Double-valued strong-coupling corrections to Bardeen-Cooper-Schrieffer ratios

Abstract

Experimental discovery of near-room-temperature (NRT) superconductivity in highly-compressed H${}_3$S, LaH${}_1$${}_0$ and YH${}_6$ restores fundamental interest to electron-phonon pairing mechanism in superconductors. One of prerequisites of phonon-mediated NRT superconductivity in highly-compressed hydrides is strong electron-phonon interaction, which can be quantified by dimensionless ratios of Bardeen-Cooper-Schrieffer (BCS) theory vs $k{}_{B}T{}_c$/($\hslash$$\omega {}_l{}_n$), where Tc is the critical temperature and $\omega {}_l{}_n$ is the logarithmic phonon frequency (Mitrovic et al. 1984 Phys. Rev. B 29 184). However, all known strong-coupling correction functions for BCS ratios are applicable for $k{}_{B}T{}_c$/($\hslash$$\omega {}_l{}_n$)<0.20, which is not high enough $k{}_{B}T{}_c$/($\hslash$$\omega {}_l{}_n$) range for NRT superconductors, because the latter exhibit variable values of 0.13 < $k{}_{B}T{}_c$/($\hslash$$\omega {}_l{}_n$) < 0.32. In this paper, we reanalyze full experimental dataset (including data for highly-compressed H3S) and find that strong-coupling correction functions for the gap-to-critical-temperature ratio and for the specific-heat-jump ratio are double-valued nearly-linear functions of $k{}_{B}T{}_c$/($\hslash$$\omega {}_l{}_n$).

22 pages, 8 figures