Many cuprate superconductors possess an unusual charge-ordered phase that is characterized by an approximate $d_{x^2-y^2}$ intra-unit cell form factor and a finite modulation wavevector $bq^ast$. We study the effects impurities on this charge ordered
phase via a single-band model in which bond order is the analogue of charge order in the cuprates. Impurities are assumed to be pointlike and are treated within the self-consistent t-matrix approximation (SCTMA). We show that suppression of bond order by impurities occurs through the local disruption of the $d_{x^2-y^2}$ form factor near individual impurities. Unlike $d$-wave superconductors, where the sensitivity of $T_c$ to impurities can be traced to a vanishing average of the $d_{x^2-y^2}$ order parameter over the Fermi surface, the response of bond order to impurities is dictated by a few Fermi surface hotspots. The bond order transition temperature $T_mathrm{bo}$ thus follows a different universal dependence on impurity concentration $n_i$ than does the superconducting $T_c$. In particular, $T_mathrm{bo}$ decreases more rapidly than $T_c$ with increasing $n_i$ when there is a nonzero Fermi surface curvature at the hotspots. Based on experimental evidence that the pseudogap is insensitive to Zn doping, we conclude that a direct connection between charge order and the pseudogap is unlikely. Furthermore, the enhancement of stripe correlations in the La-based cuprates by Zn doping is evidence that this charge order is also distinct from stripes.
In a multiorbital model of the cuprate high-temperature superconductors soft antiferromagnetic (AF) modes are assumed to reconstruct the Fermi surface to form nodal pockets. The subsequent charge ordering transition leads to a phase with a spatially
modulated transfer of charge between neighboring oxygen p_x and p_y orbitals and also weak modulations of the charge density on the copper d_{x^2-y^2} orbitals. As a prime result of the AF Fermi surface reconstruction, the wavevectors of the charge modulations are oriented along the crystalline axes with a periodicity that agrees quantitatively with experiments. This resolves 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.
Charge order in cuprate superconductors is a possible source of anomalous electronic properties in the underdoped regime. Intra-unit cell charge ordering tendencies point to electronic nematic order involving oxygen orbitals. In this context we inves
tigate charge instabilities in the Emery model and calculate the charge susceptibility within diagrammatic perturbation theory. In this approach, the onset of charge order is signalled 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 wavevectors 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, which has both on-site and nearest-neighbor interactions on a square lattice
. We use a variation of dynamical mean field theory in which the diagonal self-energy is solved self-consistently at each site on the lattice for each realization of the randomly-distributed disorder potential. Since the ZBA occurs in systems with both strong disorder and strong interactions, we use a simplified atomic-limit approximation for the diagonal inelastic self-energy that becomes exact in the large-disorder limit. 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 Coulomb gap when the interaction is finite-ranged.
