Hole Doping Evolution of the Quasiparticle Band in Models of Strongly Correlated Electrons for the High-T_c Cuprates

TL;DR

This study uses quantum Monte Carlo and maximum entropy methods to analyze how hole doping affects the quasiparticle band structure in a Hubbard model relevant to high-temperature cuprate superconductors, revealing features consistent with ARPES data.

Contribution

It provides new insights into the doping evolution of quasiparticle bands in the Hubbard model, including predictions about flat bands crossing the Fermi level and the competition between s-wave and d-wave pairing.

Findings

Narrow quasiparticle band observed at T=t/3.

Flat bands at (π,0) cross the Fermi energy at high doping.

Extended s-wave pairing competes with d-wave in overdoped regime.

Abstract

Quantum Monte Carlo (QMC) and Maximum Entropy (ME) techniques are used to study the spectral function $A({\bf p},\omega)$ of the one band Hubbard model in strong coupling including a next-nearest-neighbor electronic hopping with amplitude $t'/t= -0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for $Sr_2 Cu O_2 Cl_2$. A narrow quasiparticle (q.p.) 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 $< n > \sim 0.70$ 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 $(0,0)$ 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 q.p. band introduces a {\it 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 is found to compete with d-wave in the overdoped regime, i.e. when the chemical potential has almost entirely crossed the q.p.