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Emerets’s experiments on pressurized sulfur hydride have shown that H3S metal has the highest known superconducting critical temperature Tc = 203 K. The Emerets data show pressure induced changes of the isotope coefficient between 0.25 and 0.5, in disagreement with Eliashberg theory which predicts a nearly constant isotope coefficient.We assign the pressure dependent isotope coefficient to Lifshitz transitions induced by pressure and zero point lattice fluctuations. It is known that pressure could induce changes of the topology of the Fermi surface, called Lifshitz transitions, but were neglected in previous papers on the H3S superconductivity issue. Here we propose thatH3S is a multi-gap superconductor with a first condensate in the BCS regime (located in the large Fermi surface with high Fermi energy) which coexists with second condensates in the BCS-BEC crossover regime (located on the Fermi surface spots with small Fermi energy) near the and Mpoints.We discuss the Bianconi-Perali-Valletta (BPV) superconductivity theory to understand superconductivity in H3S since the BPV theory includes the corrections of the chemical potential due to pairing and the configuration interaction between different condensates, neglected by the Eliashberg theory. These two terms in the BPV theory give the shape resonance in superconducting gaps, similar to Feshbach resonance in ultracold fermionic gases, which is known to amplify the critical temperature. Therefore this work provides some key tools useful in the search for new room temperature superconductors.

Lifshitz transitions and zero point lattice fluctuations in sulfur hydride showing near room temperature superconductivity