy gap on $\mu^{\star}$, the analytical expressions for $T_{C}(\mu^{\star})$ and $\Delta(\mu^{\star})$ have been given.