  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.
