High temperature superconducting properties of atomic hydrogen at 802 GPa

•Superconducting properties of atomic hydrogen at 802 GPa.•The Eliashberg approach.•The high critical temperature.•The non-BCS value of the ratio of the energy gap to the critical temperature.•The large electron effective mass.

The Eliashberg equations have been used to calculate the thermodynamic parameters of the superconducting state in the metallic atomic hydrogen at 802 GPa. It has been shown that the superconducting transition temperature (TC) is in the range from 332.7 K to 259.4 K, depending on the assumed Coulomb pseudopotential: μ⋆∈〈0.1,0.2〉μ⋆∈〈0.1,0.2〉. Due to the strong-coupling and retardation effects, the values of the order parameter (ΔΔ), the thermodynamic critical field (HC), and the specific heat for the normal (CN) and superconducting (CS) state differ significantly from the predictions of the BCS theory. As a result, the dimensionless ratios RΔ≡2Δ(0)/kBTCRΔ≡2Δ(0)/kBTC, RH≡TCCN(TC)/HC2(0), and RC≡(CS(TC)−CN(TC))/CN(TC)RC≡(CS(TC)−CN(TC))/CN(TC) take the values: RΔ(μ⋆)∈〈4.70,4.51〉RΔ(μ⋆)∈〈4.70,4.51〉, RH(μ⋆)∈〈0.130,0.132〉RH(μ⋆)∈〈0.130,0.132〉, and RC(μ⋆)∈〈2.57,2.50〉RC(μ⋆)∈〈2.57,2.50〉.