Quantitative analysis of nonadiabatic effects in dense H3S and PH3 superconductors

The comparison study of high pressure superconducting state of recently synthesized H3S and PH3 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)/TC ratio. We found that, for a fixed value of critical temperature (178 K for H3S and 81 K for PH3), the nonadiabatic corrections reduce the Coulomb pseudopotential for H3S from 0.204 to 0.185 and for PH3 from 0.088 to 0.083, however, the electron effective mass and ratio 2Δ(0)/TC remain unaffected. Independently of the assumed method of analysis, the thermodynamic parameters of superconducting H3S and PH3 strongly deviate from the prediction of BCS theory due to the strong-coupling and retardation effects.