Vortex mobility in two-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 kω 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≈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 ω_p 2π, where ω_p=(8E_JE_c) ^{1 2}.