Pinned Balseiro-Falicov model of tunneling and photoemission in the cuprates

Abstract

The smooth evolution of the tunneling gap of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ with doping from a pseudogap state in the underdoped cuprates to a superconducting state at optimal and overdoping, has been interpreted as evidence that the pseudogap must be due to precursor pairing. We suggest an alternative explanation, that the smoothness reflects a hidden $\mathrm{SO}\mathrm{}\left(N\right)\mathrm{}$ instability group near the $(\pi ,0)$ points of the Brillouin zone (with $N=3,\hspace{0.5em}4,\hspace{0.5em}5,$ or 6). Because of this group structure, the pseudogap could actually be due to any of a number of nesting instabilities, including charge or spin density waves or more exotic phases. We present a detailed analysis of this competition for one particular model: the pinned Balseiro-Falicov model of competing charge density wave and $(s$-wave) superconductivity. We show that most of the anomalous features of both tunneling and photoemission follow naturally from the model, including the smooth crossover, the general shape of the pseudogap phase diagram, the shrinking Fermi surface of the pseudogap phase, and the asymmetry of the tunneling gap away from optimal doping. Below $T_c,$ the sharp peak at ${\Delta }_1$ and the dip seen in the tunneling and photoemission near $2{\Delta }_1$ cannot be described in detail by this model, but we suggest a simple generalization to account for inhomogeneity, which does provide an adequate description. We show that it should be possible, with a combination of photoemission and tunneling, to demonstrate the extent of pinning of the Fermi level to the Van Hove singularity. A preliminary analysis of the data suggests pinning in the underdoped, but not in the overdoped regime.