Interrelation between antiferromagnetic and superconducting gaps in high-Tc materials

We propose a phenomenological model, comprising a microscopic \sof model plus the on-site Hubbard interaction $U$ (``projected \sof model'') to understand the interrelation between the d-wave-gap modulation observed by recent angle-resolved photoemission experiments in the insulating antiferromagnet Ca$_2$CuO$_2$Cl$_2$ 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 \sof theory. The projected \sof-model explains the gap characteristics, namely both the symmetry and the different order of magnitude of the gap modulations between the \af and the \sc phases. Furthermore, it is shown that the projected \sof 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 $t'$.