Critical currents in frustrated two-dimensional Josephson arrays

Using the peak in dynamic resistance versus current to indicate the intrinsic critical current ${\mathit{I}}_{\mathit{c}0}$, the magnetic-field dependence of ${\mathit{I}}_{\mathit{c}0}$ in two-dimensional Josephson junction arrays has been inferred from differential resistance measurements at finite voltages. This peak is particularly clear when a magnetic-field-induced vortex superlattice is strongly commensurate with the underlying lattice. At weakly commensurate fields, dV/dI rises sharply at approximately 10% of the zero-field ${\mathit{I}}_{\mathit{c}0}$, in qualitative agreement with the prediction of Lobb et al. [Phys. Rev. B 27, 150 (1983)] for the pinning of isolated vortices. New exact calculations of the critical current are presented for the cases of f=1/2 and 1/3 (f is the average number of flux quanta per cell of the array), which agree well with our experimental measurements. Implications of these exact results for the effect of boundary conditions in computer simulations on small arrays are also noted.