  We investigate the spatial and doping evolutions of the superconducting
properties of tri-layer cuprate Bi2Sr2Ca2Cu3O10+x by using scanning tunneling
microscopy and spectroscopy. Both the superconducting coherence peak and gap
size exhibit periodic variations with the structural supermodulation, but the
effect is much more pronounced in the underdoped regime than at optimal doping.
Moreover, a new type of tunneling spectrum characterized by two superconducting
gaps emerges with increasing doping, and the two-gap features also correlate
with the supermodulation. We propose that the interaction between the
inequivalent outer and inner CuO2 planes is responsible for these novel
features that are unique to tri-layer cuprates.

Superconductivity;Strongly Correlated Electrons