We have investigated the ground-state properties of a model system with a strong electron-phonon interaction. It is found that as long as the renormalized intersite electron correlation is attractive, a new type of Cooper pairing will occur whether the renormalized on-site electron correlation is repulsive or attractive. Furthermore, we have shown that a new phonon coherent state, named a two-phonon coherent state, must be introduced to serve as the ground state of the phonon subsystem, so that the ground-state energy of the interacting system can be made a stable minimum and an appropriate condensation energy of the superconducting ground state may be obtained. We have performed numerical calculations for the n=1 case.
We have investigated the ground state of an electron-phonon system with strong electron-phonon interaction and a weak on-site Coulomb repulsion using the correlated squeezed-state approach. We have introduced a variational ground state in which the phonon subsystem is in a correlated squeezed state and the electron subsystem is in a superconducting pairing state. In addition to the anharmonicity of each phonon mode induced by the linear coupling with the electrons, the correlated squeezed state is able to take into account the nonlinearity of the induced interaction between different phonon modes beyond the Hartree approximation. Also, with optimal values of the variational parameters this trial state will by construction yield an energy lower than those obtained in previous studies, and thus our variational ansatz is a more stable ground state for this system. Furthermore, in this approximate ground state the reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is considerably weakened. This weakening of the reduction effect should, in turn, affect other physical properties of the system; for instance, it does suggest the possibility of higher critical temperatures for superconductivity in the strong-coupling limit where the superfluidlike bipolaronic superconductivity is supposed to occur.
The understanding of the mechanisms responsible for superconductivity in strongly correlated systems is an interesting and important subject in condensed matter physics. Several theoretical proposals were considered for these systems. The Coulomb interaction between electrons allow a new approach to study this problem. In this paper, we use a usual Hubbard model with a local repulsive interaction to describe a 2D system. The system of equations are solved using the Green's functions method, within a Hubbard-I mean field approximation, which allows to treat the strong interaction limit. We consider both cases of attractive and repulsive interactions and obtain the zero temperature phase diagram of the model. Our results show, in the repulsive case, the existence of a superconducting ground state mediated by the kinetic electronic energy and described by a non-local order parameter. A minimum value of the repulsive interaction
Umin is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature
Tc shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.
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 interaction of strongly correlated electrons with phonons in the framework of the Hubbard-Holstein model is investigated. The electron-phonon interaction is considered to be strong and is an important parameter of the model, in addition to the Coulomb repulsion of electrons and the band filling. This interaction with nondispersive optical phonons is transformed to the problem of mobile polarons using the canonical transformation of Lang and Firsov. We discuss the case where the on-site Coulomb repulsion is exactly canceled by the phonon-mediated attractive interaction. It is suggested that polarons exchanging phonon clouds can lead to polaron pairing and superconductivity. The fact that the frequency of the collective mode of phonon clouds is larger than the bare frequency then determines the superconducting transition temperature.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (
J) and correlated hopping (
K) interaction. Detailed numerical analysis of
s-,
p-, and
d-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (
t) and next-nearest- (
t2) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the
d-wave and the extended
s-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the
tt2 ratio, giving in particular for
t2=0 s-wave (
d-wave) pairing as most favorable in the low (high) density limit, but increasing
t2 can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects
s-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.
The renormalization of the electron-phonon interaction by strong electronic correlations is studied using a one-band Hubbard model with infinite repulsion and nearest (t model) and nearest and second-nearest (tt\ensuremath{'} model) neighbor hopping terms and an on-site electron-phonon coupling. Using Hubbard's X operators and an extension from 2 to N degrees of freedom for the electrons the leading contributions for the electron self-energy and the vertex function in 1/N and the electron-phonon coupling constant are given and numerically evaluated for a square lattice. We find that the momentum dependence of the vertex function depends strongly on doping: For large dopings it is rather weak, with decreasing doping it becomes more and more pronounced leading to a strong reduction of the vertex at larger momentum transfers until, for very small dopings, the vertex essentially consists of a forward scattering peak with a width proportional to the doping. This behavior occurs both in the t and the tt\ensuremath{'} models and also in one dimension where analytic expressions are derived. Correlation effects also change ${\mathrm{\ensuremath{\alpha}}}^{2}$F in general: The full-symmetric component ${\mathrm{\ensuremath{\alpha}}}^{2}$
F1 is in the t model somewhat, in the tt\ensuremath{'} model rather strongly suppressed, especially near half-filling; the other symmetry components ${\mathrm{\ensuremath{\alpha}}}^{2}$
Fi with i=2,...,5 increase strongly with decreasing doping and are of similar magnitude as ${\mathrm{\ensuremath{\alpha}}}^{2}$
F1 near half-filling.Including also direct Coulomb repulsion nontrivial symmetries such as d wave become more stable than the s-wave order parameter below a critical value for the doping even for the considered phonon-mediated superconductivity. Most dramatic, however, is the quenching of the resistivity due to electron-phonon scattering both in the t and the tt\ensuremath{'} models at intermediate and small dopings. This result may explain the absence of phonon features in the experimental transport coefficients of high-
Tc compounds. \textcopyright{} 1996 The American Physical Society.