Cuprate High Temperature Superconductors and the Vision for Room Temperature Superconductivity

Superconducting transition temperatures of 164 K in cuprate high temperature superconductors (HTS) and recently 200 K in H3S under high pressure encourage us to believe that room temperature superconductivity (RTS) might be possible. In considering paths to RTS, we contrast conventional (BCS) SC, such as probably manifested by H3S, with the unconventional superconductivity (SC) in the cuprate HTS family. Turning to SC models, we show that in the presence of one or more van Hove singularities (vHs) near the Fermi level, SC mediated by classical phonons (k(B)T(c) > (h) over bar x phonon frequency) can occur. The phonon frequency in the standard T-c formula is replaced by an electronic cutoff, enabling a much higher T-c independent of phonon frequency. The resulting T-c and isotope shift plot versus doping strongly resembles that seen experimentally in HTS. A more detailed theory of HTS, which involves mediation by classical phonons, satisfactorily reproduces the chief anomalous features characteristic of these materials. We propose that, while a path to RTS through an H3S-like scenario via strongly-coupled ultrahigh frequency phonons is attractive, features perhaps unavailable at ordinary pressures, a route involving SC mediated by classical phonons which can be low frequency may be found.