Pinning-Induced Formation of Vortex Clusters and Giant Vortices in Mesoscopic Superconducting Disks

I. V. Grigorieva, W. Escoffier, V. R. Misko, B. J. Baelus, F. M. Peeters, L. Y. Vinnikov, and S. V. Dubonos

Phys. Rev. Lett. 99, 147003 – Published 3 October 2007

Abstract

Merged, or giant, multiquanta vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualize vortices in small Nb disks with varying degrees of disorder, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below $T_{c}$ and $H_{c 2}$ , in contrast to well-defined shells of individual vortices found in the absence of pinning.

Received 8 November 2006

DOI:https://doi.org/10.1103/PhysRevLett.99.147003

Authors & Affiliations

I. V. Grigorieva^1,*, W. Escoffier¹, V. R. Misko², B. J. Baelus², F. M. Peeters², L. Y. Vinnikov³, and S. V. Dubonos³

¹School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
²Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
³Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka 142432, Russia

^*Corresponding author.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 99, Iss. 14 — 5 October 2007

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Main panel: Diamagnetic response of single-crystal-based disks with weak (○) and strong (●) disorder; data for individual thin-film disks from Ref. 5 included for comparison (⋄). Solid lines are guides to the eye. Top-left and bottom-right insets show vortex configurations in disks with strong and weak disorder, respectively ( $H = 70 Oe$ ). Top-right inset: Vortices in and around a $1.4 μ m$ high disk decorated after field cooling in $H = 60 Oe$ . (b),(c) Vortex distributions in the bulk ( $\sim 100 μ m$ away from mesoscopic disks) of Nb crystals with strong and weak disorder, respectively.Reuse & Permissions
Figure 2
Vortex configurations in disks with strong disorder for different values of $L_{\max }$ (see text). $L^{*}$ is the vorticity of GVs or clusters estimated from their diameters.Reuse & Permissions
Figure 3
Diameters of individual and merged vortices found from image intensity profiles on disks containing only one vortex, either individual or merged (○), one merged and several individual vortices, as in the bottom-right inset (●), a mixture of individual and merged vortices of different sizes, as in the image of Fig. 2 for $L_{\max } = 36$ (half solid, half open circle). Top-left inset shows a typical radially averaged intensity profile for a vortex image. $L^{*}$ are estimated values of vorticity for clusters of different diameters.Reuse & Permissions
Figure 4
Vortex patterns for $L = 8$ (a)–(d), $L = 10$ (e),(f), and $L = 20$ (g),(h) in disks with different pinning potentials. (a) No pinning. (b) Weak pinning, $f_{p} / f_{0} = 2$ , $r_{p} = 0.08$ ; dashed line shows the pinning range. (c),(d) Strong pinning, $f_{p} / f_{0} = 4$ , $r_{p} = 0.16$ , and $f_{p} / f_{0} = 6$ , $r_{p} = 0.24$ , respectively; combination of merged and individual vortices. (e),(f) $f_{p} / f_{0} = 8$ , $r_{p} = 0.32$ : (e) Pinning site close to the boundary, combination of merged vortices with $L = 7$ and 3 individual vortices; (f) enhancement of pinning strength for a pin near the center: $L = 8$ vortices are merged, while other vortices are expelled from the disk by strong repulsion from the cluster. (g),(h) Formation of multiquanta vortices for $f_{p} / f_{0} = 10$ , $r_{p} = 0.16$ , and different $r_{\min }$ : (g) $r_{\min } = 0.048$ , vortices form clusters with $L = 5$ (near center) and $L = 4$ (out of center); (h) $r_{\min } = 0.064$ , GVs with $L = 5$ (near center) and $L = 4$ (out of center).Reuse & Permissions
Figure 5
(a) Cooper pair density $| Ψ |^{2}$ in a disk with $R = 20 ξ$ , $H = 0.2 H_{c 2}$ , for two pinning sites with $U_{0} = 1$ , and $w = 5 ξ$ , at the center and out of center. (b) Phase pattern corresponding to (a) showing a GV with $L = 5$ (center) and a cluster with $L = 3$ (out of center).Reuse & Permissions

Physical Review Letters