Quantum Phenomena in Mesoscopic Superconducting Tunnel Junctions.

We report a low temperature study of very small superconducting tunnel junctions. The samples were fabricated by using electron-beam lithography and thermal evaporation in single-junction, double-junction and eleven-junction -array configurations. The junctions had normal resistances between 0.5 and 140 kOmega and areas between 0.1 and 0.02 (mu m) ^2. We measured the current-voltage characteristics of the devices at low temperatures (20 mK -4 K), using a dilution refrigerator. In general, the devices had a large single electron charging energy E_{c} equiv e^2/2 C of order 1 K. By varying the ratio of E_{c} to the Josephson coupling energy E_{J }, we studied the crossover between the conventional Josephson regime, in which E_{J} gg E_{c }, and the Coulomb blockade regime, in which charging effects are dominant. For comparable charging and Josephson energies the I-V curve is resistive at all currents, and exhibits a novel low-voltage resistance R_{o} at currents less than the critical current I_{c} . Moreover, I_{c} is greatly reduced when compared to conventional Josephson junction results, and scales at low temperatures with R_{n}^{-2}. If a magnetic field is applied to the junctions, reducing E_{J} so that E _{J} << E_{c}, we find a striking regime in which aspects of the Coulomb blockade of tunneling coexist with features typical of Josephson tunneling. We develop a number of semiquantitative 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 models. At low temperatures, however, quantum fluctuations of the phase appear to become much more important, as thermal fluctuations and quasiparticle damping freeze out. We then turn to quantum mechanical methods to analyze our measurements. We use the semiclassical WKB approach, valid in the low E_{c }/E_{J} limit (and extend it to regions nearer the E_ {c} ~ E _{J} limit by a numerical method), to obtain estimates of R_{o} in reasonably good agreement with our measurements. Moreover, by assuming that I_{c} scales with the binding energy of the ground state phase wavefunction in the Josephson potential, we account for its experimental R_{n}^ {-2} dependence. Finally, we use a charge -space model to provide a semiquantitative account of the measurements in the high E_{c} /E_{J} limit.