Resonant multi-gap superconductivity at room temperature near a Lifshitz topological transition in sulfur hydrides

The maximum critical temperature for superconductivity in pressurized hydrides appears at the top of superconducting domes in T c vs pressure curves at a particular pressure, which is not predicted by standard superconductivity theories. The high-order anisotropic Van Hove singularity near the Fermi level observed in band-structure calculations of pressurized sulfur hydride, typical of a supermetal, has been associated with the array of metallic hydrogen wire modules forming a nanoscale heterostructure at an atomic limit called the superstripe phase. Here, we propose that pressurized sulfur hydrides behave as a heterostructure made of a nanoscale superlattice of interacting quantum wires with a multicomponent electronic structure. We present first-principles quantum calculation of a universal superconducting dome where T c amplification in multi-gap superconductivity is driven by the Fano-Feshbach resonance due to a configuration interaction between open and closed pairing channels, i.e., between multiple gaps in the BCS regime, resonating with a single gap in the BCS-Bose-Einstein condensation crossover regime. In the proposed three dimensional phase diagram, the critical temperature shows a superconducting dome where T c is a function of two variables: (i) the Lifshitz parameter ( eta) measuring the separation of the chemical potential from the Lifshitz transition normalized by the inter-wire coupling and (ii) the effective electron-phonon coupling (g) in the appearing new Fermi surface including phonon softening. The results will be of help for material design of room-temperature superconductors at ambient pressure.