Superconductivity of UHV Grown Pb Nanocrystals at the Anderson Limit

What is the size limit for the existence of superconductivity in isolated superconducting nanocrystals? In 1959, P.W. Anderson predicted that superconductivity should disappear in nanocrystals where the mean level spacing becomes larger than the superconducting gap energy. Despite many attempts, this Anderson limit has never been demonstrated experimentally.
In this work, we demonstrated the Anderson limit by low-temperature STM spectroscopy of single Pb nanocrystals grown on the (110) surface of InAs. Following the growth of the Pb nanocrystals, we found that nanocrystals of area smaller than the Fermi wavelength of the 2D electron gas at the surface of InAs are only weakly connected to this 2D gaz and leads to Coulomb blockade in the Pb nanocrystals, which leads to sharp peaks in the tunneling spectrum. The interval between the Coulomb peaks provides a measure of the addition energy in the Pb nanocrystals. Because of the formation of the Cooper pairs, the addition energy is 2e periodic. Measuring the addition energy for nanocrystals volume ranging from 0.01 V_^Anderson to 10 V^_Anderson, as function of temperature, we observed the drop in the superconducting gap energy and critical temperature at the Anderson limit.