  We report high-resolution scanning tunneling microscopy (STM) study of
nano-sized Pb islands grown on SrTiO3, where three distinct types of gaps with
different energy scales are revealed. At low temperature, an enlarged
superconducting gap ({\Delta}s) emerges while there is no enhancement in
superconducting transition temperature (Tc), giving rise to a larger BCS ratio
2{\Delta}s/kBTc ~ 6.22. The strong coupling here may originate from the
electron-phonon coupling on the metal-oxide interface. As the superconducting
gap is suppressed under applied magnetic field or at elevated temperature,
Coulomb gap and pseudogap appear, respectively. The Coulomb gap is sensitive to
the lateral size of Pb islands, indicating that quantum size effect is able to
influence electronic correlation, which is usually ignored in low-dimensional
superconductivity. Our experimental results shall shed important light on the
interplay between quantum size effect and correlations in nano-sized
superconductors.
