Effect of pointlike impurities ondx2−y2charge-density waves in cuprate superconductors

Abstract

Many cuprate superconductors possess an unusual charge-ordered phase that is characterized by an approximate ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ intraunit cell form factor and a finite modulation wave vector ${\mathbf{q}}^{*}$. We study the effects of impurities on this charge-ordered phase via a single-band model in which bond order is the analog of charge order in the cuprates. Impurities are assumed to be pointlike and are treated within the self-consistent $t$-matrix approximation. We show that suppression of bond order by impurities occurs through the local disruption of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ 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 ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ 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.