BIPOLARONS

Cooperative properties of self-localized carriers on a lattice are discussed and reviewed at a fairly basic level with an emphasis on developments of the strong-coupling theory of superconductivity for the interpretation of high-T-c superconductors. Small polaron and bipolaron formation is shown to provide a number of new physical phenomena both in the normal and superconducting states. Two mechanisms of superconductivity are discussed in detail. The first one arises from the Cooper pairing of small polarons in momentum space (polaronic superconductivity) while the second one is due to polaron pairing in real space and analogous to the superfluidity of He-4 (bipolaronic superconductivity). Highly non-adiabatic motion of bipolarons results in fundamental differences of bipolaronic superconductivity with respect to the scs one including its well known strong-coupling generalization. The review covers the theoretical development and some experimental results in the past decade paying special attention to the physical properties of high-T-c oxides and their explanation with (bi)polarons. Basic properties of charged bosons are also considered.