EFFECT OF FINITE-SIZE ON THE KOSTERLITZ-THOULESS TRANSITION IN 2-DIMENSIONAL ARRAYS OF PROXIMITY-COUPLED JUNCTIONS

We have investigated the Kosterlitz-Thouless (KT) transition in a seri es of proximity-coupled Josephson junction arrays of varying widths. O ur results indicate that the KT transition in any experimentally reali zable sample is almost always obscured by the presence of thermally ge nerated, finite-size-induced free vortices. While the existence of the se finite-size-induced foe vortices has been known for some time, our work suggests that they are much more prevalent and thus have a far gr eater effect on the transition than had been previously thought. As a consequence of this, the vortex-unbinding transition temperature T-KT may not occur when the experimentally measured current-voltage exponen t a(T)=3, but in fact may occur at significantly higher temperatures. We present a detailed picture of these finite-size effects applied spe cifically to arrays, but which may have implications for other two-dim ensional systems.