Superconducting Polarons and Bipolarons
  The BCS theory has been extended by us to the strong-coupling regime where carriers are small lattice polarons and bipolarons. Here I review the multi-polaron strong-coupling theory of superconductivity. Attractive electron correlations, prerequisite to any superconductivity, are caused by an almost unretarded electron-phonon interaction sufficient to overcome the direct Coulomb repulsion in this regime. Low energy physics is that of small polarons and bipolarons, which are itinerant quasiparticles existing in the Bloch states at temperatures below the characteristic phonon frequency. I identify the long-range Froehlich electron-phonon interaction with c-axis polarised optical phonons as the most essential for pairing in superconducting cuprates. A number of key observations have been predicted or explained with polarons and bipolarons including unusual isotope effects and upper critical fields, normal state (pseudo)gaps, kinetic properties and diamagnetism, and giant proximity effects. These and some other observations provide strong evidence for a novel state of electronic matter in layered cuprates, which is a charged Bose-liquid of small mobile bipolarons. 
A. S. Alexandrov