Tunneling and Photoemission in an SO ( 6 ) Supercon - ductor

—————————————————— Combining the results of tunneling, photoemission and thermodynamic studies, the pseudogap is unambiguously demonstrated to be caused by Van Hove nesting: a splitting of the density of states peak at (π, 0). The fact that the splitting remains symmetric about the Fermi level over an extended doping range indicates that the Van Hove singularity is pinned to the Fermi level. Despite these positive results, an ambiguity remains as to what instability causes the pseudo-gap. Charge or spin density waves, superconducting fluctuations, and flux phases all remain viable possibilities. This ambiguity arises because the instabilities of the two-dimensional Van Hove singularity are associated with an approximate SO(6) symmetry group, which contains Zhang's SO(5) as a subgroup. It has two 6-component superspins, one of which mixes Zhang's (spin-density wave plus d-wave superconductivity) superspin with a flux phase operator. This is the smallest group which can explain striped phases in the cuprates. Evidence for a prefered hole density in the charged stripes is discussed. Early work on the Van Hove model of high-T c superconductivity was criticized for a number of reasons , chiefly (1) the perfect nesting of the Fermi surface would cause instabilities which would overwhelm superconductivity; and (2) the Van Hove singularity (VHS) is associated with a special doping, and hence would require 'fine tuning' of the model parameters to fall at the Fermi level, whereas superconductiv-ity exists over an extended doping range. In June, 1987, I suggested[1] the picture which has become the heart of the generalized Van Hove scenario[2]. First, introduction of next-nearest-neighbor hopping – t ′ (t OO) in a one (three)-band model – would push the VHS off of half filling, leading to imperfect nesting , with residual hole pockets and ghost Fermi sur-faces[3]. Secondly, this very sensitivity to instability ——— could in turn lower the free energy precisely when the Fermi surface coincides with the VHS, thereby stabilizing this special doping – and that the reason su-perconductivity might persist over such an extended doping range is that the material is inhomogeneous, with one phase pinned at the VHS. Due to charging effects, such phase separation would be nanoscale[4]. While a microscopic model only appeared in 1989[5], I quickly found that the doping dependence of both resistivity and Hall effect could be understood in the context of a percolation model[3,6], and Bill Giessen and I noted that the Uemura plot[7] could be interpreted in terms …