Using the improved U(1) and SU(2) slave-boson approaches of the $t\ensuremath{-}J$ Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B 64, 052501 (2001)] that we developed recently, we study the doping and temperature dependence of superfluid weight and spectral function and discuss our finding of the universal scaling behavior of the pseudogap. It is shown that at low hole doping concentrations
x and at low temperatures
T, there exists a propensity of linear decrease in the superfluid weight
ns∕m∗ with temperature
T, and a tendency of doping independence in the linearly decreasing slopes of
(ns∕m∗)(x,T) with
T in qualitative agreement with the experimentally observed relation; that is, $({n}_{s}∕{m}^{*})(x,T)=({n}_{s}∕{m}^{*})(x,0)\ensuremath{-}\ensuremath{\alpha}T$, where $\ensuremath{\alpha}$ is a constant. It is also demonstrated that there exists a boomerang behavior; that is, both
Tc and
ns∕m∗ increase with hole doping concentration
x in the underdoped region, reach a saturation (maximum) at a hole doping above optimal doping, and decrease beyond the saturation point in the overdoped region, in agreement with $\ensuremath{\mu}\mathrm{SR}$ measurements. Based on our improved SU(2) slave-boson approach to the $t\ensuremath{-}J$ Hamiltonian, we further investigate the doping and temperature dependence of the spectral function and discuss our theoretical finding of a scaling behavior of the pseudogap. In addition, we discuss the cause of the hump and quasiparticle peak in the observed spectral functions of high
Tc cuprates. It is demonstrated that the sharpening of the observed quasiparticle peak below
Tc is attributed to the bose condensation of holon pair, in agreement with observations. From the predicted ratios of the pseudogap ${\ensuremath{\Delta}}_{0}$ to both the superconducting temperature
Tc and the pseudogap temperature
T∗, i.e., $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}_{c}$ and $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}^{*}$, respectively, as a function of hole doping concentration
x, we find that there exists a universal scaling behavior (sample independence) of these ratios with doping, by showing a nonlinearly decreasing behavior of the former; that is, $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}_{c}\ensuremath{\sim}{x}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\sim}2$ and a near doping independence of the latter; that is, $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}^{*}\ensuremath{\approx}4--6$.
Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature
Tc is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/
kTc\ensuremath{\simeq}4.
Based on an improved U(1) slave-boson approach to the t-J Hamiltonian, we invest igate a relationship between the superfluid weight
ns/m∗(the superconducting charge carrier density/the effective mass of the charge carrier) and the superc onducting temperature
Tc. From the present study we find a linear increase of
ns/m∗ with
Tc with th e doping concentration in the underdoped region, a saturation around the optimal doping and a decrease in both
ns/m∗ and
Tc in the overdoped region. Such a trend of the `boomerang' shaped locus in
ns/m∗ vs.
Tc with increas ing doping concentration from the underdoped to the heavily overdoped region is predicted to be in complete agreement with muon-spin-relaxation measurements. The boomerang behavior is found to occur in correlation with reduction in the sp in singlet pairing(spinon pairing) order in the heavily overdoped region.
We study the t-J and the Hubbard models at zero temperature using exact-diagonalization techniques on \ensuremath{\surd}10 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}10 and 4\ifmmode\times\else\texttimes\fi{}4 sites clusters. Quantum Monte Carlo simulation results on larger lattices are also presented. All electronic fillings have been analyzed for the three models. We have measured equal-time correlation functions corresponding to various types of order (ranging from ``standard'' staggered spin order to more ``exotic'' possibilities like chiral order), as well as various dynamical properties of these models. Upper bounds for the critical hole doping (
xc), where long-range antiferromagnetic order disappears, are presented. It was found that
xc is very small in agreement with experiments for the high-
Tc superconductors. For example, in the t-J model, ${\mathit{x}}_{\mathit{c}}$0.08 at J/t=0.4. However, short-distance spin correlations are important up to much higher dopings producing a sharp well-defined spin-wave-like peak in S(q=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega}). Regarding the possibility of phase separation in the Hubbard model, we have studied the behavior of the density of particles, 〈n〉, as a function of the chemical potential, using the Lanczos method on a 4\ifmmode\times\else\texttimes\fi{}4 Hubbard cluster, finding no indications of phase separation for any value of U/t. Then, we conclude that the t-J model at small J/t should not phase separate.In order to compare theoretical predictions with photoemission experiments, we evaluated the electronic density of states N(\ensuremath{\omega}), of the Hubbard and t-J models at several doping fractions. We found that upon doping the antiferromagnetic gap is filled for U\ensuremath{\sim}8t or smaller. The chemical potential moves across the insulating gap as one goes from electron to hole doping of the half-filled cluster, in agreement with x-ray absorption experiments but at variance with photoemission experiments. We have also calculated the optical conductivity, ${\mathrm{\ensuremath{\sigma}}}_{1}$(\ensuremath{\omega}), of the Hubbard and t-J models at all dopings on 4\ifmmode\times\else\texttimes\fi{}4 clusters. Results are compared with experiments and the weight of the Drude peak is presented as a function of couplings and dopings. Spectral weight found at small frequencies is associated with the mid-infrared band observed experimentally in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$
SrxCuO4, and with the states filling the insulating gap in photoemission experiments. An overall good agreement with experiments in the normal state was found. Regarding the possibility of superconductivity n these models, we have studied s-, d-, and p-wave pairing correlations. Naively, the d-wave channel seems enhanced near half filling while the extended s-wave channel seems enhanced from half filling up to 40% doping.However, we found that the enhancement comes from short-distance effects and, thus, no numerical indications of superconductivity were found in these models. We emphasize the importance of analyzing the pairing correlations as a function of distance to distinguish between short- and long-distance effects in the susceptibilities. We also observed that spiral order is enhanced at small J/t and low doping. Uniform chiral rder is suppressed by dynamical holes while staggered chiral order may be enhanced, although with a small plaquette order parameter. We conclude with the observation that the simple one-band Hubbard model with intermediate values of U\ensuremath{\sim}8t may account for many of the ``anomalous'' properties of the normal state of the high-
Tc superconductors.
We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.
How superconductivity emerges in the vicinity of an antiferromagnetic insulating state is a long-standing issue of strong correlation physics. We study the transition from an antiferromagnetic insulator to a superconductor by hole doping based on a bilayer generalization of a Hubbard model. The projector quantum Monte Carlo simulations are employed, which are sign problem free both at and away from half filling. An anisotropic Ising antiferromagnetic Mott insulating phase occurs at half filling, which is weakened by hole doping. Below a critical doping value, antiferromagnetism coexists with the singlet superconductivity, which is a pairing across each rung with an extended
s-wave symmetry. As doping further increases, the antiferromagnetic order vanishes, leaving only a superconducting phase. These results provide important information on how superconductivity appears upon doping the parent Mott-insulating state.