VORTEX MOBILITY IN 2-DIMENSIONAL ARRAYS OF SMALL JOSEPHSON-JUNCTIONS

We have measured the temperature and magnetic field dependencies of the zero bias resistance for several 2D arrays of small aluminum Josephson junctions. The normal state resistances R(N) of the junctions vary between 2.2 and 7.5 kOMEGA whereas the ratio of Josephson coupling energy E(J) to the charging energy E(c) ranges between 4.3 and 0.6, where E(c)=e2/2C, C being the junction capacitance. The vortex mobility is deduced from the frustration (i.e. the number of flux quantum per unit cell) dependence of zero bias resistance. The mobility decreases when the temperature is lowered, resulting in a decrease of resistance. Fitting the data to a simple exponential form, we find the barrier for the vortex hopping to be -aE(J), with a almost-equal-to 0.3. For all arrays, there exists a crossover temperature T(cr) which separates the regime of thermally assisted hopping from that of quantum creep of vortices. For our samples, T(cr) is close to the theoretically predicted value of HBARomega(p)/2pi, where HBARomega(p)=(8E(J)E(c))1/2.