Effect of van Hove singularities on a spin liquid

We determine the properties and leading instabilities of a spin liquid with a Fermi surface passing near a van Hove singularity. Our study is motivated by recent photoemission experiments on high-${\mathit{T}}_{\mathit{c}}$ cuprates in which it is found that for the optimally doped material the experimental Fermi surface passes near a van Hove singularity, while for underdoped materials, a pseudogap in the electron spectral function is formed in the vicinity of the van Hove point. We show theoretically that proximity to the van Hove singularity suppresses the inelastic scattering due to the gauge field and permits the formation of a d-wave RVB state in which the gap exists only near the van Hove points while finite regions of the Fermi surface remain gapless. This d-wave pairing provides a natural explanation of the pseudogap observed in photoemission. We also discuss the relation of the pseudogap observed in the spectral function to the pseudogaps observed in the magnetic susceptibility. © 1996 The American Physical Society.