Quantifying the nonadiabaticity strength constant in recently discovered highly-compressed superconductors

Abstract: Superconductivity in highly-pressurized hydrides became primary direction for the exploration of fundamental upper limit for the superconducting transition temperature, Tc, after Drozdov et al (Nature 2015, 525, 73) discovered superconducting state with $T_c=203 K$ in highly-compressed sulphur hydride. To date several dozens of high-temperature superconducting polyhydrides have been discovered. In addition, recently, it was reported that highly-compressed titanium and scandium exhibit record-high $T_c$ (up to 36 K), which is by manifold exceeded $T_c=9.2 K$ of niobium, which is the record high-$T_c$ ambient pressure metallic superconductor. Here we analysed experimental data on for recently discovered high-pressure superconductors (which exhibit high transition temperatures within their classes): elemental titanium (Zhang et al, Nature Communications 2022; Liu et al, Phys. Rev. B 2022), $TaH_3$ (He et al, Chinese Phys. Lett. 2023), $LaBeH_8$ (Song et al, Phys. Rev. Lett. 2023), and black (Li et al, Proc. Natl. Acad. Sci. 2018) and violet (Wu et al, arXiv 2023) phosphorous, to reveal the nonadiabaticity strength constant, $T_{\theta}/T_F$ (where $T_{\theta}$ is the Debye temperature, and $T_F$ the Fermi temperature) in these superconductors. The analysis showed that ${\delta}$-phase of titanium and black phosphorous exhibit the $T_{\theta}/T_F$ which are nearly identical to ones associated in A15 superconductors, while studied hydrides and violet phosphorous exhibit the constants in the same ballpark with $H_3S$ and $LaH_{10}$.