Superconducting Polarons and Bipolarons

Abstract

The seminal work by Bardeen, Cooper and Schrieffer (BCS) extended further by Eliashberg to the intermediate coupling regime solved one of the major scientific problems of Condensed Matter Physics in the last century. The BCS theory provides qualitative and in many cases quantitative descriptions of low-temperature superconducting metals and their alloys, and some novel high-temperature superconductors like magnesium diboride. The 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 (e-ph) interaction sufficient to overcome the direct Coulomb repulsion in this regime. Low energy physics is that of small polarons and bipolarons, which are real-space electron (hole) pairs dressed by phonons. They are itinerant quasiparticles existing in the Bloch states attemperatures below the characteristic phonon frequency. Since there is almost no retardation (i.e. no Tolmachev–Morel–Anderson logarithm) reducing the Coulomb repulsion, e-ph interactions should be relatively strong to overcome the direct Coulomb repulsion, so carriers mustbe polaronic to form pairs in novel superconductors. I identify the long-range Fröhlich electron-phonon interaction 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 and kinetic properties, normal state diamagnetism, and giant proximity effects. These and many 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.