Recent experiments on the Fermi surface and the electronic structure of the cuprate-supercondutors showed the importance of short range antiferromagnetic correlations for the physics in these systems. Theoretically, features like shadow bands were predicted and calculated mainly for the Hubbard model. In our approach we calculate an approximate selfenergy of the t-J model. Solving the U = ∞ Hubbard model in the Dynamical Mean Field Theory (DMFT) yields a selfenergy that contains most of the local correlations as a starting point. Effects of the nearest neighbor spin interaction J are then included in a heuristical manner. Formally like in J-perturbation theory all ring diagrams, with the single bubble assumed to be purely local, are summed to get a correction to the DMFT-self engergy This procedure causes new bands and can furnish strong deformation of quasiparticle bands. The obvious importance of antiferromagnetic (AF) correlations for the physics of cuprate superconductors found an impressing confirmation through ARUPS-experiments performed by Aebi et al. [1]. There, in a Fermi surface (FS) mapping of Bi2Sr2CaCu2O8(001) shadows of the FS were observed. The interpretation as an effect of short range antiferromagnetic correlations led to an intensive discussion of so called shadow features, which have been predicted by Kampf and Schrieffer [2] in a semi-phenomenological theory for the Hubbard model. In the paper we present an approximate evaluation of the self energy for the t-J model HtJ consisting of two parts: The hopping term Ht = − t∗
The two-dimensional Hubbard model is studied within the composite operator method (COM) with the self-energy computed in the self-consistent Born approximation (SCBA). The COM describes interacting electrons in terms of the new elementary excitations that appear in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. On decreasing the doping (from the overdoped to underdoped region), anomalous features develop in the spectral function $A(\mathbf{k},\ensuremath{\omega})$, the Fermi surface, the momentum distribution function
n(k), the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime
(U=8) at low temperatures
(T=0.01−−0.02). At high doping
(n=0.7), the system resembles an ordinary weakly interacting metal. At low doping
(n=0.92), a pseudogap opens, hot and cold spots appear, and non-Fermi-liquid features develop. This behavior, together with the presence of kinks in the calculated electronic dispersion, is in agreement with angle-resolved photoemission spectroscopy data for high-
Tc cuprates superconductors.
The superconducting phase of the 2D one-band Hubbard model is studied within the FLEX approximation and by using an Eliashberg theory. We investigate the doping dependence of T c , of the gap function Δ( k ,ω) and of the effective pairing interaction. Thus we find that T c becomes maximal for 13% doping. In overdoped systems T c decreases due to the weakening of the antiferromagnetic correlations, while in the underdoped systems due to the decreasing quasi-particle lifetimes. Furthermore, we find shadow states below T c which affect the electronic excitation spectrum and lead to fine structure in photoemission experiments.
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.
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.
The line shape of photoemission spectra for underdoped cuprates is studied within the two-dimensional extended Hubbard model. Strong anisotropic scattering along the Fermi surface and the destruction of the Fermi surface near $(0,\ensuremath{\pi})$ are obtained for underdoped cuprates. These features are fully consistent with the recent angle-resolved photoemission experiments for underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ as well as with the recent QMC calculations.