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

TL;DR

This paper investigates how quasiperiodic pinning arrays, including 1D chains and 2D Penrose lattices, influence the critical depinning current in superconductors, revealing self-similar structures and broadening the range of high critical currents.

Contribution

It provides a detailed analysis of critical currents in quasiperiodic pinning arrays, highlighting the role of Fibonacci sequences and self-similarity, and compares their effectiveness to periodic and random arrays.

Findings

Peaks in J_c(Phi) follow Fibonacci harmonics in 1D chains.

Self-similarity observed in J_c(Phi) for QP lattices.

QP lattices yield broader high J_c(Phi) ranges than periodic or random arrays.

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.