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Debye temperature in LaHx-LaDy superconductors

The Debye temperature, T${_θ}$=(h/2$π$)/k${_B}$$ω$$_θ$, where the Debye frequency $ω$$_θ$ is integrated characteristic frequency of full phonon spectrum, $α$$^2$($ω$)F($ω$). In the BCS theory, T${_θ}$ in conjunction with electron-phonon coupling strength parameter, $λ$$_{e-ph}$, determines the superconducting transition temperature, Tc. Despite a fact that more accurate theory of electron-phonon mediated superconductivity requires the knowledge of full phonon spectrum, $α$$^2$($ω$)F($ω$), which can be very accurately computed by first principles calculation technique, there is no experimental technique which can measure $α$$^2$($ω$)F($ω$) in highly-compressed near-room-temperature (NRT) superconductors. Thus, $ω$$_θ$ remains to be the only measurable parameter of full phonon spectrum, $α$$^2$($ω$)F($ω$), which can be deduced by the fit of experimental temperature-dependent resistance data, R(T), to Bloch-Grüneisen equation. Taking in account that within electron-phonon mediated theory of superconductivity two isotopic counterparts (or, in case of NRT superconductors, the same superconducting phase at different pressures), designated by subscripts of 1 and 2, should be obey the relation of T${_θ}_1$/T${_θ}_2$=T${_c}_1$/T${_c}_2$, there is a way to reaffirm/disprove the electron-phonon mechanism of NRT superconductivity. In this paper, we perform the analysis for R3m-phase of H3S at different pressure, as well as for several superconductors in LaHx-LaDy system and show that there is a large disagreement between experimental data and T${_θ}_1$/T${_θ}_2$=T${_c}_1$/T${_c}_2$. Taking in account that similar disagreement has recently reported in H3S-D3S system, it can be concluded that primary origin for NRT superconductivity remains to be discovered.