Superconductivity above the lowest Earth temperature in pressurized sulfur hydride

Abstract: A recent experiment has shown a macroscopic quantum coherent condensate at 203 K, about 19 degrees above the coldest temperature recorded on the Earth, 184 K, in pressurized sulfur hydride. This discovery is relevant not only in material science and condensed matter but also in other fields ranging from quantum computing to quantum physics of living matter. It has given the start to a gold rush looking for other macroscopic quantum coherent condensates in hydrides at the temperature range of living matter 200<Tc<400K. We present here a review of the experimental results and the theoretical works and we discuss the Fermiology of H3S focusing on Lifshitz transitions as a function of pressure. We discuss the possible role of the shape resonance near a neck disrupting Lifshitz transition, in the Bianconi-Perali Valletta (BPV) theory, for rising the critical temperature in a multigap superconductor, as the Feshbach resonance rises the critical temperature in Fermionic ultracold gases.