Possible "Magn\'eli" phases and self-alloying in the superconducting sulfur hydride

We theoretically give an infinite number of metastable crystal structures for the superconducting sulfur hydride H${}_x$S under pressure. It has been thought that theoretically predicted structures of H${}_2$S and H${}_3$S exhibit low and high $T_{\mathrm{c}}$ in the experiment, respectively. The newly found structures are long-period modulated crystals where slab-like H${}_2$S and H${}_3$S regions intergrow in a microscopic scale. The extremely small formation enthalpy for the H${}_2$S–H${}_3$S boundary indicated with the first-principles calculations suggests possible alloying of these phases through formation of local H${}_3$S regions. The modulated structures and gradual alloying transformations between them not only explain the peculiar pressure dependence of $T_{\mathrm{c}}$ in sulfur hydride observed experimentally, but also could prevail in the experimental samples under various compression schemes.