The superconducting state in metallic hydrogen under pressure at 2000 GPa

In this study, we have analysed the properties of the superconducting phase in metallic hydrogen under pressure at 2000 GPa. In particular, we have calculated the dependence of the basic thermodynamic quantities on the value of Coulomb pseudopotential ( μ ∗ ). The main results are the following: (i) The critical temperature ( T C ) is large even for high values of μ ∗ . (ii) The values of the ratios R 1 ≡ 2 Δ ( 0 ) / k B T C , R 2 ≡ Δ C ( k B T C ) / C N ( k B T C ) and R 3 ≡ T C C N ( k B T C ) / H C 2 ( 0 ) differ from the BCS values. (iii) The electron effective mass is large and reaches its maximum value for T = T C . Additionally, we have given the analytical formulas for T C , R 1 and R 2 which reproduce results originating from exact numerical calculations very well.