Quantitative analysis of nonadiabatic effects in dense H3S and PH3 superconductors.

Artur P Durajski

doi:10.1038/srep38570

Abstract

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.

Highlights

The first-principles theoretical studies of the metallization and high-temperature superconductivity of dense hydrogen sulfide were reported for the first time by Li et al.[1]
Drozdov et al who found that H2S compressed in a diamond anvil cell exhibits the superconductivity ranging from 30 to 150 K measured in the low-temperature runs[2,3], which is consistent with calculations mentioned[1]
We discuss the validity of the conventional Migdal-Eliashberg theory by introduce the lowest-order vertex correction and we examine its effect on Coulomb pseudopotential, energy gap, 2Δ(0)/TCC N (TC) ratio and electron effective mass

Summary

Theoretical model and computational methods

Most of the theoretical studies concluded that compressed H3S and PH3 are phonon-mediated strong-coupling superconductors[8,11,25,28,29]. The application of the above Eliashberg equations to describe the electron-phonon superconductivity is justified for systems in which the value of the phonon energy scale (Debye frequency, ωD) to the electron energy scale (Fermi energy, εF) ratio is negligible. Our ab-initio studies showed that ratio λωD/εF is equal to 0.020 for H3S and 0.014 for PH3 These values are rather small in comparison to fullerene compounds or high-Tc cuprates, are not zero. We decided to conduct our calculations simultaneously using the conventional Eliashberg equations and equations with the lowest-order vertex correction, which allows us to examine the influence of nonadiabatic effects on the thermodynamic properties in studied compounds.

Results and Discussion

Conclusions

Additional Information