Charging energy and phase delocalization in single very small Josephson tunnel junctions

We have measured current-voltage characteristics of very small [0.4--0.02 ({μ}m)²] Sn-SnOₓ-Sn tunnel junctions, having estimated charging energy e²/2C comparable to their other characteristic energies. In the higher-Rₙ devices, after rising just below Tc, Ic decreases as the temperature is decreased further, and then increases again, at the lowest temperatures. Although the junctions are hysteretic, a significant resistance is found at currents below Ic. We suggest an interpretation involving the quantum nature of {φ} and the competition between the charging, Josephson, and thermal energies of the system.