Gap Inhomogeneity-Induced Electronic States in Superconducting $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$

We use STM to measure nearly optimally doped $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$ in zero field. Focusing on the superconducting gap, we find patches of what appear to be two different phases in a background of some average gap, one with a relatively small gap and sharp large coherence peaks and one characterized by a large gap with broad weak coherence peaks. We compare these spectra with calculations of the local density of states for a simple phenomenological model in which a $2\xi_0 \times 2\xi_0$ patch with an enhanced or supressed d-wave gap amplitude is embedded in a region with a uniform average d-wave gap.