Properties of the superconducting state in molecular metallic hydrogen under pressure at 347 GPa

Abstract: The thermodynamic properties of the superconducting state induced in metallic molecular hydrogen under the influence of pressure 347 GPa were determined. In particular, it has been shown that the critical temperature ($T_{C}$) changes in the range from 120 K to 90 K for $\mu^{*}\in<0.08,0.15>$, where $\mu^{*}$ is the value of the Coulomb pseudopotential. Next, the energy gap near the temperature of zero Kelvin ($2\Delta(0)$) was calculated. It has been stated, that the dimensionless ratio $2\Delta(0)/k_{B}T_{C}$ slightly decreases with the increase of $\mu^{*}$ from 3.98 to 3.84. In the last step, the ratio of effective electron mass ($m^{*}_{e}$) to the bare electron mass ($m_{e}$)) was determined. It has been proved that $m^{*}{e}/m{e}$ takes its highest value equal to 1.96 for $T=T_{C}$.