Dynamics of vortex shells in mesoscopic superconducting Corbino disks

V. R. Misko and F. M. Peeters

Phys. Rev. B 74, 174507 – Published 14 November 2006

Abstract

In mesoscopic superconducting disks vortices form shell structures as recently observed in Nb disks. We study the dynamics of such vortices, driven by an external current $I_{0}$ , in a Corbino setup. At very low $I_{0}$ , the system exhibits rigid-body rotation while at some critical current $I_{c, i}$ vortex shells rotate separately with angular velocities $ω_{i}$ . This critical current $I_{c, i}$ has a remarkable nonmonotonous dependence on the applied magnetic field which is due to a dynamically induced structural transition with a rearrangement of vortices over the shells similar to the Coster-Kronig transition in hollow atoms. Thermally activated externally driven flux motion in a disk with pinning centers explains experimentally observed $ω_{i}$ as a function of $I_{0}$ and $T$ and the dynamically induced melting transition.

Received 17 October 2006

DOI:https://doi.org/10.1103/PhysRevB.74.174507

Authors & Affiliations

V. R. Misko and F. M. Peeters

Department of Physics, University of Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium

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Issue

Vol. 74, Iss. 17 — 1 November 2006

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Images

Figure 1
(Color online) The Corbino setup: the applied current is injected at the center and removed at the perimeter of the disk to induce a radial current density $J$ (shown by dark blue/dark grey arrows) that decays as $1 ∕ ρ$ along the radius. As a result, vortices near the center of the disk experience a stronger Lorentz force $F_{L}$ (shown by yellow/light grey arrows) than those near the disk’s edge. The vortices are shown by red-to-yellow/grey-to-light grey tubes and by red/grey spots on the surface. The direction of the external applied magnetic field $H_{0}$ , which is perpendicular to the surface of the disk, is shown by dark yellow/grey arrow.Reuse & Permissions
Figure 2
(Color online) The angular velocities $ω_{1}$ (orange/light grey solid circles) and $ω_{2}$ (blue/dark grey open squares), measured in units of $ω_{0} = 4 π μ_{0} H_{c}^{2} ξ^{2} ∕ η R^{2}$ , of vortices in the first and second shells, respectively, as a function of applied current $I_{0}$ , measured in units of $μ_{0} Λ I_{ext} ∕ Φ_{0}$ , for $L = 19$ and different magnetic fields $h$ : (a) $h = 24$ , a rigid-body rotation for $I_{0} < I_{c} \approx 10.4$ ; the shells rotate separately for $I_{0} > I_{c}$ ; (b) $h = 25$ , the critical current decreases, $I_{c} \approx 6.5$ ; (c) $h = 26.25$ , the $I_{c}$ further decreases, $I_{c} \approx 3$ , and the motion becomes unstable; (d) $h = 26.5$ , bistable motion, a second critical current $I_{c 1} \approx 7.1$ appears; (e) $h = 30$ , the motion stabilizes, and first critical current $I_{c}$ disappears, and critical current $I_{c} = I_{c 1}$ .Reuse & Permissions
Figure 3
(Color online) The critical current $I_{c}$ (in units of $μ_{0} Λ I_{ext} ∕ Φ_{0}$ ) versus $h$ [in units of $(H_{0} ∕ 2 H_{c 2}) {(R ∕ ξ)}^{2}$ ] near the structural transition between the states (1,6,12) (solid black circles) and (1,7,11) (solid red/grey triangles), insets. Empty symbols correspond to bistable vortex motion, with two critical currents, $I_{c}$ and $I_{c 1}$ . The jump in $I_{c}$ is related to an intershell vortex transition from a higher to a lower orbit, similar to the Coster-Kronig transition in hollow atoms.Reuse & Permissions
Figure 4
(Color online) The angular velocities $ω_{i}$ (in units of $ω_{0} = 4 π μ_{0} H_{c}^{2} ξ^{2} ∕ η R^{2}$ ) versus $I_{0}$ (in units of $μ_{0} Λ I_{ext} ∕ Φ_{0}$ ) in first (orange/light grey open circles), second (black solid line), and third (blue/dark grey open squares) shells, for a three-shell vortex configuration with $L = 37$ . The inset shows a triangular-lattice ground-state configuration (1,6,12,18) for $h = 37$ at $I_{0} = 0$ . The critical currents are $I_{c 12} \approx 9.1$ and $I_{c 23} \approx 9.5$ .Reuse & Permissions
Figure 5
(Color online) The angular velocities of vortices $ω_{i}$ (in units of $ω_{0} = 4 π μ_{0} H_{c}^{2} ξ^{2} ∕ η R^{2}$ ) versus $T$ (in units of $T_{0} = 4 π μ_{0} H_{c}^{2} ξ^{2} d ∕ k_{B}$ ) in first, second, and third shells (using the same symbols as in Fig. 4), for $L = 37$ , $I_{0} = 0.4$ , $f_{p} ∕ f_{0} = 2.5$ . The onset of motion occurs in the form of rigid-body rotation. At $T = T_{c 1}^{⋆}$ , the inner shell splits off, the second shell unlocks at $T = T_{c 21}^{⋆}$ , and shells rotate independently (angular melting). The radial melting, i.e., dissolving of the shells, occurs at $T = T_{M, r}$ . Inset, the experimental $T$ dependence of $ω_{i}$ obtained from the resistivity measurements at three different distances from the center of a Corbino disk (Ref. 3).Reuse & Permissions

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