Charge ordering in three-band models of the cuprates.

We examine trends in the wave vectors and form factors of charge density wave instabilities of three-band models of the underdoped cuprates. For instabilities from a high-temperature state with a large Fermi surface, we extend a study by Bulut et al. [Phys. Rev. B 88, 155132 (2013)] to include a direct antiferromagnetic exchange coupling between the Cu sites. As in previous work, we invariably find that the primary instability has a diagonal wave vector (±Q0, ±Q0) and a d-form factor. The experimentally observed wave vectors along the principal axes (±g0,0), (0, ±Q0) have higher energy, but they also have a predominantly d-form factor. Next, we gap out the Fermi surface in the antinodal regions of the Brillouin zone by including static, long-range antiferromagnetic order at the wave vector (π,π): this is a simple model of the pseudogap in which we assume the antiferromagnetic order averages to zero by "renormalized classical" thermal fluctuations in its orientation, valid when the antiferromagnetic correlation length is large. The charge density wave instabilities of this pseudogap state are found to have the optimal wave vector (±Q0,0), (0, ±Q0), with the magnitude of the d-form factor decreasing with increasing magnetic order. [ABSTRACT FROM AUTHOR]