We study the doping dependence of photoemission spectra for the t-t′-t″-J model by using the exact diagonalization technique and present a consistent theoretical analysis. Both calculations show that upon doping the enhancement of incoherent motion of holes due to the t′ and t″ terms accounts for the formation of the flat region around (π,0) in the quasiparticle dispersion at underdoped and optimally doped region, despite the absence of the flat band at half filling. Our results are in excellent agreement with resent photoemission experiments on Bi 2 Sr 2 Ca 1 Cu 2 O 8+δ [Marshall et al., Phys. Rev. Lett.76, 4841 (1996)] and Sr 2 CuO 2 Cl 2 [Wells et al., Phys. Rev. Lett.74, 964 (1995)].
We present an exact diagonalization study of the single-particle spectral function in the so-called t-
t∣IH-t\ensuremath{''}-J model in two dimensions. As a key result, we find that hole doping leads to a major reconstruction of the quasiparticle band structure near (\ensuremath{\pi},0): whereas for the undoped system the quasiparticle states near (\ensuremath{\pi},0) are deep below the top of the band near (\ensuremath{\pi}/2,\ensuremath{\pi}/2), hole doping shifts these states up to
EF, resulting in extended flat band regions close to
EF and around (\ensuremath{\pi},0).
The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on
La1.28Nd0.6Sr0.12CuO4.The spectral weight A(p,\ensuremath{\omega}) of the two-dimensional t-J and Hubbard models has been calculated using exact diagonalization and quantum Monte Carlo techniques, at several densities 0.5\ensuremath{\le}〈n〉\ensuremath{\le}1.0. The photoemission (\ensuremath{\omega}0) region contains two dominant distinct features, namely a low-energy quasiparticle peak with bandwidth of order J, and a broad valence band peak at energies of order t. This behavior persists away from half-filling, as long as the antiferromagnetic correlations are robust. The results give support to theories of the copper oxide materials based on the behavior of holes in antiferromagnets, and they also provide theoretical guidance for the interpretation of experimental photoemission data for the cuprates.
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.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for
Sr2CuO2Cl2. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation
T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density
〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from
(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended
s-wave character is found to compete with the
d wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as
〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.