THE VAN HOVE SINGULARITY IN THE CUPRATE SUPERCONDUCTORS - A REASSESSMENT

Recent theoretical advances in the superconductivity of the cuprates have found that (1) Fermi surface nesting is enhanced in Luttinger liquids over conventional Fermi liquids, and (2) nesting associated with the van Hove singularity (vHS) is considerably stranger than conventional nesting. Meanwhile, angle-resolved photoemission experiments have unambiguously demonstrated that the vHS is present at the Fermi level of optimum T-c in all of the highest-T-c materials studied: YBa2Cu3O7, YBa2Cu4O8, and Bi2Sr2CaCu2O8. Some implications of these results are discussed. In particular, this paper stresses the close connection between the 1D Hubbard model and the 2D vHS model. The origin of the ''ghost'' Fermi surfaces is shown to be the same in both models: a large density of low-energy 2k(F) electron-hole pairs. (In a doped antiferromagnet, these electron-hole pairs can be identified with spinons.) The insulating state of the one-dimensional Hubbard model can be described as a ''correlation-induced vHS''. It is shown that correlation effects are essential for restoring the Mott picture of the insulator instability in the 2D vHS model.