Formation of Stripelike Flux Patterns Obtained by Freezing Kinematic Vortices in a Superconducting Pb Film

We demonstrate experimentally and theoretically that the dissipative state of superconducting samples with a periodic array of holes at high current densities consists of flux rivers resulting from a short-range attractive interaction between vortices. This dynamically induced vortex-vortex attraction results from the migration of quasiparticles out of the vortex core (kinematic vortices). We have directly visualized the formation of vortex chains by scanning Hall probe microscopy after freezing the dynamic state by a field cooling procedure at a constant bias current. Similar experiments carried out in a sample without holes show no hint of flux river formation. We shed light on this nonequilibrium phenomena modeled by time-dependent Ginzburg-Landau simulations.

Figure 1

(a) Voltage signal as a function of time ($\Delta t$) for a $150\mu \mathrm{s}$ current pulse of 90 mA amplitude. The inset shows an oblique view of the sketched system consisting of a superconducting film with a periodic array of antidots, in an applied magnetic field $H$ and dc current $J$. The lines illustrate the inhomogeneous current distribution due to the array of antidots. (b) Differential images obtained by subtracting two consecutive pictures for $\Delta t=40$ and $50\mu \mathrm{s}$ and (c) for $\Delta t=110$ and $100\mu \mathrm{s}$, for $H/H_1=0.1$. The black (white) spots indicate the initial (final) position of vortices before (after) the last pulse. The frames in (b) and (c) are $13.5\times 13.5\mu {\mathrm{m}}^2$. The arrows indicate the direction of the applied current.

Figure 2

Number of displaced vortices as a function of applied field after a current pulse of fixed amplitude and duration—experiment versus theory. The experimental data were obtained at $T=6.5\mathrm{K}$ with pulses of 36 mA amplitude.

Figure 3

SHPM image obtained at $T=6.5\mathrm{K}$ and $H=H_{1/2}$ after field cooling (a) and after current pulses of duration $100\mu \mathrm{s}$ and amplitude 36 mA (b). Panels (c) and (d) are the corresponding images from TDGL simulations on a $12\times 24\mu {\mathrm{m}}^2$ sample. The arrows indicate the direction of the applied current.

Figure 4

Vortex configurations, imaged by SHPM at $T=4.2\mathrm{K}$: (a) field cooled without applied current and (b) field cooled with applied current of 36 mA. The arrows indicate the direction of the applied current.

Figure 5

Calculated voltage drop as a function of temperature, for four different cooling rates ${\zeta }_T$. Panels (a)–(c) show the Cooper-pair density (top panel) and magnetic field profiles in the sample (bottom panel), for the fastest cooling case at three different $T$ as indicated in the main panel.