Charge ordering instabilities are studied in a multiorbital model of the cuprate superconductors. A known, key feature of this model is that the large local Coulomb interaction in the Cud x 2 −y 2 orbitals generates local moments with short range antiferromagnetic correlations. The strong simplifying ansatz that these moments are static and ordered allows us to explore a regime not generally accessible to weakcoupling approaches. The antiferromagnetic correlations lead to a pseudogap-like reconstruction of the Fermi surface. We find that the leading charge instability within this pseudogap-like state is to a phase with a spatially modulated transfer of charge between neighboring oxygen p x and p y orbitals accompanied by weak modulations of the charge density on the Cud x 2 −y 2 orbitals. As a prime result of the antiferromagnetic Fermi-surface reconstruction, the wavevectors of the charge modulations are oriented along the crystalline axes with a periodicity that agrees quantitatively with experiments. This suggests a resolution to a discrepancy between experiments, which find axial order, and previous theoretical calculations, which find modulation wavevectors along the Brillouin zone (BZ) diagonal. The axial order is stabilized by hopping processes via the Cu4s orbital, which is commonly not included in model analyses of cuprate superconductors. The main implication of our results is that charge order emerges from the pseudogap state, and is not the primary source of the pseudogap.

Charge order in cuprate superconductors is a possible source of anomalous electronic properties in the underdoped regime. Intraunit cell charge ordering tendencies point to electronic nematic order involving oxygen orbitals. In this context, we investigate charge instabilities in the Emery model and calculate the charge susceptibility within diagrammatic perturbation theory. In this approach, the onset of charge order is signaled by a divergence of the susceptibility. Our calculations reveal three different kinds of order: a commensurate (q = 0) nematic order, and two incommensurate nematic phases with modulation wave vectors that are either axial or oriented along the Brillouin zone diagonal. We examine the nematic phase diagram as a function of the filling, the interaction parameters, and the band structure. We also present results for the excitation spectrum near the nematic instability, and show that a soft nematic mode emerges from the particle-hole continuum at the transition. The Fermi surface reconstructions that accompany the modulated nematic phases are discussed with respect to their relevance for magneto-oscillation and photoemission measurements. The modulated nematic phases that emerge from the three-band Emery model are compared to those found previously in one-band models.

We study the effect of strong correlations on the zero-bias anomaly (ZBA) in disordered interacting systems. We focus on the two-dimensional extended Anderson-Hubbard model (EAHM) on a square lattice. The EAHM has both on-site and nearest-neighbour interactions and randomly chosen site energies. We use a mean-field theory that incorporates strong correlations and treats the disorder potential exactly. We use a simplified atomic-limit approximation for the diagonal inelastic self-energy that becomes exact in the large-disorder limit, and the off-diagonal self-energy is treated within the Hartree-Fock approximation. The validity of these approximations is discussed in detail. We find that strong correlations have a significant effect on the ZBA at half-filling, and enhance the ZBA gap when the interaction is finite ranged.