1. Superconducting vortex avalanches D. Shantsev Åge A. F. Olsen, D. Denisov, V. Yurchenko, Y. M. Galperin, T. H. Johansen AMCS (COMPLEX) group Department of Physics University of Oslo Norway

2. T c Temperature T c Mixed state (vortex matter) Meissner state Normal state H c1 H c2 Type II Vortex lattice A.A. Abrikosov (published 1957) 2003 Vortices in Superconductors

3. Lorentz force F = j   Vortices are driven by Lorentz force and their motion creates electric field E ~ dB/dt BaBa J pinning force Lorentz force Vortices get pinned by tiny defects and start moving only if Lorentz force > Pinning force Resistance is zero only due to pinning Stronger pinning => larger currents current

4. Critical state Vortices : driven inside due to applied field get pinned by tiny inhomogeneities => Metastable critical state Picture: R.Wijngarden Avalanches ?

5. “Applied” Motivation to study vortex avalanches The slope of the vortex pile - the critical current density J c – is the key parameter for many applications of superconductors JcJc Trapped field magnets Record trapped field: 17 Tesla ~100 times better than Cu wire High-current cables

6. Power-law Avalanche size (number of vortices) Number of avalanches E. Altshuler et al. Self-organized criticality for vortex avalanches in Nb Phys. Rev. B 70, 140505 (2004)

7. Peaked or Power Law (dep. on H & T) Internal Hall probe arrang. Nb film Planar Behnia et al PRB (2000) Exp or Power law (dep. on T & t) Off the edge SQUID BSCCO crystal Planar Aegerter PRE (1998) Peaked or Power law (dep. on T) Off the edge & internal 2 Hall probes Nb film Ring Nowak et al PRB (1997) Peaked Internal 1 Hall probe YBCO crystal Planar Zieve et al PRB (1996) Power law (slow ramps) Off the edge CoilNb-Ti Hollow cylinder Field et al PRL (1995) Exponential Off the edge CoilPb-In Hollow cylinder Heiden & Rochlin PRL (1968) Avalanche distribution Avalanche type SensorMaterialGeometryReference Statistics of vortex avalanches T-effect ? Table from Altshuler&Johansen, RMP 2004

8. current velocity E ~ dB/dt Vortex motion dissipates energy, J*E Local Temperature Increases +kT It is easier for vortices to overcome pinning barriers Vortices move faster positive feedback

9. Thermal avalanches THEORYEXPERIMENT Phys. Rev. B 70, 224502 (2004) Phys. Rev. B 73, 014512 (2006) Phys. Rev. B 72, 024541 (2005) Size of small avalanches Shape of dendritic avalanches Dendrites Threshold fields for dendritic avalanches Phys. Rev. Lett. 97, 077002 (2006) Phys. Rev. ? (200?) Anistropic dendritic avalanches Phys. Rev. Lett. 98, 117001 (2006)

10. MgB 2 ring How to determine T without measuring T ?

11. Some avalanches perforate the ring: they connect the outer and inner edges and can bring FLUX into the hole

12. Flux in the hole Applied field Every step: a perforating avalanche

13. current Stage 1: Propagation of the tip Speed: ~100 km/s (P. Leiderer) Time: ~ 10 ns current Stage 2: Heated resistive channel Decrease of current Injection of flux into the hole 

14. I Temperature evolution in the heated channel: T t 100 K ~2.5T c L = 4 nH

15. Perforation reduces the total current in the ring by just ~15% I I = 0 WRONG

16. Distribution of current density in the ring outer radius inner radius perforation-induced change

17. Types of vortex avalanches: 1.non-thermal (power-law size distribution) : SOC 2.thermal (peaked size distribution) : their size, topology and threshold fields are in agreement with theory Rings: two-stage avalanches 1.tip crosses the ring 2.short-lived heated channel transferring flux into the hole Maximal T during avalanche: 100 K in MgB 2 ring with T c =40 K Phys. Rev. B 74, 064506 (2006) Phys. Rev. B ? (cond-mat/0705.0997) Conclusions

19.   nm J B(r) vortex core Vortex lattice seen at the superconductor surface 2003 Nobel prize to Alexei Abrikosov for prediction of Vortices Superconductor has “internal” magnetic nanostructure superconductor magnetic field lines 50 nm (at 1 Tesla)  0 flux quantum

21. r0r0 r1r1 Φ J