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

Abstract

We study the critical depinning current Jc, as a function of the applied magnetic flux Φ, 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 Jc(Φ) 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 Jc(Φ) 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 γ = aS/aL of lengths of the short aS and the long aL segments, starting from γ = 1 for a periodic sequence. We find that the peaks related to the Fibonacci sequence are most pronounced when γ is equal to the "golden mean". The critical current Jc(Φ) 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 Jc(Φ) 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 Jc(Φ) for Penrose lattices. Comparing the Jc'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 Jc(Φ), that could be useful for practical applications demanding high Jc's over a wide range of fields.

Superconducting vortex pinning with artificial magnetic nanostructures

“…For these, commensurability develops between the vortex lattice and the array implying a high degree of order with long vortex-lattice correlation lengths. However, as reviewed in Section 5.2, commensurability effects have also been observed on arrays with only local order but lacking periodic order (quasiperiodic [33,34,[182][183][184] and fractal arrays [33]) and with nonperiodic long-range order [33]. Moreover, matching effects have been recently observed in some systems with only short-range periodic pinning [185].…”

Magnetic flux pinning in superconductors with hyperbolic-tessellation arrays of pinning sites

“…The free-of-pinning region between the HT APS and the boundary of the simulation cell serves as a reservoir of vortices that mimics the externally applied magnetic field. This approach has been successfully used in numerous simulations in the past (see, e.g., 17,18,21,[23][24][25] ). To study the dynamics of vortex motion, we numerically integrate the overdamped equations of motion (see, e.g., Refs.…”

Surface Effects on the Dynamic Behavior of Vortices in Type II Superconducting Strips with Periodic and Conformal Pinning Arrays

“…Several works had investigated the effects of periodic , quasi-periodic [41][42][43][44][45][46][47][48], and randomly distributed [49][50][51][52][53][54] pinning centers in superconducting films. For periodic pinning, such as square [12][13][14][15][16][17][18][19][20][21], triangular [30][31][32][33][34][35]55], honeycomb [27,29,30,38], and Kagomé [27-29, 32, 37], vortices tend to match the pinning lattice in commensurate patterns, which greatly enhances the critical current density.…”

“…However, these enhancements occur at specific values of magnetic fields, resulting in high oscillations of the critical current as a function of the applied field [13,14,29,[33][34][35][36][37][38][39][40]. On the other hand, quasiperiodic arrays, such as Penrose [43,44,48], hyperbolic tessellations [47], and Archimedean tilings [41,46], show unusual commensurability effects for several values of applied magnetic fields; besides that, for a wide range of fields, the critical depinning currents are high. Recently, Ray et al [56] proposed conformal pinning arrays created by a conformal angle-preserving transformation of a regular pinning array.…”