We investigate the possibility of superconductivity in the large-
U limit of the Hubbard model near half filling, using a slave-boson representation. The local constraint is treated in a novel way, incorporating short-range fluctuations in addition to the global constraint. We find slave-boson pairing and a superconducting extended
s-wave phase at hole concentrations $\ensuremath{\delta}$-above 4% and below 32%.
We investigate the superconductivity in the
t−J−U model within a slave-spin formalism. We show that the BCS mean-field theory implemented with the slave spin formalism naturally predicts two distinct gaps which are the pairing gap of the spinons
Δf and the Cooper pairing gap of the electrons
ΔSC=ZΔf, where
Z is the quasiparticle weight. Furthermore, we find that the nature of the superconducting state depends crucially on the interaction providing the pairing mechanism. For spin interactions, the bandwidth of the spinon hopping term is renormalized by
Z but the its pairing term is not. As a result, if
U exceeds the critical value for the Mott insulating state at half-filling,
Z develops a strong doping dependence, leading to a doping-driven crossover from strong to weak pairing states. In the strong pairing state, while
Δf is enhanced as
x→0,
ΔSC∼x due to the renormalization of
Z. In the weak pairing state,
Z does not change with
x significantly. Therefore,
ΔSC is mainly controlled by
Δf, and both of them go to zero at larger doping. The crossover from strong to weak pairing states is well captured by the slave spin formalism within reasonable range of parameters just at the mean-field level, indicating the slave spin formalism is a powerful tool to study correlated materials. For charge interactions, we find that the bandwidth of the spinon hopping term and its pairing term are renormalized by
Z and
Z2 respectively. Consequently, both
Δf and
ΔSC are suppressed at small
x in large U, and no crossover will occur. The implication of our results for the superconducting states in correlated materials will be discussed.
A mean-field treatment of the phase string effect in the $t\ensuremath{-}J$ model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and the metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long-range ordering (AFLRO) at half-filling and superconducting condensation in the metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.
The ground state of two-dimensional t – J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J , due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d x 2 - y 2 -wave superconductivity for the doping rate, δ, less than 10%. At half-filling, the renormalization of the J -term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the d-wave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to δ in underdoped region and has a maximum near δ=0.11, which probably determines T c . We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.
A new kind of symmetry, called Supersymmetry, is introduced in t-J model and its corresponding Supersymmetric Formulation is constructed. The new formulation unifies the so-called slave-fermion and slave-boson formulations to the model in a single framework and is able to incorporate the advantage of the two approaches. The formulation is analysed at mean-field level where we found that antiferromagnetism described by slave-fermion-like state is stable at low doping regime, and the slave-boson-like d-wave RVB superconducting state becomes favorable at optimal doping. The global phase diagram is determined. To remedy the relaxation of non-double-occupancy constraint in a simple mean-field theory, the Gutzwiller's approximation is applied. Surprisingly the resulting phase diagram is in rather close agreement with experiment. Several physical quantities such as spin-spin correlation lengths, electron spectral functions, magnetic dynamical structure factors and spin susceptibilities are also calculated at the mean-field level where the new effect coming from finite spin and charge excitations of opposite statistics allowed by supersymmetry is pointed out. Finally, future research direction of the formulation is discussed.
The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.