Quantitative analysis of nonadiabatic effects in dense H(3)S and PH(3) superconductors

The comparison study of high pressure superconducting state of recently synthesized H(3)S and PH(3) compounds are conducted within the framework of the strong-coupling theory. By generalization of the standard Eliashberg equations to include the lowest-order vertex correction, we have investigated the influence of the nonadiabatic effects on the Coulomb pseudopotential, electron effective mass, energy gap function and on the 2Δ(0)/T(C) ratio. We found that, for a fixed value of critical temperature (178 K for H(3)S and 81 K for PH(3)), the nonadiabatic corrections reduce the Coulomb pseudopotential for H(3)S from 0.204 to 0.185 and for PH(3) from 0.088 to 0.083, however, the electron effective mass and ratio 2Δ(0)/T(C) remain unaffected. Independently of the assumed method of analysis, the thermodynamic parameters of superconducting H(3)S and PH(3) strongly deviate from the prediction of BCS theory due to the strong-coupling and retardation effects.