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.

中文翻译：

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高级麦克米兰方程及其在高压缩超导体分析中的应用

电子-声子介导的超导理论需要全声子光谱的知识来计算超导转变温度 T$_c$。然而，迄今为止，还没有可以测量高压缩近室温 (NRT) 超导体中声子谱的实验技术。在本文中，我们建议推进 McMillan 的方法 (1968 Phys Rev 167 331)，该方法利用德拜温度 T$_{\theta}$（全声子光谱的综合参数），我们通过实验测量温度的拟合推导出依赖电阻数据 R(T) 对高度压缩黑磷、硼、GeAs、SiH$_4$、H$_x$S、D$_y$S、LaH$_x$ 和 LaD$ 的 Bloch-Gruneisen 方程_y$。利用T$_c$、德拜温度和电子-声子耦合强度常数之间的关系，$\lambda_{e-ph}$ 可以肯定/反驳给定超导体中的电子-声子机制。我们表明，为高度压缩的黑磷、硼、GeAs、SiH$_4$ 和 LaH$_{10}$ 的一个样本计算的 $\lambda_{e-ph}$ 与 $\lambda_{ 非常一致从实验数据推导出 e-ph}$ 值。还发现H$_3$S在不同老化阶段的德拜温度具有显着的恒定性。我们还表明，如果两个同位素对应物的声子谱具有相似的形状，那么在电子-声子现象学中，这些材料应遵循 T$_{c,1}$/T$_{c,2}$=T$_ 的关系{\theta,1}$/T$_{\theta,2}$（其中 1 和 2 表示同位素）。我们报告说，这些由电子声子现象学预测的 H$_3$SD$_3$S 的比率与从实验推导出的比率有很大不同。