Multigap superconductivity at extremely high temperature: a model for   the case of pressurized H2S
  It is known that in pressurized H2S the complex electronic structure in the energy range of 200 meV near the chemical potential can be separated into two electronic components, the first characterized by steep bands with a high Fermi velocity and the second by flat bands with a vanishing Fermi velocity. Also the phonon modes interacting with electrons at the Fermi energy can be separated into two components: hard modes with high energy around 150 meV and soft modes with energies around 60 meV. Therefore we discuss here a multiband scenario in the standard BCS approximation where the effective BCS coupling coefficient is in the range 0.1- 0.32. We consider a first (second) BCS condensate in the strong (weak) coupling regime 0.32 (0.15). We discuss different scenario segregated in different portions of the material. The results show the phenomenology of unconventional superconducting phases in this two-gap superconductivity scenario where there are two electronic components in two Fermi surface spots, the pairing is mediated by either by a soft or a hard phonon branch where the inter-band exchange term, also if small, plays a key role for the emergence of high temperature superconductivity in pressurized sulfur hydride. 
A. Bussmann-Holder, J. Kohler, A. Simon, M. Whangbo, A. Bianconi
cond-mat.str-el