Unified theory of colossal magnetoresistance in manganites and high temperature superconductivity in cuprates

The bipolaron theory of superconductivity provides a parameter-free fit of the superconducting critical temperature and the upper critical field of cuprates, It describes their non-Fermi-liquid normal state, including the in-plane and out-of-plane resistivity, Hall effect, magnetic susceptibility and tunnelling and photoemission spectra. The theory is based on the experimental fact that the electron-phonon interaction in doped oxides is the largest one. We show that the same interaction together with the p-d exchange interaction explains the ferromagnetism and colossal magnetoresistance (CMR) of doped manganites as a result of the pairing Df polaronic carriers in the paramagnetic phase and a pair-breaking effect in the ferromagnetic phase. The theory is largely independent of the type of the electron-phonon interaction and the size of bipolarons and, in addition to perovskite manganites, applies to pyrochlore manganites where the Jahn-Teller phonons and double-exchange mechanism are absent. It accounts for the de and ac colossal magnetoresistivity, for low mobility, for the sudden spectral weight transfer with temperature in the optical conductivity and photoemission, for a strongly suppressed Drude weight in the ferromagnetic phase, and for the giant isotope effect. The theory suggests that by replacing the magnetic ions of Mn by nonmagnetic Cu one can turn a doped charge-transfer magnetic insulator into a high-temperature superconductor owing to the Bose-Einstein condensation of bipolarons as observed in cuprates.