Structural and superconducting parameters of highly compressed sulfur

Abstract

Sulfur was the first nonmetal element which was transformed to a superconductor by applying megabar pressure. Recent pioneering experimental developments in measuring the superconducting energy gap $\Delta(T)$ in compressed sulfur using tunneling spectroscopy (Du $\textit{et al}$., $\textit{Phys. Rev. Lett.}$ $\textbf{133}$, 036002 (2024)) initiated an interest in better understanding real atomic structure and superconducting properties of this element at high pressure. Here, we analyzed available experimental data on highly compressed sulfur, and, from the $\Delta(T)$ data reported by Du $\textit{et al}$. (2024), we extracted the specific heat jump at the transition temperature of ${\Delta}C_{el}/{\gamma}T_{c} = 1.8$. We also developed a model to extract the Debye temperatures ${\Theta}_D$ for sulfur and $H_{3}S$ in two-phases sample from the temperature-dependent resistance $R(T)$. for better understanding of material structure, here we proposed to use a size-strain map for highly compressed samples, and we revealed this size-strain map for laser-heated sulfur in a diamond anvil cell with a mixture of sulfur and $H{_3}S$. Finally, we found that superconducting sulfur exhibits a moderate level of nonadiabaticity $0.04 \leq {\Theta}_{D}/T_{F} \leq 0.15$ (where $T_{F}$ is the Fermi temperature), which is similar to $MgB_2$, pnictides, cuprates, $La_{4}H_{23}$, $ThH_{9}$, $H_{3}S$, $LaBeH_{8}$, and $LaH_{10}$.