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

The critical temperature ($T_C$) and the energy gap ($2\mathrm{\Delta }(T)$) 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 $2\mathrm{\Delta }(0)$ 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: $R_{\mathrm{\Delta }}\in <4.55,4.29>$. 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 $\mathrm{\Delta }({\mu }^{\star })$ have been given.