Antiferromagnetic and superconducting gaps and their interrelation in high-Tc cuprates

Abstract

This work is dedicated to Professor E. Müller-Hartmann on the occasion of his 60 th birthday.We propose a phenomenological model, comprising a microscopic SO(5) model plus the on-site Hubbard interaction U (projected SO(5) model) to understand the interrelation between the d-wave-gap modulation observed by recent angle-resolved photoemission experiments in the insulating antiferromagnet Ca2CuO2Cl2 and the d-wave gap of high-Tc superconducting materials. The on-site interaction U is important in order to produce a Mott gap of the correct order of magnitude, which would be absent in an exact SO(5) theory. The projected SO(5)-model explains the gap characteristics, namely both the symmetry and the different order of magnitude of the gap modulations between the antiferromagnetic and the superconducting phases. Furthermore, it is shown that the projected SO(5) theory can provide an explanation for a recent observation [E. Pavarini et al., Phys. Rev. Lett. 87, 47003 (2001)], i. e. that the maximum Tc observed in a large variety of high-Tc cuprates scales with the next-nearest-neighbor hopping matrix element Ann. Phys. (Leipzig) 12, No. 5 (2003) 321 the Hilbert space. The central hypothesis of the projected-SO(5) (p-SO(5) ) theory is that the model is accurate in describing both the static and dynamic properties in the high-T c superconductors (HTSC).On the basis of a numerically exact Quantum-Monte-Carlo (QMC) calculation of the p-SO(5) bosonic model, it has recently indeed been shown that this model gives a realistic description of the phase diagram of the HTSC materials and properly accounts for many of their physical properties [10]. Among those are the neutron-scattering resonance, which appears as a Goldstone mode in the p-SO(5) description, as well as an unusual chemical potential dependence on doping found in the prototype material La 2−x Sr x CuO 4 [11], which signals a possible (microscopic) phase separation [12]. One crucial point of this bosonic p-SO(5) model is that, on the basis of a newly implemented Stochastic Series Expansion QMC technique, it can be simulated up to unprecedented system sizes of about 10 4 sites, which is more than one order of magnitude larger than corresponding fermionic QMC simulations. This fact allowed, for the first time, for an approximate finite-size-study of the p-SO(5) bosonic model in the three-dimensional case, and for extracting the scaling properties close to the bicritical (AF-SC) point. The numerical results point to a partial asymptotic restoring of the SO(5) symmetry at this critical point, i. e. at long distances. This is very interesting, since the projection destroys the symmetry at the Hamiltonian level (The Hamiltonian no longer commutes with the SO(5) generators). While the mean-field classical p-SO(5) Hamiltonian of [8] conserves its SO(5) invariant form, quantum fluctuations break the symmetry. However, as shown in [13], at finite temperature quantum fluctuations become less and less important, and one can hope that symmetry-breaking effects due to the proje...