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. 2017 Jul 20;8(1):85.
doi: 10.1038/s41467-017-00089-3.

Imaging of Super-Fast Dynamics and Flow Instabilities of Superconducting Vortices

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Free PMC article

Imaging of Super-Fast Dynamics and Flow Instabilities of Superconducting Vortices

L Embon et al. Nat Commun. .
Free PMC article

Abstract

Quantized magnetic vortices driven by electric current determine key electromagnetic properties of superconductors. While the dynamic behavior of slow vortices has been thoroughly investigated, the physics of ultrafast vortices under strong currents remains largely unexplored. Here, we use a nanoscale scanning superconducting quantum interference device to image vortices penetrating into a superconducting Pb film at rates of tens of GHz and moving with velocities of up to tens of km/s, which are not only much larger than the speed of sound but also exceed the pair-breaking speed limit of superconducting condensate. These experiments reveal formation of mesoscopic vortex channels which undergo cascades of bifurcations as the current and magnetic field increase. Our numerical simulations predict metamorphosis of fast Abrikosov vortices into mixed Abrikosov-Josephson vortices at even higher velocities. This work offers an insight into the fundamental physics of dynamic vortex states of superconductors at high current densities, crucial for many applications.Ultrafast vortex dynamics driven by strong currents define eletromagnetic properties of superconductors, but it remains unexplored. Here, Embon et al. use a unique scanning microscopy technique to image steady-state penetration of super-fast vortices into a superconducting Pb film at rates of tens of GHz and velocities up to tens of km/s.

Conflict of interest statement

The authors declare no competing financial interests.

Figures

Fig. 1
Fig. 1
Pb thin film sample and the experimental set-up. a 3D representation of a 10 × 5 µm2 AFM scan of the sample of 75 nm-thick Pb film patterned into a 10 µm-wide strip with a 5.7 µm wide constriction. Indicated are the directions of the applied magnetic field B a, current I, the Lorentz force acting on vortices F L, and the screening (Meissner) current density J M that is maximal along the edges. b SEM image of the same sample with corresponding distribution of the Meissner current J M(x) across the construction in absence of vortices and applied current. Scale bar is 2 µm
Fig. 2
Fig. 2
Magnetic imaging of stationary and fast moving vortices in Pb film at 4.2 K. ad B z(x, y) SQUID-on-tip images of vortex configurations at I = 0 for different values of applied field B a = 2.7 a,b, 5.4 c, and 9.0 mT d. eh Images acquired at the verge of vortex motion at I ≲ I c, at B a = 2.7 mT and I = 16 mA e,f, B a = 5.4 mT, I = 12.2 mA g, and B a = 9.0 mT, I = 6.0 mA h. il Images of onset of vortex flow at I ≳ I c at B a = 2.7 mT, I = 18.9 mA i,j, B a = 5.4 mT, I = 12.4 mA k, and B a = 9.0 mT, I = 9.1 mA l. mp Vortex flow patterns at the highest sustainable current with B a = 2.7 mT, I = 20.9 mA m,n, B a = 5.4 mT, I = 16.2 mA o, and B a = 9.0 mT, I = 11.8 mA p. The color scale represents the out-of-plane field B z(x, y) with span of 1.8 b, 2.5 c, 3.0 d, 2.9 f, 3.2 g, 3.4 h, 3.1 j, 3.4 k, 3.4 l, 3.1 n, 3.6 o, and 2.8 mT p. All 2D images are 12 × 12 µm2, pixel size 40 nm, and acquisition time 240 s/image. The scale bar is 3 µm. The top row shows zoomed-in 3D representation of B z(x, y) in the corresponding dashed areas marked in the second row. Supplementary Movies 1–4 for full set of images
Fig. 3
Fig. 3
Current-voltage-frequency characterization of vortex penetration. a Voltage V across the microbridge as a function of current I for various indicated fields. b Voltage across the bridge (blue) and the number of vortex stems n (green) as a function of current at B a = 2.7 mT. The red dashed lines are linear fits with dV/dI = 13.9 mΩ in the single stem and 25.1 mΩ in double stem regions. The insets show zoomed-in SOT images of single stem and double stem vortex flow. c Vortex penetration rate f per stem vs. current I
Fig. 4
Fig. 4
Vortex velocities and spacing along the entrance stem channel. a Spacing between successive vortices a(x) along the stem from x = 0.5 µm up to the bifurcation point x b at B a = 2.7 mT at various indicated currents. Inset: SEM image of the sample with marked x axis. The scale bar is 2 µm. b Corresponding vortex velocities v(x) along the stem from x = 0.5 µm up to the bifurcation point x b. c The vortex velocity vs. current at x = 0.5 µm (black) and at x b (blue). The dashed lines are guides to the eye. d Vortex spacing a c at the bifurcation point x b vs. the voltage V across the microbridge (blue), compared to the theoretical estimate (dashed) based on the thermal confinement model
Fig. 5
Fig. 5
TDGL simulations of stationary and fast moving vortices at the experimentally accessible velocities. a Calculated Cooper-pair density Δ 2(x, y) of a stationary vortex configuration at applied current density and magnetic field corresponding to the experimental conditions in Fig. 2f. b Corresponding distribution of the supercurrent density |J(x, y)/J d| in the sample showing edge currents in the constriction reaching J d at the verge of vortex penetration. The black arrows point to the local direction of the current. c Time-average of the Cooper-pair density over 5 × 104τGL at I = 1.05I c, revealing branching vortex trajectories coexisting with adjacent stationary vortices. d Snapshot of moving vortices in c with arrows denoting the relative displacement of each vortex following an entry of a new vortex into the sample. e,f Same as c,d but at highest applied current before an additional stem is formed. g Experimental vortex velocity along the stem for B a = 2.7 mT and indicated applied currents with the TDGL data from d and f in normalized units (scaled to v GL = ξ/τ GL). The animation of the vortex flow dynamics corresponding to e,f is presented in Supplementary Videos 5 and 6. The scale bar in a is 20 ξ
Fig. 6
Fig. 6
Different morphologies of ultra-fast vortices at velocities significantly higher than in our experiment. a,b A snapshot a and time-averaged Cooper-pair density Δ 2(x, y) b as in Fig. 5, but for twice higher applied field and twice the current. Three vortex phases are found with distinctly different core structure, level of quasiparticle tailgating, velocities and resulting kinematic trajectories (see text and Supplementary Movies 7 and 8), namely the extremely fast Abrikosov-Josephson vortices (marked by green dot), the ultrafast slipstreamed vortices (black dot), and conventional Abrikosov moving vortices (red dot). c Spatial profiles of vortex velocities v(x) (scaled to v GL = ξ/τ GL, see Methods) for the three main vortex phases, and for one detected branch of vortices going through an in-motion transition (dynamic transition from slipstreamed vortices to conventional Abrikosov vortices, identified by a blue dot in a). The scale bar in a is 20 ξ

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