Magnetic-field-driven phase transitions in Josephson arrays

We have studied the phase transitions induced by the magnetic field $B$ in arrays of small Josephson junctions. The number of nearest-neighbor junctions connected to a single superconducting island varied between 4 and 11 for different arrays. When frustrated by the magnetic field, the arrays demonstrated several quantum phase transitions at different critical values of the resistance between $R $=3-10~k, which is in line with earlier observations. In particular, with increasing $B$ we observed transitions between three states$: $ a) the superconducting state with zero $R$, b) the ``metallic'' state with a weak $R$ dependence on T in the range 40mK$<$T$<$200mK, and c) the ``insulating'' state with an activation dependent $R(T)$. The activation energy, extracted from the current-voltage characteristics and the Arrhenius fitting of $R(T)$ in the ``insulating'' regime, has been studied in detail as a function of the temperature and the magnetic field. The data indicate the possible development of a strongly inhomogeneous state when approaching the superconducting-to-insulating transition.