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Physical Review Letters

Odd-parity singlet pairing in the positive-UHubbard model

Richard T. Scalettar, Rajiv R. P. Singh, Shoucheng Zhang

Published Jul 15, 1991• 25 citations
Publisher

Abstract

We consider the possibility of an odd-parity singlet pairing in the positive-U Hubbard model, which naturally incorporates short-ranged antiferromagnetic correlations in the ground state. In a quantum Monte Carlo simulation of a nearly half-filled Hubbard model, we find that the repulsive U enhances the tendency for this type of pairing more strongly than for other pairing channels considered earlier. We propose a BCS-type wave function for this pairing where the gap has no nodes over the Fermi surface, and discuss various experimental consequences in connection to high-${\mathit{T}}_{\mathit{c}}$ superconductivity.

DOI
10.1103/physrevlett.67.370

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We consider the possibility of an odd-parity singlet pairing in the positive-U Hubbard model, which naturally incorporates short-ranged antiferromagnetic correlations in the ground state. In a quantum Monte Carlo simulation of a nearly half-filled Hubbard model, we find that the repulsive U enhances the tendency for this type of pairing more strongly than for other pairing channels considered earlier. We propose a BCS-type wave function for this pairing where the gap has no nodes over the Fermi surface, and discuss various experimental consequences in connection to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductivity.
We show that superconductive pairing is possible in the presence of an arbitrarily strong short-range repulsion between electrons if the gap is an odd function of k-kF{\mathit{k}}_{\mathit{F}}kF​. We discuss how the behavior of \ensuremath{\Delta}(k-kF{\mathit{k}}_{\mathit{F}}kF​) close to the Fermi surface is related to (i) the low-energy tunneling density of states, and (ii) the attractive part of the potential. We show that some features of the tunneling data in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates, including the fact that the maximum hardly moves when T approaches Tc{\mathit{T}}_{\mathit{c}}Tc​, are natural consequences of this type of 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.
We have studied the behavior of pairing correlations and susceptibilities in the repulsive Hubbard model on a two-dimensional square lattice by Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8, temperatures down to T=0.083 (in units where the bandwidth W=8), interaction strengths up to U=16, and several band fillings ranging from (1/2-filled to (1/4-filled were considered. Our results suggest that the model does not exhibit superconductivity. The implications with respect to possible mechanisms for high-Tc{T}_{c}Tc​ superconductivity in oxides are discussed.
Quantum Monte Carlo simulations are used to explore the phase diagram of the negative-U Hubbard model. As the system is doped away from half filling, 〈n〉=1, the s-wave pair-field correlations are enhanced and the charge-density-wave correlations suppressed. There is no indication of phase separation. Away from half filling, the pair-field correlations are consistent with Kosterlitz-Thouless scaling and a finite Tc{\mathit{T}}_{\mathit{c}}Tc​ which peaks near 〈n〉=1 but vanishes at exactly half filling.
An extended Hubbard model for a single band, including Coulomb repulsion and correlated hopping between nearest neighbors, is studied using a generalized mean-field approach. Antiferromagnetism and superconductivity are probed for arbitrary occupation number, near and away from half filling. Binding of pairs in the superconducting state of this purely repulsive model is mediated by the correlated hopping in the form of a covalent-bond configuration, with partial intrasite and intersite pairings. A region of coexistence is conjectured, the superconductivity being suppressed by the saturation of the staggered magnetic moment. Singlet superconducting nonmagnetic states are obtained for the almost-empty- or full-band cases. On the other hand, antiferromagnetism induces mixed s- and p-type superconductivities in the neighborhood of half filling.
The quantum Monte Carlo method is used to reexamine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a ``correlated pairing,'' 〈c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\uparrow}}}$c-${\mathrm{tilde}}_{{\mathrm{i}}^{|\mathrm{I}\mathrm{H}}\mathrm{\ensuremath{\downarrow}}}$〉 with c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\equiv}${\mathrm{c}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$(1-${\mathrm{n}}_{\mathrm{i}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$), which is inferred from the t-J model, the strong-coupling limit of the Hubbard model. The pairing in the d-wave channel is found to possess both a divergence like 1/T in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.