Polaron dynamics and bipolaron condensation in cuprates

Based on the exact cluster diagonalization and recent Quantum Monte Carlo simulations we analyze dynamic properties of small polarons and bipolarons formed by short-range (Holstein) and long-range (Frohlich) electron-phonon interactions. We show that the exact results agree well with canonical Holstein theory for a cluster and with Lang-Firsov theory for a lattice. Lang-Firsov theory of a single polaron and our 1/lambda perturbation expansion for a multipolaron system are practically exact in a wide range of the adiabatic parameter omega/t and the electron-phonon coupling lambda for a long-range interaction. (Bi)polarons exist in the itinerant Bloch states at temperatures below the characteristic phonon frequency no matter which values the parameters of the system take. We show that recent claims by several authors with regards to a breakdown of Holotstein-Lang-Firsov theory of a small polaron and the impossibility of bipolaronic superconductivity are the result of an erroneous interpretation of the electronic energy levels of the two-site Holstein model and a misunderstanding of the electron-phonon interaction in ionic solids with polaronic carriers. A phase diagram in t/omega-lambda space is proposed to elucidate the BCS and (bi)polaronic domains. Bipolaron theory provides a parameter-free expression for the superconducting critical temperature of layered cuprates. Crystallization of the (bi)polaronic liquid is shown to;be impossible in the range of the parameters typical for cuprates. The small Frohlich polaron has spectral features compatible with single-particle tunneling and photoemission in cuprates.