Advanced McMillan's equation and its application for the analysis of highly-compressed superconductors

Abstract

A theory of electron-phonon mediated superconductivity requires the knowledge of full phonon spectrum to calculate superconducting transition temperature, T${}_c$. However, there is no experimental technique which can measure phonon spectrum in highly-compressed near-room-temperature (NRT) superconductors to date. In this paper we propose to advance McMillan's approach (1968 Phys Rev 167 331) which utilizes the Debye temperature, T${}_{\theta }$ (an integrated parameter of full phonon spectrum), that we deduced by the fit of experimentally measured temperature-dependent resistance data, R(T), to Bloch-Gruneisen equation for highly-compressed black phosphorous, boron, GeAs, SiH${}_4$, H${}_x$S, D${}_y$S, LaH${}_x$ and LaD${}_y$. By utilizing relations between T${}_c$, Debye temperature and electron-phonon coupling strength constant, ${\lambda }_{e-ph}$ it is possible to affirm/disprove the electron-phonon mechanism in given superconductors. We show that computed ${\lambda }_{e-ph}$ for highly-compressed black phosphorous, boron, GeAs, SiH${}_4$ and for one sample of LaH${}_{10}$ are in a good agreement with ${\lambda }_{e-ph}$ values deduced from experimental data. It is also found remarkable constancy of Debye temperature in H${}_3$S at different ageing stages. We also show that if phonon spectra of two isotopic counterparts have similar shape then within electron-phonon phenomenology these materials should obey the relation of T${}_{c,1}$/T${}_{c,2}$=T${}_{\theta ,1}$/T${}_{\theta ,2}$ (where 1 and 2 designate isotopes). We report that these ratios for H${}_3$S-D${}_3$S predicted by electron-phonon phenomenology are largely different from ratios deduced from experiment. This alludes that NRT superconductivity in H3S-D3S system is originated from more than one mechanism, where the electron-phonon coupling lifts T${}_c$ in H${}_3$S vs D${}_3$S, but primary origin for NRT background of in both H${}_3$S and D${}_3$S remains to be discovered.

arXiv comment52 pages, 19 figures, 11 tables

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