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Physical review. B, Condensed matter

SU(2) superconductivity in the negative-UHubbard model

Vikram Soni, J. S. Thakur

Published Nov 1, 1993• 3 citations
Publisher

Abstract

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 ${\mathit{H}}_{\mathit{c}}$ 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.

DOI
10.1103/physrevb.48.12917

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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.
In this paper, we discuss the physical consequences of pseudospin SU(2)-symmetry breaking in a negative-U Hubbard model at half-filling. If pseudospin symmetry is spontaneously broken while its unique subgroup U(1) remains invariant, this will lead to a charge-density-wave (CDW) ground state. Furthermore, if the U(1) symmetry is also broken, the ground state will have off-diagonal long-range order, signalling a superconductor. In this case, CDW and superconductivity coexist and form a supersolid. Finally, we show that CDW suppress, but do not destroy superconductivity.
We study the attractive (i.e., negative-U) Hubbard model with nearest (t) and next-nearest-neighbor (t2{\mathit{t}}_{2}t2​) hopping on a square lattice. A spin-down particle-hole transformation maps the negative-U model at any band filling onto a repulsive model with a magnetic field and at zero chemical potential; the sign of the second-neighbor hopping constant in this model depends on the spin state. For large \ensuremath{\Vert}U\ensuremath{\Vert}, t2{\mathit{t}}_{2}t2​ induces a coupling between spin operators in next-nearest-neighbor sites: antiferromagnetic between the z components and ferromagnetic along the transverse direction. The superconducting transition is investigated through Monte Carlo simulations on the attractive model. Fixing both U and the band filling, we find that the critical temperature increases steadily with t2{\mathit{t}}_{2}t2​.
Symmetries of the Hubbard model in the large-U limit are discussed. WE show that the global SU(2) symmetry of the full even-lattice Hubbard model generated by Yang's \ensuremath{\eta}-pairing operators becomes a local symmetry in the large-U limit and is applicable to even-odd mixed lattices. This extends the well-known SU(2) local symmetry of Anderson, for which we construct the generators. The associated local gauge theory of the extended symmetry can be similarly formulated and has interesting physical implications: new mean-field theories with parity-changed pairings. We point out the importance of searching for the parity-dependent Aharanov-Bohm-type of effects related to these local gauge symmetries.
Inspired by recent advances in the fabrication of surface superlattices, and in particular the triangular lattice made of tin (Sn) atoms on silicon, we study an extended Hubbard model on a triangular lattice. The observations of magnetism in these systems justify the inclusion of a strong on-site repulsion, and the observation of superconductivity suggests including an effective, nearest-neighbor attractive interaction. The attractive interaction mimics the effect of strong on-site repulsion near half filling, which can be seen in strong-coupling vertex calculations such as the Eliashberg method. With this extended Hubbard model on a triangular lattice with its geometrical frustration, we find a rich phase diagram of various magnetic orders and pairing functions, within the framework of self-consistent mean field theory. We uncover the competition between magnetism and unconventional superconductivity, and their coexistence for triplet pairings. We follow the Fermi surface of the system as the system is doped away from half filling and find nesting vectors and a Lifshitz transition, which provide an intuitive understanding of the phase transitions between the many orders we consider.
Superconductivity in the strongly correlated electronic systems described by the Hubbard model for slightly less than half-filled band is shown to arise from the condensation of charge + e holons which are bosons. The holon effective mass is found to be very close to that of the band electrons and they have a strong nearest neighbour repulsion induced by the spin fluctuations. They interact with an U(1) part of the collective SU(2) gauge field (named S-gauge field) of the spin system. This results in spontaneous symmetry breaking of the holon field and the appearance of the Anderson-Higgs phenomenon. The interesting possibility of the SU(2) gauge field-spinon coupled system retaining some gapless excitation spectrum inspite of the spontaneous symmetry breaking in the holon field is pointed out.
Motivated by recent experiments on the triangular lattice Mott-Hubbard system $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{C}\mathrm{N})}_{3}$, we develop a general formalism to investigate quantum spin liquid insulators adjacent to the Mott transition in Hubbard models. This formalism, dubbed the SU(2) slave-rotor formulation, is an extension of the SU(2) gauge theory of the Heisenberg model to the case of the Hubbard model. Furthermore, we propose the honeycomb lattice Hubbard model (at half filling) as a candidate for a spin liquid ground state near the Mott transition; this is an appealing possibility, as this model can be studied via quantum Monte Carlo simulation without a sign problem. The pseudospin symmetry of Hubbard models on bipartite lattices turns out to play a crucial role in our analysis, and we develop our formalism primarily for the case of a bipartite lattice. We also sketch its development for a general Hubbard model. We develop a mean-field theory to describe spin liquids and some competing states, and apply it to the honeycomb lattice. On the insulating side of the Mott transition, we find an SU(2) algebraic spin liquid (ASL), described by gapless S=1∕2S=1∕2S=1∕2 Dirac fermions (spinons) coupled to a fluctuating SU(2) gauge field. This result contrasts with that obtained via a U(1) slave-rotor approach, which instead found a U(1) ASL. That formulation does not respect the pseudospin symmetry, and is therefore not correct on the honeycomb lattice. We construct a low-energy effective theory describing the ASL phase, the conducting semimetal phase and the Mott transition between them. This physics can be detected in numerical simulations via the simultaneous presence of substantial antiferromagnetic and valence-bond solid correlations. In the SU(2) ASL, these observables have slowly decaying fluctuations in space and time, described by power laws with the same critical exponent. We recover the results of the U(1) slave-rotor formulation in the presence of a strong breaking of pseudospin symmetry. Our analysis suggests that both a third-neighbor electron hopping, and/or pseudospin-breaking terms such as a nearest-neighbor density interaction, may help to stabilize a spin liquid phase.