Room temperature superconductivity dome at a Fano resonance in superlattices of wires

Recently room temperature superconductivity with degrees Celsius has been discovered in a pressurized complex ternary hydride, CSH x , which is a carbon- and hydrogen-doped H3S alloy. The nanoscale structure of H3S is a particular realization of the 1993 patent claim of superlattice of quantum wires for room temperature superconductors and the maximum T C occurs at the top of a superconducting dome. Here we focus on the electronic structure of materials showing nanoscale heterostructures at the atomic limit made of a superlattice of quantum wires like hole-doped cuprate perovskites, and organics focusing on A15 intermetallics and pressurized hydrides. We provide a perspective of the theory of room temperature multigap superconductivity in heterogeneous materials tuned at a shape resonance or Fano resonance in the superconducting gaps near a Lifshitz transition focusing on H3S where the maximum T C occurs where the multiband metal is tuned by pressure near a Lifshitz transition. Here the superconductivity dome of T C vs. pressure is driven by both electron-phonon coupling and contact exchange interaction. We show that the T C amplification up to room temperature is driven by the Fano resonance between a superconducting gap in the anti-adiabatic regime and other gaps in the adiabatic regime. In these cases the T C amplification via contact exchange interaction is the missing term in conventional multiband BCS and anisotropic Migdal-Eliashberg theories including only Cooper pairing.