First-principles study of the pressure and crystal-structure dependences of the superconducting transition temperature in compressed sulfur hydrides

We calculate the superconducting transition temperatures (${T}_{\mathrm{c}}$) in sulfur hydrides ${\text{H}}_{2}\text{S}$ and ${\text{H}}_{3}\text{S}$ from first principles using the density functional theory for superconductors. At pressures of $\ensuremath{\lesssim}150$ GPa, the high values of ${T}_{\mathrm{c}}$ ($\ensuremath{\ge}130$ K) observed in a recent experiment (A. P. Drozdov, M. I. Eremets, and I. A. Troyan, arXiv:1412.0460) are accurately reproduced by assuming that ${\text{H}}_{2}\text{S}$ decomposes into $R3m$ ${\text{H}}_{3}\text{S}$ and S. For higher pressures, the calculated ${T}_{\mathrm{c}}$'s for $Im\overline{3}m$ ${\text{H}}_{3}\text{S}$ are systematically higher than those for $R3m$ ${\text{H}}_{3}\text{S}$ and the experimentally observed maximum value (190 K), which suggests the possibility of another higher-${T}_{\mathrm{c}}$ phase. We also quantify the isotope effect from first principles and demonstrate that the isotope effect coefficient can be larger than the conventional value (0.5) when multiple structural phases energetically compete.