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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., Comment: 25 pages, 5 figures in main articles, 9 in supplementary

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Submitted to PRL; Opening of several gaps in the surface band structure of vicinal Au(23 23 21) surface has been evidenced by high resolution photoemission spectroscopy whereas the energy dependence of the surface electronic density have been determined by scanning tunneling spectroscopy. From a methodological point of view, the values of the gaps and the phase of the electronic density allow to estimate the reconstruction potential which yields the electronic Bragg diffraction, the gap formation and the modulation of the electronic density. These spectroscopic behaviors give a pedagogical illustration of one of the basic concepts of solid state physics.