Finite-size and boundary effects on the I-V characteristics of two-dimensional superconducting networks

The effect of finite-size and boundary conditions on the I-V characteristics of a resistively shunted, two-dimensional Josephson-junction array in zero magnetic field is studied both analytically and numerically. Through a detailed analysis of activation, driven diffusion, and destruction of free vortices under periodic boundary conditions, we obtain a two-scale finite-size scaling expression which, in particular, resolves a previously reported discrepancy between the analytical treatment of Ambegaokar et al. [Ambegaokar, Halperin, Nelson, and Siggia, Phys. Rev. Lett. 40, 783 (1978)] and numerical simulations. The effect of finite array width on the I-V curves in the experimentally studied open networks is governed by a different, one-scale scaling expression with a different underlying physical mechanism. For arrays of sufficiently large width, data from the two types of boundary conditions provide lower and upper bounds on the asymptotic value of the voltage. Large-scale simulations (up to 2304x512 nodes) are carried out to verify the phenomenological analysis.