Superconducting parity effect across the Anderson limit

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.