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

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}$).