Observation of large tunneling-conductance variations in direct mapping of the energy gap of single-crystal ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8\mathrm{-}\mathit{x}}$

The tunneling conductance G(V,x,y) is mapped with 5 Å resolution on cleaved a-b planes of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8\mathrm{-}\mathit{x}}$ crystals (${\mathit{T}}_{\mathit{c}}$=90 K) using scanning (vacuum) tunneling spectroscopy at 4.2 K. A strong, spatially varying G(V,x,y), evidently arising from a superconducting gap ${\mathrm{\Delta }}_{\mathit{c}}$, is observed on the a-b plane. A more highly peaked G(V) with reduced peak spacing is seen near (∼50 Å) specific sites, and over broader areas. It is suggested that the striking variations in G(V,x,y) probably indicate local variations in BiO-layer metallicity, revealing an internal superconducting proximity effect between BiO and ${\mathrm{CuO}}_2$ layers.