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Physica C Superconductivity

Phonon-mediated pairing correlations in the generalized Hubbard model

J Zieliński, Mariusz Gębarowski, Marcin Mierzejewski, P. Entel

Published Sep 1, 2002• 0 citations
Publisher
DOI
10.1016/s0921-4534(02)01246-7

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A general theory of superconductivity is formulated within the thermodynamic Green function method for various types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models.A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function.By applying the noncrossing approximation for the self-energy, a closed selfconsistent system of equations is obtained, similar to the conventional Eliashberg equations.A brief discussion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given.

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A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting Tc by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-Tc mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.
The Hamiltonian describing a system of strongly correlated electrons coupled to dispersionless phonons was solved numerically for a ring of 8 atoms using the density matrix renormalization group (DMRG) method. It was found that electron correlation and electron-phonon coupling compete against each other, and strong electron correlations suppress the charge-ordered insulating state. This allows extended polarons to form in the strong electron-phonon coupling regime. It is shown that in this regime two polarons may form a pair via phonon mediated charge-fluctuation interaction. Based on the results we propose a novel mechanism of hole pairing. This mechanism could be relevant to High-Tc cuprates.
A general theory of superconductivity is formulated within the thermodynamic Green function method for various types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models.A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function.By applying the noncrossing approximation for the self-energy, a closed selfconsistent system of equations is obtained, similar to the conventional Eliashberg equations.A brief discussion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given.