High-pressure superconducting state in hydrogen

•The superconducting state in hydrogen.•The value of the critical temperature.•The non BCS value of the thermodynamic parameters.

The paper determines the thermodynamic parameters of the superconducting state in the metallic atomic hydrogen under the pressure at 1 TPa, 1.5 TPa, and 2.5 TPa. The calculations were conducted in the framework of the Eliashberg formalism. It has been shown that the critical temperature is very high (in the range from 301.2 K to 437.3 K), as well as high are the values of the electron effective mass (from 3.43me to 6.88me), where me denotes the electron band mass. The ratio of the low-temperature energy gap to the critical temperature explicitly violates the predictions of the BCS theory: 2Δ(0)/kBTC∈〈4.84,5.85〉2Δ(0)/kBTC∈〈4.84,5.85〉. Additionally, the free energy difference between the superconducting and normal state, the thermodynamic critical field, and the specific heat of the superconducting state have been determined. Due to the significant strong-coupling and retardation effects those quantities cannot be correctly described in the framework of the BCS theory.