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

Abstract

Any theory of electron-phonon mediated superconductivity requires knowledge of the full phonon spectrum in order to calculate superconducting transition temperature, Tc. However, there is currently no experimental technique for measuring in highly-compressed near-room-temperature (NRT) superconductors. In this paper, we propose to advance McMillan’s approach (1968 Phys Rev 167 331), which utilises the Debye temperature (an integrated parameter for the full phonon spectrum), deduced via the fit of experimentally measured temperature-dependent resistance data R(T) to the Bloch-Grüneisen equation for highly-compressed black phosphorous, boron, GeAs, SiH4, HxS, DxS, LaHx, and LaDy. By utilizing the relations between Tc, Tθ, and the electron-phonon coupling strength constant λe-ph (which can be computed from first-principles calculations), it is possible to affirm/disprove the electron-phonon coupling mechanism in given superconductors. We show that computed λe-ph for highly-compressed black phosphorous, boron, GeAs, SiH4, and for one sample of LaH10 are in a good agreement with λe-ph values deduced from experimental data. A remarkable constancy of for H3S at different ageing stages is also found. We also show that if the phonon spectra of two isotopic counterparts share an identical shape (or, in the case of highly-compressed superconductors, the same material at different pressures), then within electron-phonon phenomenology, these materials should obey the relation of Tθ,1/Tθ,2 = Tc,1/Tc,2 = ωln,1/ωln,2 (where subscripts 1 and 2 designate two isotopic counterparts). We further report that H3S-D3S pair ratios of Tc,H3S/Tc,D3S = ωln,H3S/ωln,D3S = 1.27 are largely different from deduced Tθ,H3S/Tθ,D3S = 1.65. This implies that NRT superconductivity in H3S-D3S systems originates from more than one mechanism, where the electron-phonon coupling lifts Tc in H3S vs D3S, but the primary origin for the NRT background of Tc ∼ 150 K in both H3S and D3S remains to be discovered.