Spectral properties and pseudogaps in a model with d-wave pairing symmetry

A model with d-wave pairing symmetry is studied by employing a non-perturbative sum rule approach. At low temperature the magnitude of a normal state pseudogap shows strong $\vec{k}$ or angle dependence well fitted by $\cos 2\phi$ form. With increasing temperature, the pseudogap closes at some critical angle $\phi_{c}$ and beyond this angle a single quasiparticle-like peak appears. The resulting Fermi surface is strongly temperature dependent. Both in the spectral function and the density of states, the pseudogap disappears in a manner that the spectral weight fills in the pseudogap instead of closing it with increasing temperature. All these features are qualitatively consistent with ARPES for underdoped cuprates.