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 ${\mathit{E}}_{\mathit{C}}$≊1 K, and normal-state resistances ${\mathit{R}}_{\mathit{N}}$ in the range of 4–150 kΩ. From the IV characteristics we can deduce the zero-bias resistance ${\mathit{R}}_0$ and the threshold voltage ${\mathit{V}}_{\mathit{t}}$ which reveal important information about the dynamics and statics of charge solitons in the array. ${\mathit{R}}_0$(T) increases with decreasing temperature and may be described by thermal activation of charge solitons, characterized by an activation energy ${\mathit{E}}_{\mathit{a}}$. When the electrodes are in the normal state, ${\mathit{E}}_{\mathit{a}}$ is close to 1/4${\mathit{E}}_{\mathit{C}}$. At low T, the thermal activation behavior breaks down, and ${\mathit{R}}_0$(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, ${\mathit{E}}_{\mathit{a}}$ is much larger and dependent on B. In several samples, both ${\mathit{E}}_{\mathit{a}}$ and ${\mathit{V}}_{\mathit{t}}$ oscillate with B, having a period corresponding to one flux quantum per unit cell. For increasing magnetic fields, ${\mathit{V}}_{\mathit{t}}$ increases until B≊250–450 G where it starts to decrease rapidly. We interpret the B dependence of ${\mathit{E}}_{\mathit{a}}$ and ${\mathit{V}}_{\mathit{t}}$ as a result of competition between Cooper-pair solitons and single-electron solitons.