Charge solitons and quantum fluctuations in two-dimensional arrays of small Josephson junctions

We have measured the current-voltage (IV) characteristics of several two-dimensional arrays of small Josephson junctions as a function of temperature, T and magnetic field B. The junctions have relatively large charging energies EC{}1 K, and normal-state resistances RN in the range of 4--150 k{Ω}. From the IV characteristics we can deduce the zero-bias resistance R₀ and the threshold voltage Vₜ which reveal important information about the dynamics and statics of charge solitons in the array. R₀(T) increases with decreasing temperature and may be described by thermal activation of charge solitons, characterized by an activation energy Eₐ. When the electrodes are in the normal state, Eₐ is close to 1/4EC. At low T, the thermal activation behavior breaks down, and R₀(T) levels off to a value that can be attributed to the quantum fluctuations in the array. This interpretation places limitations on the observability of the charge unbinding, Kosterlitz-Thouless-Berezinskii transition for single electrons. When the electrodes are superconducting, Eₐ is much larger and dependent on B. In several samples, both Eₐ and Vₜ oscillate with B, having a period corresponding to one flux quantum per unit cell. For increasing magnetic fields, Vₜ increases until B{}250--450 G where it starts to decrease rapidly. We interpret the B dependence of Eₐ and Vₜ as a result of competition between Cooper-pair solitons and single-electron solitons.