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Advances in Condensed Matter Physics
Volume 2010 (2010), Article ID 752943, 36 pages
Review Article

Antiadiabatic Theory of Superconducting State Transition: Phonons and Strong Electron Correlations—The Old Physics and New Aspects

Chemical Physics Division, Institute of Chemistry, Faculty of Natural Science, Comenius University, Mlynská dolina CH2, 84215 Bratislava, Slovakia

Received 31 May 2009; Accepted 3 September 2009

Academic Editor: Sasha Alexandrov

Copyright © 2010 Pavol Baňacký. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Complex electronic ground state of molecular and solid state system is analyzed on the ab initio level beyond the adiabatic Born-Oppenheimer approximation (BOA). The attention is focused on the band structure fluctuation (BSF) at Fermi level, which is induced by electron-phonon coupling in superconductors, and which is absent in the non-superconducting analogues. The BSF in superconductors results in breakdown of the adiabatic BOA. At these circumstances, chemical potential is substantially reduced and system is stabilized (effect of nuclear dynamics) in the antiadiabatic state at broken symmetry with a gap(s) in one-particle spectrum. Distorted nuclear structure has fluxional character and geometric degeneracy of the antiadiabatic ground state enables formation of mobile bipolarons in real space. It has been shown that an effective attractive e-e interaction (Cooper-pair formation) is in fact correction to electron correlation energy at transition from adiabatic into antiadiabatic ground electronic state. In this respect, Cooper-pair formation is not the primary reason for transition into superconducting state, but it is a consequence of antiadiabatic state formation. It has been shown that thermodynamic properties of system in antiadiabatic state correspond to thermodynamics of superconducting state. Illustrative application of the theory for different types of superconductors is presented.