Hole-doping evolution of the quasiparticle band in models of strongly correlated electrons for the high-$T_c$ cuprates

Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\omega )$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude $t^{\prime }/t=-0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation $T=t/3\mathrm{}$, 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 $〈n〉\sim 0.70$ it has crossed it entirely. The region near momentum $(0,\pi )$ and $(\pi ,0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from $\mathrm{}(0,0)\mathrm{}$ to $(\pi ,\pi )$. 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 $(\pi ,0)$ 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.