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 (Tc) in sulfur hydrides H₂S and H₃S from first principles using the density functional theory for superconductors. At pressures of 150 GPa, the high values of Tc (≥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 H₂S decomposes into $R3m$ H₃S and S. For higher pressures, the calculated Tc's for Im3̄m H₃S are systematically higher than those for $R3m$ H₃S and the experimentally observed maximum value (190 K), which suggests the possibility of another higher-Tc 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.