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Physical review. B, Condensed matter

Anyonic superconductivity in a modified large-UHubbard model

Asim Gangopadhyaya, Prasanta Kumar Panigrahi

Published Nov 1, 1991• 2 citations
Publisher

Abstract

A modified large-U Hubbard model at half filling is analyzed by a mean-field approach. Preserving a local U(1) symmetry of the action, the fluctuations about half filling are studied in the spirit of the commensurate-flux-phase condition. The fluctuations then contribute a Chern-Simons term to the tree-level Lagrangian with a coefficient appropriate to that of a half fermion. With the Coulomb repulsion term, we study the low-energy excitations of the model and show the existence of superconductivity in the presence of a four-Fermi interaction term.

DOI
10.1103/physrevb.44.9749

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A modified large-U Hubbard model at half filling is analyzed by a mean-field approach. Preserving a local U(1) symmetry of the action, the fluctuations about half filling are studied in the spirit of the commensurate-flux-phase condition. The fluctuations then contribute a Chern-Simons term to the tree-level Lagrangian with a coefficient appropriate to that of a half fermion. With the Coulomb repulsion term, we study the low-energy excitations of the model and show the existence of superconductivity in the presence of a four-Fermi interaction term.
We show how it is possible to include the constraint of single site-occupancy in the large U limit of the Hubbard model at half-filling by means of a local chemical potential. The formalism which is in principle exact allows for finite temperature mean field results satisfying the constraint within 10%. The method is here applied to the dimerized phase and the commensurate flux phase which are still found as local saddle points of the action. The symmetry properties of these actions have been studied. One loop static corrections have been added to obtain an effective free energy and an estimate of the specific heat. In the limit of zero temperature our results reproduce those of the conventional mean field theory of these phases, because quantum fluctuations have not been included. We find that the temperature destabilizes the flux phase more than it does with the dimer phase, especially due to the constraint, which does not suppress phase fluctuating modes, provided the flux is conserved.
We exhibit an additional SU(2) symmetry of the Hubbard model at half-filling, which suggests a simple physical manifestation of this symmetry in the presence of an applied magnetic field. The system governed by a negative-U Hubbard Hamiltonian will lose its superconductivity at an applied magnetic field well below the critical Hc{\mathit{H}}_{\mathit{c}}Hc​ associated with a conventional superconductor. Though departure from half-filling and the inclusion of a repulsive nearest-neighbor interaction break this symmetry, the above physical effect should still persist strongly and is indicative of a new type of SU(2) superconductor for the negative-U or attractive on-site Hubbard model.
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The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.
We investigate the fermionic SU(N) Hubbard model on the two-dimensional square lattice for weak to moderate interactions using renormalization group and mean-field methods. For the repulsive case U>0 at half filling and small N the dominant tendency is towards breaking of the SU(N) symmetry. For N>6 staggered flux order takes over as the dominant instability, in agreement with the large-N limit. Away from half filling for N=3 two flavors remain half filled by cannibalizing the third flavor. For U<0 and odd N a full Fermi surface coexists with a superconductor. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.
The search for realistic one-dimensional (1D) models that exhibit dominant superconducting (SC) fluctuations effects has a long history. In these 1D systems, the effects of commensurate band fillings---strongest at half-filling---and electronic repulsions typically lead to a finite charge gap and the favoring of insulating density wave ordering over superconductivity. Accordingly, recent proposals suggesting a gapless metallic state in the Holstein-Hubbard (HH) model, possibly superconducting, have generated considerable interest and controversy, with the most recent work demonstrating that the putative dominant superconducting state likely does not exist. In this paper we study a model with nonlocal electron-phonon interactions, in addition to electron-electron interactions. This model unambiguously possesses dominant superconducting fluctuations at half filling in a large region of parameter space. Using both the numerical multi-scale functional renormalization group (MFRG) for the full model and an analytic conventional renormalization group for a bosonized version of the model, we demonstrate the existence of these dominant SC fluctuations and show that they arise because the spin-charge coupling at high energies is weakened by the nonlocal electron-phonon interaction and the charge gap is destroyed by the resultant suppression of the Umklapp process. The existence of the dominant SC pairing instability in this half-filled 1D system suggests that nonlocal boson-mediated interactions may be important in the superconductivity observed in the organic superconductors.