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Physical review. B, Condensed matter

Superconducting correlations in the one-band Hubbard model with intermediate on-site and weak attractive intersite interactions

K. P. Jain, R. Ramakumar, C. C. Chancey

Published Dec 1, 1990• 9 citations
Publisher

Abstract

In this paper, we analyze a simple extended Hubbard model with an intermediate on-site interaction (both repulsive and attractive) and a weak intersite attractive interaction. Following Hubbard decoupling approximations and introducing Hubbard subband operators, we obtain a generalized gap function for singlet s-wave pairing that explicitly depends on the Hubbard subband energies. For the on-site repulsive-interaction case, we find that the superconductivity is not destroyed in the intermediate-interaction regime, contrary to the prediction of a Hartree-Fock mean-field treatment. The essential consequence of the on-site repulsion is the formation of the Hubbard subbands separated by the Mott-Hubbard gap, and it is within these subbands that pairing induced by the intersite interaction occurs. For the attractive on-site interaction case, the on-site pairing amplitude is found to be proportional to the bandwidth, and the gap function has contributions from both on-site and intersite pairing. The relevance of the model to high-temperature superconductivity is discussed.

DOI
10.1103/physrevb.42.9896

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In this paper, we analyze a simple extended Hubbard model with an intermediate on-site interaction (both repulsive and attractive) and a weak intersite attractive interaction. Following Hubbard decoupling approximations and introducing Hubbard subband operators, we obtain a generalized gap function for singlet s-wave pairing that explicitly depends on the Hubbard subband energies. For the on-site repulsive-interaction case, we find that the superconductivity is not destroyed in the intermediate-interaction regime, contrary to the prediction of a Hartree-Fock mean-field treatment. The essential consequence of the on-site repulsion is the formation of the Hubbard subbands separated by the Mott-Hubbard gap, and it is within these subbands that pairing induced by the intersite interaction occurs. For the attractive on-site interaction case, the on-site pairing amplitude is found to be proportional to the bandwidth, and the gap function has contributions from both on-site and intersite pairing. The relevance of the model to high-temperature superconductivity is discussed.
We study superconductivity in the extended Hubbard model with a strong on-site repulsion U and weak attractive density-density interaction Vij{\mathit{V}}_{\mathit{ij}}Vij​. The electron correlation effects, beyond the weak-coupling regime of U, are included approximately by employing Hubbard decoupling approximations. The formulas for superconducting transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ of the present approach are compared to those obtained with the strong-coupling expansion and slave-boson techniques. The methods share some common features. We discuss behavior of Tc{\mathit{T}}_{\mathit{c}}Tc​ for superconducting phases with s- and d-wave symmetry of the superconducting order parameter. In contrast to the mean-field treatment of U, we find that the strong on-site repulsion does not destroy superconductivity induced by ${\mathit{V}}_{\mathit{ij}}$0 even when U\ensuremath{\gg}|${\mathit{V}}_{\mathit{ij}}$|. \textcopyright{} 1996 The American Physical Society.
Abstract Collective excitations in the superconducting state of an extended Hubbard model with an intrasite attraction are investigated using the random phase approximation method. The results for the energy of gapless excitations are consistent with the well known result of Anderson in the limit of weak attraction and the result of the perturbation theory (with respect to the band term) in the limit of strong attraction. Investigating the dependence of the excitation energy on the density of electrons in the band conditions are found of instability of the singlet superconducting state with respect to the disordered state (for attractive intersite interactions) and to the charge ordered superconducting state (for intersite repulsion).
We study the extended Hubbard model with on-site density-density U and intersite pair hopping J interactions, i.e. the Penson-Kolb-Hubbard model.This report focuses mainly on the properties of the model at T ≥ 0 in the case of repulsive J (J < 0) which may stabilize superconductivity with η-pairing.The analysis is performed within the (broken symmetry) Hartree-Fock approximation for arbitrary interaction parameters (J < 0 and U ) and electron concentration (0 < n < 2) on the d = 2 square lattice.The phase diagrams of the model at T = 0 and at finite temperatures are examined taking into account magnetic and charge-ordered phases and superconducting states with η-and s-wave pairing.
A theoretical study of BCS pairing in an extended Hubbard model with on-site repulsion (U) and a BCS pairing field (V) is presented. Treating the effect of U in the Gutzwiller approximation, we study the effect of increasing U in the Fermi-liquid phase, on the BCS pairing due to V. It is found that the superconducting energy gap (\ensuremath{\Delta}) is strongly enhanced in the correlated metallic phase near half-filling of the band due to the localization effects of U. Further, the ground state is found to be superconducting even when \ensuremath{\Vert}V\ensuremath{\Vert}U, contrary to the prediction in a Hartree-Fock treatment.
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.
We study the superfluid properties of short-coherence-length superconductors described by the extended Hubbard model with on-site repulsive and intersite attractive interaction. We have analysed the superfluid stiffness and thermodynamic properties of the model versus electron concentration and pairing interaction on a two-dimensional square lattice with nearest- and next-nearest-neighbour hopping. The effects of phase fluctuations on anisotropic superconductivity of extended s-and d x 2 − y 2 -wave type were examined within the Kosterlitz–Thouless (KT) scenario. The KT critical temperatures were determined and compared with those from the BCS–Hartree–Fock approximation. The Uemura-type plots, i.e. the critical temperature versus zero-temperature phase stiffness, were obtained for both extended s- and d-wave pairings. The states with mixed (s ∗ and d x 2 − y 2 ) symmetry, and in particular the time-reversal breaking state of s + id symmetry, were analysed and the phase diagrams taking into account these states are presented. We also briefly discuss the crossover from BCS to local pair superconductivity for the d x 2 − y 2 -wave pairing. A comparison of the theoretical results with the experimental data, in particular those of T c versus λ −2 (0), for high- T c cuprate superconductors is made.