We evaluate numerically several superconducting correlation functions in a generalized
t−J model derived for hole-doped CuO
2 planes. The model includes a three-site term
t′′ similar to that obtained in the large
U limit of the Hubbard model but of opposite sign for realistic O-O hopping. For realistic parameters we obtain strong evidence of superconductivity of predominantly
dx2−y2 character. The ground state has a large overlap with a very simple resonating-valence-bond wave function with off-diagonal long-range order. This function reproduces the main features of the magnetic and superconducting correlation functions.
It remains an open question whether the two-dimensional single-band pure Hubbard model and its related pure $t\text{\ensuremath{-}}J$ model truly capture the superconducting order in cuprates. Recent numerical studies on this issue have raised a notable disparity in superconducting order between the pure Hubbard model and the pure $t\text{\ensuremath{-}}J$ model. Inspired by these works, we investigate the role of the three-site hopping term in
d-wave superconductivity, such a term is usually neglected in the effective Hamiltonian of the Hubbard model, although its amplitude is of the same order as the superexchange coupling
J in the $t\text{\ensuremath{-}}J$ model. Our slave-boson mean-field solution demonstrates the suppression of
d-wave superconducting order by incorporating the three-site hopping term, consistent with numerical observations by the density-matrix renormalization group. This suppression could be understood as a result of competition between superexchange interaction and three-site hopping, the former favors
d-wave pairing while the latter favors
s-wave pairing. We also discussed its role in quasiparticle dispersion and boson-condensation temperature. Our findings may offer an alternative understanding of the recent numerical contrasting findings in the strong-coupling regime: the absent or weak superconductivity in the pure Hubbard model, while the robust superconductivity in the $t\text{\ensuremath{-}}J$ model without including the three-site hopping term.
We consider the slave-fermion--Schwinger-boson decomposition of a t-J model for a two-dimensional antiferromagnet in which the next-nearest-neighbor hopping is taken into account by an explicit t' term. This technique is particularly suitable to describe systems with low hole density, as in the parent phases of high-
Tc superconducting (HTSC) materials, and we examine the experimental consequences of the model. Using mean-field states which admit finite spiral and off-diagonal order, we compute first the dynamic susceptibility \ensuremath{\chi}(q,\ensuremath{\omega}) from fluctuations in the boson (spin) degrees of freedom, and investigate a selected parameter regime for the model to seek features consistent with inelastic neutron scattering experiments on underdoped HTSC crystals. We find peaks in the scattered intensity at incommensurate wave vectors (\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2
k0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}) and (\ensuremath{\pi},\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2
k0), but within our approximation the q-integrated susceptibility as a function of frequency and temperature resembles that from spin-wave theory, which does not contain the scaling behavior over all values of \ensuremath{\omega}/T found experimentally. We show also the form of the nuclear magnetic resonance relaxation time ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$(T), which measures the zero-frequency limit of the susceptibility. The imaginary part of the physical electron Green function is a convolution of both fermionic (hole) and bosonic Green functions, and so incorporates the effect of spin dynamics on the charge motion. We calculate the photoemitted intensity, a direct experimental measurement of this quantity, focusing on its behavior near the hole pockets at (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) which characterize this type of model. The peak photocurrent occurs not at the hole Fermi surface, but at points separated from it by
k0 due to the boson incommensuration.
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.
The high-temperature superconducting cuprates host unidirectional spin- and charge-density-wave orders that can intertwine with superconductivity in nontrivial ways. While the charge components of these stripes have now been observed in nearly all cuprate families, their detailed evolution with doping varies across different materials and at high and low temperatures. We address this problem using nonperturbative determinant quantum Monte Carlo calculations for the three-band Hubbard model. Using an efficient implementation, we can resolve the model's fluctuating spin and charge modulations and map their evolution as a function of the charge transfer energy and doping. We find that the incommensurability of the charge modulations is decoupled from the spin modulations and decreases with hole doping, consistent with experimental measurements at high temperatures. These findings support the proposal that the high-temperature charge correlations are distinct from the intertwined stripe order observed at low-temperature and in the single-band Hubbard model.
We consider an extended Hubbard model with nearest-neighbor correlated hopping and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ obtained as an effective model for cuprate superconductors. Using a generalized Hartree-Fock BCS approximation, we find that for high enough ${t}^{\ensuremath{'}}$ and doping, antiferromagnetism is destroyed and the system exhibits d-wave superconductivity. Near optimal doping we consider the effect of antiferromagnetic spin fluctuations on the normal self-energy using a phenomenological susceptibility. The resulting superconducting critical temperature as a function of doping is in good agreement with experiment.