The Fröhlich-Coulomb model of high-temperature superconductivity and charge segregation in the cuprates

We introduce a generic Fröhlich-Coulomb model of the oxides, which also includes infinite on-site (Hubbard) repulsion, and describe a simple analytical method of solving the multi-polaron problem in complex lattice structures. Two particular lattices, a zigzag ladder and a perovskite layer, are studied. We find that, depending on the relative strength of the Fröhlich and Coulomb interactions, these systems are either polaronic Fermi (or Luttinger) liquids, bipolaronic superconductors, or charge-segregated insulators. In the superconducting phase the carriers are superlight mobile bipolarons. The model describes key features of the cuprates such as their T c -values, the isotope effects, the normal-state diamagnetism, the pseudogap, and spectral functions measured in tunnelling and photoemission. We argue that a low Fermi energy and strong coupling of carriers with high-frequency phonons is the cause of high critical temperatures in novel superconductors.