a 5$\times 5$ patch around the impurity, described by an onsite potential $V_3=2.5t$. Black curves show the LDOS in the absence of an impurity, while colored curves correspond to the situation where an impurity is present. Hoppings are not modulated, $\delta t=0$[]{data-label="fig4"}](Fig4a_wT.eps){width="1.0\columnwidth"}

We now examine the conventional point of view that, since Zn$^{2+}$ is a closed shell ion, it creates a strong localized screened Coulomb potential[@LLWang:2005] in a BSCCO host. A strong impurity potential of this type is typically represented as a $\delta$-function potential in the Hamiltonian with $V_3>>t$ and $V_0=0$ in the notation of Eq.(\[potH\]), and it is well-known that such a perturbation generates an in-gap resonant state in a $d$-wave superconductor.[@bsr] In a particle-hole symmetric normal state band, this LDOS resonance can be tuned to $\Omega_0=0$ with $V_3=\infty$, but in a more general band a specific fine-tuned value of the potential is required to produce a resonance at zero energy (unitarity) or any other particular subgap energy.[@joynt; @ahmphysica] For the band we have adopted here, which roughly reproduces the correct Fermi surface of optimally doped BSCCO, tuning the resonance to the nominal resonance frequency observed by STS[@panzn] of $\Omega_0\simeq-2$meV$\simeq 0.013t$ requires a potential of approximately $V_3=2.5t$. In Fig. 