Franco Nori's Group.

Vortex Dynamics - An Overview

The nature of the motion of penetrating magnetic flux lines is one of the major unsolved puzzles in superconductivity. As these flux lines move through stationary magnetic vortices in the superconductor, they exhibit "stick-slip" type motion and collective "jamming" that resembles transport in other types of media: grains of sand, colloids, even cars moving in city traffic.

Among other results, our group has obtained the following:

Theoretical derivations, without electrodynamical assumptions, of several measurable quantities (e.g., B(x,y,H(t)), M(H(t)), Jc(H(t)), Jc(x,y,H(t)) as a function of microscopic pinning parameters. This fills a significant gap in the theory because some of these results were empirically known (and often used in many labs) for over 30 years, but never derived starting from the microscopic dynamics of individual flux lines.

This approach provides an effective way to understand how the microscopic pinning affects macroscopic measurements.

Systematic study of dynamical instabilities leading to vortex-bundle motion in superconductors. First theoretical prediction and experimental verification of avalanche scaling behavior at the threshold of instability. These results prove that flux lines in superconductors exhibit avalanche dynamics similar to the one observed in other (at first seemingly unrelated) systems, like granular assemblies and water droplet avalanches.

Numerical and analytical systematic derivation of the very rich and complex non-equilibrium dynamic phase diagram for driven vortices in samples with a periodic array of pinning sites.

Derivation of the non-equilibrium phase diagram for vortices driven in random media. Our results show that the delta of river-like vortex channels of magnetic flux flowing in a superconductor is a fractal network with geometric features--such as the fractal dimension and the tortuosity (or sinuosity) of the rivers--that are strongly correlated with macroscopic dynamical quantities, such as the fraction of moving vortices and the voltage noise. Indeed, for growing roughness of the terrain (corresponding to increasing disorder in the sample), the vortex motion changes from shifting braiding channels, where vortices frequently "switch lanes," to unbraided channels. At the point when this change in motion occurs, there is a remarkabl universal drop in the voltage noise and the tortuosity of the intermittently flowing rivers of quantized magnetic flux.

Our calculations are compared with experiments, which can measure macroscopic averages, such as the voltage, but cannot easily access the degree of braiding or sinuosity or the fractal dimension of the network of flux channels.

Our work on vortex dynamics has been featured in APS News 4, 8, June 1995; and also in APS News 5, 9, June 1996.
Also, it appeared in the APS DMP webpage.

References (The abstracts in HTML and the articles [in PS, PDF, RevTex, etc.] are available here )

• O. Pla and F. Nori, Phys. Rev. Lett. 67, 919 (1991); R. Richardson and F. Nori, preprint.
• R. Richardson, S.D. Peacor, C. Uher, and F. Nori, Phys. Rev. Lett. 67, 3856 (1991).
• R. Richardson, O. Pla, and F. Nori, Phys. Rev. Lett. 72, 1268 (1994).
• S. Field, J. Witt, F. Nori, and X. Ling, Phys. Rev. Lett. 74, 1208 (1995).
• C. Reichhardt, C.J. Olson, J. Groth, S. Field, and F. Nori, Phys. Rev. B 52, 10441 (1995).
• C. Reichhardt, C.J. Olson, J. Groth, S. Field, and F. Nori, Phys. Rev. B 53, R8898 (1996).
• J. Groth, C. Reichhardt, C.J. Olson, S. Field, and F. Nori, Phys. Rev. Lett. 77, 3625 (1996).
• C. Reichhardt, J. Groth, C.J. Olson, S. Field, and F. Nori, Phys. Rev. B 54, 16108 (1996).
• F. Nori, Science 271, 1373 (1996).
• C.J. Olson, C. Reichhardt, J. Groth, S. Field, and F. Nori, Physica C 290, 89 (1997).
• C.J. Olson, C. Reichhardt, and F. Nori, Phys. Rev. B 56, 6175--6194 (1997).
• C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. Lett. 78, 2648 (1997).
• C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. B 57, 7937 (1998).
• C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. B 58 , 6534--6564 (1998).
• C.J. Olson, C. Reichhardt, and F. Nori, Phys. Rev. Lett. 80, 2197 (1998).
• C.J. Olson, C. Reichhardt, and F. Nori, Phys. Rev. Lett. 81, 3757 (1998).
• C. Reichhardt and F. Nori, Phys. Rev. Lett. 82, 414 (1999).
• A. Mehta, C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. Lett. 82, 3641 (1999).
• J. Wambaugh, C. Reichhardt, C.J. Olson, F. Marchesoni, and F. Nori, Phys. Rev. Lett., 83 , in press (1999).
• C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. B 60, in press (1999).
• F. Nori and C. Reichhardt, Physica C , in press (2000).

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