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Thermodynamical properties of the superconducting state in metallic hydrogen were determined on the basis of the model of two compressed hydrogen planes. We took into account both the on-site and the inter-site electronic correlations ( U  and  K ), as well as the relevant non-conventional electron-phonon coupling functions ( g   U   and  g   K  ). We proved, within the Eliashberg formalism, that the maximum value of the critical temperature of transition into the superconducting state is about 200 K for the harmonic approximation, and about 84 K for the Morse anharmonic approximation. Omission of the electronic correlations results in a considerable overstatement of the  T   C   value. On the other hand, the  T   C   value is remarkably understated if the non-conventional interactions are disregarded. Other thermodynamic quantities, such as the order parameter, the jump in the specific heat value, the thermodynamic critical field, and the upper critical field, take the values for which the non-dimensional ratios  R  Δ ,  R   C  ,  R   H   and  R   H 2  do not differ substantially from the predictions of the BCS theory.

journal of superconductivity and novel magnetism

Thermodynamic Properties of the Superconducting State in Metallic Hydrogen: Electronic Correlations, Non-conventional Electron-Phonon Couplings and the Anharmonic Effects