Superconducting Vortex Avalanches

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Abstract
We monitor the dynamics of superconducting vortices in the Bean state, as the system is driven to the threshold of instability by the slow ramping of an external field. Individual avalanches, containing as few as 50 vortices, are detected in real time. Thus our experiment is the superconducting analog of monitoring the granular avalanches produced by slowly dropping sand on a sandpile. The observed distribution of vortex avalanche sizes shows a power-law behavior over two decades, proving that the vortex dynamics in the Bean state is characterized by avalanches of many length scales. Some 30 years ago Bean (1) and de Gennes (2) noted the close analogy between the marginally stable state of vortices in a hard superconductor and the marginally stable slope of sand in a sandpile. We can picture building up a sandpile by slowly dropping grains on a flat surface. The slope of the pile soon reaches a certain "maximal angle of stability," determined by a balance between gravity and intergrain frictional forces. A similar situation is present in a hard superconductor (i.e., with strong pinning). Vortices nucleate at the surface as an external magnetic field is slowly ramped. In the simplest model, due to Bean (1), the vortex density decreases linearly with distance into the superconductor. This again is due to a balance between vortex density gradients which drive vortices into the bulk and pinning forces which hamper their entry. These early analogies were invoked mainly in order to understand the static distribution of flux in a hard superconductor. More recently, interest has focused on the dynamics of systems slowly driven to the threshold of instability. A large number of diverse physical systems are characterized by such dynamics, including charge- density waves, pinned Wigner crystals, earthquake faults, granular assemblies, and superconducting vortices. These systems have received renewed attention due to their relation to spatiotemporal dynamics, instabilities, and self- organized criticality. Sandpiles have received particularly intensive theoretical and experimental attention as a model system exhibiting such threshold dynamics. In light of the strong static analogies between sandpiles and the Bean state in hard superconductors, it is natural to ask whether there are quantitative similarities between the dynamic processes (e.g., similar avalanche size distributions) in the two systems. Here we report results of an experiment on the dynam- ics of vortices, which is closely analogous with those done on sandpiles. The magnetic field outside a tubular super- conducting sample is ramped slowly, driving flux into the tube's outer wall. Eventually, the flux front will reach the inner wall of the tube and spill out into the tube's interior. We can detect, in real time, this entrance of flux into the tube's interior (Fig. 1). In particular, we can measure whether flux leaving the superconductor does so in dis- crete bundles or avalanches; if so, we can measure the sizes, lifetimes, and arrival times of these avalanches. Our experiment is thus the superconducting analog (3) of sand- pile experiments (4,5) where the sand is slowly added to the apex of the pile; any sand which falls off the edge in the form of avalanches is then measured. Sandpile ex- periments which use a slowly tilting table (6) or rotating drum (7) may be more closely analogous to current-driven depinning of vortices (8).