Pseudogap in cuprates driven by d-wave flux-phase order proximity effects: A theoretical analysis from Raman and ARPES experiments

One of the puzzling characteristics of the pseudogap phase of high-$T_c$ cuprates is the nodal-antinodal dichotomy. While the nodal quasiparticles have a Fermi liquid behaviour, the antinodal ones show non-Fermi liquid features and an associated pseudogap. Angle-resolved photoemission spectroscopy and electronic Raman scattering are two valuable tools which have shown universal features which are rather material-independent, and presumably intrinsic to the pseudogap phase. The doping and temperature dependence of the Fermi arcs and the pseudogap observed by photoemission near the antinode correlates with the non-Fermi liquid behaviour observed by Raman for the B$_{1g}$ mode. In contrast, and similar to the nodal quasiparticles detected by photoemission, the Raman B$_{2g}$ mode shows Fermi liquid features. We show that these two experiments can be analysed, in the context of the $t$-$J$ model, by self-energy effects in the proximity to a d-wave flux-phase order instability. This approach supports a crossover origin for the pseudogap, and a scenario of two competing phases. The B$_{2g}$ mode shows, in an underdoped case, a depletion at intermediate energy which has attracted a renewed interest. We study this depletion and discuss its origin and relation with the pseudogap.