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

Abstract

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.

arXiv comment18 pages, 15 figures (figures 7, 9, 10, 13, 15 in separate "png" files)

References in corpus (14)

• The Flux-Line Lattice in Superconductors
• Dynamic Phases of Vortices in Superconductors with Periodic Pinning
• Commensurate and Incommensurate Vortex States in Superconductors with Periodic Pinning Arrays
• Spatio-temporal dynamics and plastic flow of vortices in superconductors with periodic arrays of pinning sites
• Vortex Plastic Flow, $B(x,y,H(t)),M(H(t)),J_c(B(t))$, Deep in the Bose Glass and Mott-Insulator Regimes
• Critical Currents in Quasiperiodic Pinning Arrays: Chains and Penrose Lattices
• Intermittently Flowing Rivers of Quantized Magnetic Flux
• Microscopic Derivation of Magnetic Flux Density Profiles, Magnetization Hysteresis Loops, and Critical Currents in Strongly Pinned Superconductors
• Directional vortex motion guided by artificially induced mesoscopic potentials
• Anisotropic vortex pinning in superconductors with a square array of rectangular submicron holes
• Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals
• Field-dependent Vortex Pinning Strength in a Periodic Array of Antidots
• Quasiperiodic extended Bloch states in a surface wave experiment
• Soliton pinning by long-range order in aperiodic systems

Cited by in corpus (30)

• Commensurability effects in superconducting Nb films with quasiperiodic pinning arrays
• Enhancing the Critical Current of a Superconducting Film in a Wide Range of Magnetic Fields with a Conformal Array of Nanoscale Holes
• Freezing and melting of vortex ice
• Symmetry-induced giant vortex state in a superconducting film with a Penrose array of magnetic pinning centers
• Dynamical Ordering and Directional Locking For Particles Moving Over Quasicrystalline Substrates
• Enhancement of pinning properties of superconducting thin films by graded pinning landscapes
• Magnetic flux pinning in superconductors with hyperbolic-tesselation arrays of pinning sites
• Negative differential resistivity in superconductors with periodic arrays of pinning sites
• Physical properties of weak-coupling quasiperiodic superconductors
• Effect of hexagonal patterned arrays and defect geometry on the critical current of superconducting films
• Enhancing the critical current in quasiperiodic pinning arrays below and above the matching magnetic flux
• Moving Vortex Phases, Dynamical Symmetry Breaking, and Jamming for Vortices in Honeycomb Pinning Arrays
• Vortex states in mesoscopic superconducting squares: Formation of vortex shells
• Suppression of dissipation in Nb thin films with triangular antidot arrays by random removal of pinning sites
• Commensurability Effects at Nonmatching Fields for Vortices in Diluted Periodic Pinning Arrays
• Formation and Size-Dependence of Vortex Shells in Mesoscopic Superconducting Niobium Disks
• Dynamics of self-organized driven particles with competing range interaction
• Pinning, Ordering, and Dynamics of Vortices in Conformal Crystal and Gradient Pinning Arrays
• Vortex dynamics in superconducting channels with periodic constrictions
• Ultradense Tailored Vortex Pinning Arrays in Superconducting YBa${}_2$Cu${}_3$O${}_{7-\delta }$ Thin Films Created by Focused He Ion Beam Irradiation for Fluxonics Applications
• Enhancing superconducting critical current by randomness
• Guided nucleation of superconductivity on a graded magnetic substrate
• Pattern formation in vortex matter with pinning and frustrated inter-vortex interactions
• Collective vortex phases in periodic plus random pinning potential
• Supercurrent Distribution in Real-Space and Anomalous Paramagnetic Response in a Superconducting Quasicrystal
• The solitons redistribution in Bose-Einstein condensate in quasiperiodic optical lattice
• Unconventional superfluidity of superconductivity on Penrose lattice
• The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
• Brillouin zone folding method for quasiperiodic superconductivity in multilayer systems: application to electronic structure and optical responses
• Pinning of Vortices by impurities in Unconventional superconductors