Charge and vortex dynamics in arrays of tunnel junctions

Arrays of tunnel junctions can be fabricated with small nearest-neighbor capacitances between the islands and with even smaller self-capacitances of the islands. It has been suggested by Mooij et al. that electric charges on the islands of such an array interact logarithmically over large distances, and as a consequence, a Kosterlitz-Thouless-Berezinskii transition can occur where charge-anticharge pairs dissociate. Furthermore, in superconducting junction arrays the more familiar vortex-unbinding transition can occur. We investigate the effect of single-electron and Cooper-pair tunneling on these transitions and discuss the competition between the charge and the vortex unbinding.