the measurement temperature, leaving the impurity in the local moment (nonresonant) regime. More recently, however, it has been observed by STM that spatial charge variations are in fact quite small, of order a few percent, and that the presence of dopants [*correlates*]{} (rather than anticorrelates) with the large-gap regions.[@mcelroyscience] In addition, resonances that have been observed in underdoped samples at temperatures well above the Kondo temperature expected from NMR[@alloul] are similar to the low temperature impurity spectra.[@hudson; @kambara; @vershinin] Nevertheless, recently Kirćan proposed a mechanism by which the size of the superconducting gap can modify the impurity moment exchange coupling to the $d$-wave quasiparticle bath.[@kircan] In the large-gap regions, states are pushed further away from the Fermi level, thus decreasing the ability of the quasiparticle system to screen the impurity, leading to a lower $T_K$. This does not appear to address the set of critiques above, but is consistent with the STM results on BSCCO at low $T$. We return to this scenario below, after discussing other possibilities.

Zn as screened Coulomb impurity
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![(Color online) LDOS at impurity site (IS) and nearest neighbor sites (NN) plotted in left and right panels respectively for various gap modulations $\delta \Delta=-0.05t,0,+0.05t$ over 