High temperature superconductivity due to a long-range electron-phonon interaction, application to isotope effects, thermomagnetic transport and nanoscale heterogeneity in cuprates

Strong electron-phonon (e-ph) interaction in cuprates and other high-temperature superconductors has gathered support over the last decade in a large number of experiments. I briefly review the Frohlich-Coulomb multi-polaron model of high-temperature superconductivity, which includes strong onsite repulsive correlations and the long-range Coulomb and e-ph interactions. The extension of the BCS theory to the strong-coupling regime with a long-range unscreened e-ph interaction naturally explains the isotope effects, unconventional thermomagnetic transport, and checkerboard modulations of the tunnelling density of states (DOS) in cuprates.