High temperature superconductivity due to the long-range electron-phonon   interaction, application to isotope effects, thermomagnetic transport and   nanoscale heterogeneity in cuprates
  Strong electron-phonon interactions in cuprates and other high-temperature superconductors have gathered support over the last decade in a large number of experiments. Here I briefly introduce the Froehlich-Coulomb multi-polaron model of high-temperature superconductivity, which includes strong on-site repulsive correlations and the long-range Coulomb and electron-phonon (e-ph) interactions. Our extension of the BCS theory to the strong-coupling regime with the long-range \emph{unscreened} electron-phonon interaction could naturally explain the isotope effects, unconventional thermomagnetic transport, and checkerboard modulations of the tunnelling density of states in cuprates. 
A. S. Alexandrov