Charge Kosterlitz-Thouless-Berezinskii Transition in Arrays of Tunnel Junctions
In recent years much attention has been devoted to the study of junction arrays . When the islands become superconducting a phase transition, in which the system reaches a state of phase coherence, takes place. In two-dimensional (2D) arrays the transition is driven by the dissociation of vortex-anti-vortex pairs. When the dimensions of the islands become such that it is not possible to disregard charging energy quantum fluctuations become important. The main effect is the suppression of the vortex unbinding transition temperature  and also at T = 0 it is possible to have a disordered phase. The tunneling of quasi-particles or Ohmic shunts introduce dissipation . The most striking consequence is the existence of a critical value of the normal sheet resistance below which the superconductivity is recovered even when the charging energy exceeds the Josephson term , Experiments of fabricated 2D networks show a similar transition between an insulating and a superconductive state as the resistance of the sample is varied .
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