Unbinding of charge-anticharge pairs in two-dimensional arrays of small tunnel junctions

We describe the behavior of charges in two-dimensional arrays of normal-metal tunnel junctions with very small capacitance. A Kosterlitz-Thouless-Berezinskii phase transition with unbinding of charge-anticharge pairs occurs at a transition temperature of about ${\mathit{T}}_{\mathit{c}}$=${\mathit{e}}^2$/8π${\mathit{Ck}}_{\mathit{B}}$, with C the junction capacitance. We calculate the influence of tunneling conductance; ${\mathit{T}}_{\mathit{c}}$ is reduced with increasing conductance and no transition occurs for junction conductance above (14 kΩ${)}^{\mathrm{-}1}$. In the superconducting state a similar transition occurs at a 4 times higher ${\mathit{T}}_{\mathit{c}}$. We present the first experimental results on the conductive transition of an array in the normal and superconducting states.