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

Abstract

We have measured current-voltage characteristics of very small [0.4–0.02 (μm${)}^2$] Sn-${\mathrm{SnO}}_{\mathrm{x}}$-Sn tunnel junctions, having estimated charging energy $e^2$/2C comparable to their other characteristic energies. In the higher-$R_n$ devices, after rising just below $T_c$, $I_c$ 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 $I_c$. We suggest an interpretation involving the quantum nature of φ and the competition between the charging, Josephson, and thermal energies of the system.