Critical Currents in Quasiperiodic Pinning Arrays: Chains and Penrose Lattices

We study the critical depinning current $J_c$ versus the applied magnetic flux $\Phi$, for quasiperiodic (QP) chains and 2D arrays of pinning centers placed on the nodes of a fivefold Penrose lattice. In QP chains, the peaks in $J_c(\Phi )$ are determined by a sequence of harmonics of the long and short segments of the chain. The critical current $J_c(\Phi )$ has a remarkable self-similarity. In 2D QP pinning arrays, we predict analytically and numerically the main features of $J_c(\Phi )$, and demonstrate that the Penrose lattice of pinning sites provides an enormous enhancement of $J_c(\Phi )$, even compared to triangular and random pinning site arrays. This huge increase in $J_c(\Phi )$ could be useful for applications.