in the $5\times 5$ gap patch. As expected, small-gap regions support well-defined Andreev resonant states, which are however much weaker in large-gap regions. Thus at least at a qualitative level the phase impurity scenario seems to be fully consistent with the present experimental STM data near Zn impurities. Note that the results in Fig. \[fig7\] are shown without the filter effect, and with $\delta t=0$ and a constant smearing factor $\eta=0.01t$ as opposed to an inelastic scattering rate $\Gamma(\omega)=0.1 |\omega |$ used in Figs. \[fig1\]-\[fig5\]. We find that local suppression of the hopping mainly renormalizes $\alpha$ ($\delta t < 0$ leads to smaller effective $\alpha$) whereas $\Gamma(\omega)$, which dominates the large-gap regions,[@alldredge] obviously leads to further smearing preferentially of the high-energy features $\omega \gtrsim \Delta$.

Discussion
==========

Several rather general points and caveats need to be mentioned in connection with the overall problem. First, we have assumed that the impurity resonances are extinguished because of some effect of the electronic system, i.e. we ignore the possibility that the impurities themselves are simply absent due to nonrandom processes during the crystal growth (for a discussion, see Ref. ).

Second, we have assumed that the spectral gap is a quantity characterizing the 