  How small superconductors can be? For isolated nanoparticles subject to
quantum size effects, P.W. Anderson conjectured in 1959 that superconductivity
could only exist when the electronic level spacing $\delta$ is smaller than the
superconducting gap energy $\Delta$.
  Here, we report a scanning tunneling spectroscopy study of superconducting
lead (Pb) nanocrystals grown on the (110) surface of InAs. We find that for
nanocrystals of lateral size smaller than the Fermi wavelength of the 2D
electron gas at the surface of InAs, the electronic transmission of the
interface is weak; this leads to Coulomb blockade and enables the extraction of
the electron addition energy of the nanocrystals. For large nanocrystals, the
addition energy displays superconducting parity effect, a direct consequence of
Cooper pairing. Studying this parity effect as function of nanocrystal volume,
we find the suppression of Cooper pairing when the mean electronic level
spacing overcomes the superconducting gap energy, thus demonstrating
unambiguously the validity of the Anderson criterion.
