Critical currents in superconductors with quasiperiodic pinning arrays: One-dimensional chains and two-dimensional Penrose lattices

We study the critical depinning current J_c, as a function of the applied magnetic flux Phi, for quasiperiodic (QP) pinning arrays, including one-dimensional (1D) chains and two-dimensional (2D) arrays of pinning centers placed on the nodes of a five-fold Penrose lattice. In 1D QP chains of pinning sites, the peaks in J_c(Phi) are shown to be determined by a sequence of harmonics of long and short periods of the chain. This sequence includes as a subset the sequence of successive Fibonacci numbers. We also analyze the evolution of J_c(Phi) while a continuous transition occurs from a periodic lattice of pinning centers to a QP one; the continuous transition is achieved by varying the ratio gamma = a_S/a_L of lengths of the short a_S and the long a_L segments, starting from gamma = 1 for a periodic sequence. We find that the peaks related to the Fibonacci sequence are most pronounced when gamma is equal to the "golden mean". The critical current J_c(Phi) in QP lattice has a remarkable self-similarity. This effect is demonstrated both in real space and in reciprocal k-space. In 2D QP pinning arrays (e.g., Penrose lattices), the pinning of vortices is related to matching conditions between the vortex lattice and the QP lattice of pinning centers. Although more subtle to analyze than in 1D pinning chains, the structure in J_c(Phi) is determined by the presence of two different kinds of elements forming the 2D QP lattice. Indeed, we predict analytically and numerically the main features of J_c(Phi) for Penrose lattices. Comparing the J_c's for QP (Penrose), periodic (triangular) and random arrays of pinning sites, we have found that the QP lattice provides an unusually broad critical current J_c(Phi), that could be useful for practical applications demanding high J_c's over a wide range of fields.Comment: 18 pages, 15 figures (figures 7, 9, 10, 13, 15 in separate "png" files

Dirac fermion time-Floquet crystal: manipulating Dirac points

We demonstrate how to control the spectra and current flow of Dirac electrons in both a graphene sheet and a topological insulator by applying either two linearly polarized laser fields with frequencies $\omega$ and $2\omega$ or a monochromatic (one-frequency) laser field together with a spatially periodic static potential(graphene/TI superlattice). Using the Floquet theory and the resonance approximation, we show that a Dirac point in the electron spectrum can be split into several Dirac points whose relative location in momentum space can be efficiently manipulated by changing the characteristics of the laser fields. In addition, the laser-field controlled Dirac fermion band structure -- Dirac fermion time-Floquet crystal -- allows the manipulation of the electron currents in graphene and topological insulators. Furthermore, the generation of dc currents of desirable intensity in a chosen direction occurs when applying the bi-harmonic laser field which can provide a straightforward experimental test of the predicted phenomena.Comment: 9 pages, 7 figures, version that will appear in Phys. Rev.