Competition between Electron-Phonon coupling and Spin Fluctuations in superconducting hole-doped BiOCuS

BiOCuS is a band insulator that becomes metallic upon hole doping. Superconductivity was recently reported in doped BiOCu$_{1-x}$S and attributed to spin fluctuations as a pairing mechanism. Based on first principles calculations of the electron-phonon coupling, we argue that the latter is very strong in this material, and probably drives superconductivity, which is however strongly depressed by the proximity to magnetism. We find however that BiOCu$_{1-x}$S is a quite unique compound where both a conventional phonon-driven and an unconventional triplet superconductivity are possible, and compete with each other. We argue that, in this material, it should be possible to switch from conventional to unconventional superconductivity by varying such parameters as doping or pressure.