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It is known that in pressurized H2S the complex electronic structure in theenergy range of 200 meV near the chemical potential can be separated into twoelectronic components, the first characterized by steep bands with a high Fermivelocity and the second by flat bands with a vanishing Fermi velocity. Also thephonon modes interacting with electrons at the Fermi energy can be separatedinto two components: hard modes with high energy around 150 meV and soft modeswith energies around 60 meV. Therefore we discuss here a multiband scenario inthe standard BCS approximation where the effective BCS coupling coefficient isin the range 0.1- 0.32. We consider a first (second) BCS condensate in thestrong (weak) coupling regime 0.32 (0.15). We discuss different scenariosegregated in different portions of the material. The results show thephenomenology of unconventional superconducting phases in this two-gapsuperconductivity scenario where there are two electronic components in twoFermi surface spots, the pairing is mediated by either by a soft or a hardphonon branch where the inter-band exchange term, also if small, plays a keyrole for the emergence of high temperature superconductivity in pressurizedsulfur hydride.

Multigap superconductivity at extremely high temperature: a model for the case of pressurized H2S