Charging effects and quantum properties of small superconducting tunnel junctions

We have fabricated small superconducting tunnel junctions with a large single-electron charging energy $E_c$ and measured the low-temperature current-voltage characteristics of devices having a wide range of ratios of $E_c$ to the Josephson coupling energy $E_J$. For $E_c$≊$E_J$, the I-V curve is resistive at all currents and the critical current is greatly reduced relative to that of conventional Josephson junctions. If $E_J$≪$E_c$, we find a novel regime in which aspects of the Coulomb blockade of tunneling coexist with features typical of Josephson tunneling. We describe a number of models which appear to explain the salient new features of our observations. In the high-temperature regime, thermal activation and damping effects are very important, since $E_c$ and $E_J$ are only of order 1 K, and the experimental results are fitted by extending well-established classical methods. At low temperatures, however, quantum fluctuations of the phase appear to become much more important, as thermal fluctuations and quasiparticle damping freeze out. We thus present a number of quantum-mechanical treatments, based in phase and charge space, which provide a semiquantitative account of the measurements in the low-temperature regime.