  Using low-temperature scanning tunneling microscopy and spectroscopy, we have
studied the proximity effect at the interfaces between superconducting Pb
island structures and metallic Pb-induced striped-incommensurate phase formed
on a Si(111) substrate. Our real-space observation revealed that the step
structures on the two-dimensional metallic layer exhibit significant roles on
the propagation of the superconducting pair correlation; the proximity effect
is terminated by the steps, and in the confined area by the interface and the
steps the effect is enhanced. The observed results are explained quantitatively
with an elastic reflection of electrons at the step edges based on calculations
with the quasi-classical Green's function formulation using Usadel equation.
