  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.
