Critical Currents in Quasiperiodic Pinning Arrays: Chains and Penrose Lattices

Abstract

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.

Commensurability Effects in Superconducting Nb Films with Quasiperiodic Pinning Arrays

“…We studied I c (B) at variable temperature T close to the superconducting transition temperature T c , and we compare Penrose lattices with triangular lattices, with random arrangements of antidots and with thin films without antidots. Our experimental results on Penrose arrays confirm essential features in the I c (B) patterns as predicted in [13].The experiments were carried out on d = 60 nm thick Nb films which were deposited by dc magnetron sputtering in the same run on five separate substrates. Patterning was performed by e-beam lithography and lift-off to produce cross-shaped Nb bridges with circular antidots arranged in different geometries.…”

“…This situation occurs in particular at the so-called first matching field B 1 = Φ 0 /A, i.e., when the applied field B corresponds to one flux quantum Φ 0 = h/2e per unit-cell area A of the pinning array. In general, I c (B) may show a strongly non-monotonic behavior, with local maxima at matching fields B m = mB 1 (m: integer or a rational number), which reflects the periodicity of the array of artificial pinning sites.As pointed out by Misko et al [13], an enhancement of I c occurs only for an applied field close to matching fields, which makes it desirable to use artificial pinning arrays with many built-in periods, in order to provide either very many peaks in I c (B) or an extremely broad peak in * Electronic address: koelle@uni-tuebingen.de I c (B). Accordingly, Misko et al studied analytically and by numerical simulation vortex pinning by quasiperiodic chains and by 2D pinning arrays, the latter forming a fivefold Penrose lattice [14], and they predicted that a Penrose lattice of pinning sites can provide an enormous enhancement of I c , even compared to triangular and random pinning arrays.…”

“…As pointed out by Misko et al [13], an enhancement of I c occurs only for an applied field close to matching fields, which makes it desirable to use artificial pinning arrays with many built-in periods, in order to provide either very many peaks in I c (B) or an extremely broad peak in * Electronic address: koelle@uni-tuebingen.de I c (B). Accordingly, Misko et al studied analytically and by numerical simulation vortex pinning by quasiperiodic chains and by 2D pinning arrays, the latter forming a fivefold Penrose lattice [14], and they predicted that a Penrose lattice of pinning sites can provide an enormous enhancement of I c , even compared to triangular and random pinning arrays.…”

“…Figure 3 shows I c (B)-patterns of a Penrose array at three different temperatures close to T c . Here, I c is defined by a dynamic criterion, i.e., via the detection of [13] (for N p =301 pinning sites), without any adjustable parameter. For these calculations a static I c definition (number of pinned vortices over the number of vortices) was used.…”

Microfluidic manipulation of magnetic flux domains in type-I superconductors: droplet formation, fusion and fission

“…For that reason, much attention has been given in the past to hampering vortex motion by introducing arrays of artificial pinning centers in superconductors, nanoengineered in size and geometry for optimal vortex pinning and enhancement of maximal sustainable magnetic field and electric current in the superconducting state [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] . Pinning is also of importance in type-I superconductors, for example in defining the structure of the intermediate state (IS) 18,19 , which is a very rich study object and has received a revival of interest in recent years [20][21][22][23][24][25][26][27][28][29][30][31][32] .…”