Critical currents in quasiperiodic pinning arrays: chains and Penrose lattices

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