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.