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AIP conference proceedings

Electron phonon interaction in high-Tc superconductors

Subhadip Nath, N. S. Mondal, S. K. Bhowmick, Nanda Kumar Ghosh

Published Jan 1, 2013• 0 citations
Publisher

Abstract

An exact diagonalization study of the 2D Hubbard model extended with nearest neighbor (NN) phonon mediated interaction shows an interplay between on-site Coulomb interaction and intersite electron-phonon interaction. Initially, phonon mediated interaction between electrons is suppressed by onsite Coulomb repulsion. But after certain larger strength (depending on U) of phonon mediated interaction there is an effective attraction between electrons which forms onsite bipolaron (S0) and neighboring site bipolaron (S1).

DOI
10.1063/1.4810232

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An exact diagonalization study of the 2D Hubbard model extended with nearest neighbor (NN) phonon mediated interaction shows an interplay between on-site Coulomb interaction and intersite electron-phonon interaction. Initially, phonon mediated interaction between electrons is suppressed by onsite Coulomb repulsion. But after certain larger strength (depending on U) of phonon mediated interaction there is an effective attraction between electrons which forms onsite bipolaron (S0) and neighboring site bipolaron (S1).
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In this paper we have studied the properties of a two-fermion system interacting with the phonon field in the framework of the Holstein Hubbard model in one, two and three dimensions. We have chosen the modified Lang-Firsov variational wave function with on-site and nearest-neighbour lattice distortion for the phonon subsystem to obtain an effective electronic Hamiltonian. This effective electronic Hamiltonian is then solved exactly to obtain the binding energy and effective mass of the bipolaron. We investigated the stability of the bipolaronic phase by comparing the ground-state energy of a bipolaron and two free polarons. We observed a critical repulsive on-site Hubbard interaction U c below which the bipolaronic phases are stable for a fixed electron-phonon coupling g . In the absence of on-site repulsion, bipolaronic phases are stable over the entire range of electron-phonon coupling for one dimension, whereas there is a critical electron-phonon coupling g c for formation of a stable bipolaron in two and three dimensions.
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.