A simple physical picture of superconductivity is proposed for extremely doped CuO2 planes. It possesses features that are observed for HTSC, such as a high superconducting transition temperature, 
$$d_{x^2 - y^2 } $$

 the symmetry of order parameter, and the coexistence of a one-electron Fermi surface and the Bose-Einstein condensate of preformed electron pairs.

Electron pairs for HTSC

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.

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

Ab initio theory of complex electronic ground state of superconductors: I. Nonadiabatic modification of the Born-Oppenheimer approximation

The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The ground-state (GS) and excited-state energies of the Frohlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck–Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given.

Ground and Excited States of Bipolarons in Two and Three Dimensions

The authors used Landau-Pekar variational method to investigate a strong-coupling singlet optical bipolaron in different configuration of quantum confinement. Numerical and analytical results showed that when configuration changes from quantum dot and wire to well, confinement shows different effect on the formation of a bipolaron. In contrast to a bipolaron in a quantum dot or wire, the binding energy of a bipolaron in a quantum well increases with increasing confinement, indicating that confinement favors bipolaron formation in a quantum well.

Bipolaron in different configuration of quantum confinement.

Over the last decade, several competing models of high-temperature superconductivity (HTSC) were proposed, none of which have succeeded to explain high values of the superconducting critical temperature T c without adjustable parameters. Most of the proposed models are based on the short-range electron-electron interaction or/and on a short-range electron-phonon interaction. Here we propose a model of HTSC which explicitly takes into account the long-range origin of both types of interaction. Remarkably, the long-range electron-phonon interaction binds carriers into superlight real-space pairs-bipolarons-with a relatively low mass but sufficient binding energy. The model quantitatively explains high T c values without any fitting parameters and other key features of the cuprates.

P. E. Kornilovitch

Papers

Superlight Bipolarons Explain the High Superconducting Temperature