Effect of finite size on the Kosterlitz-Thouless transition in two-dimensional arrays of proximity-coupled junctions

We have investigated the Kosterlitz-Thouless (KT) transition in a series of proximity-coupled Josephson junction arrays of varying widths. Our results indicate that the KT transition in any experimentally realizable sample is almost always obscured by the presence of thermally generated, finite-size-induced free vortices. While the existence of these finite-size-induced free vortices has been known for some time, our work suggests that they are much more prevalent and thus have a far greater effect on the transition than had been previously thought. As a consequence of this, the vortex-unbinding transition temperature $T_{\mathrm{KT}}$ may not occur when the experimentally measured current-voltage exponent $a\left(T\right)=3,$ but in fact may occur at significantly higher temperatures. We present a detailed picture of these finite-size effects applied specifically to arrays, but which may have implications for other two-dimensional systems.