Tearing transition and plastic flow in superconducting thin films


A new class of artificial atoms, such as synthetic nanocrystals or vortices in superconductors, naturally self-assemble into ordered arrays. This property makes them applicable to the design of novel solids, and devices whose properties often depend on the response of such assemblies to the action of external forces. Here we study the transport properties of a vortex array in the Corbino disk geometry by numerical simulations. In response to an injected current in the superconductor, the global resistance associated to vortex motion exhibits sharp jumps at two threshold current values. The first corresponds to a tearing transition from rigid rotation to plastic flow, due to the reiterative nucleation around the disk centre of neutral dislocation pairs that unbind and glide across the entire disk. After the second jump, we observe a smoother plastic phase proceeding from the coherent glide of a larger number of dislocations arranged into radial grain boundaries.

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Figure 1: The velocity (v) profiles as a function of the applied current (I) for N = 1032 vortices in a disk of radius D = 18.
Figure 2: The resistance and the number of fivefold vortices as a function of the current.
Figure 3: A series of snapshots illustrating dislocation dynamics.
Figure 4: The resistance noise power spectrum for N = 1032 vortices in a disk of radius D = 18 under an applied current I = 0.0375.
Figure 5: The threshold current I0 Inset: the value of I0 as a function of the number of vortices N for different disk radii D.


  1. 1

    Murray, C., Kagan, C. & Bawendi, M. Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies. Annu. Rev. Mater. Sci. 30, 545–610 ( 2000).

    CAS  Article  Google Scholar 

  2. 2

    Mitchell, T.B., Bollinger, J.J., Itano, W.M. & Dubin, D.H.E. Stick slip dynamics of a stressed ion crystal. Phys. Rev. Lett. 87 183001 ( 2001).

    Article  Google Scholar 

  3. 3

    Pertsinidis, A. & Ling, X.S. Diffusion of point defects in two-dimensional colloidal crystals. Nature 413, 47–50 ( 2001).

    Article  Google Scholar 

  4. 4

    Brandt, E.H. The flux-line lattice in type two superconductors. Rep. Prog. Phys. 58, 1465–1594 ( 1995).

    CAS  Article  Google Scholar 

  5. 5

    Abrikosov, A.A. On the magnetic properties of superconductors of the second kind. Sov. Phys. JEPT 5, 1174–1182 ( 1957).

    Google Scholar 

  6. 6

    Safar, H. et al. Experimental evidence for a first-order vortex-lattice-melting transition in untwinned, single crystal YBa2Cu3O7 . Phys. Rev. Lett. 69, 824–827 ( 1992).

    CAS  Article  Google Scholar 

  7. 7

    Avraham, N. et al. Inverse melting of a vortex lattice. Nature 411, 451–454 ( 2001).

    CAS  Article  Google Scholar 

  8. 8

    Bouquet, F. et al. An unusual phase transition to a second liquid vortex phase in the superconductor YBa2Cu3O7 . Nature 411, 448–451 ( 2001).

    CAS  Article  Google Scholar 

  9. 9

    Schilling, A., Welp, U., Kwok, W.K. & Crabtree, G.W. Vortex-lattice melting in untwinned YBa2Cu3O7-δ for Hc. Phys. Rev. B 65, 054505 ( 2002).

    Article  Google Scholar 

  10. 10

    Fisher, D.S., Fisher, M.P.A. & Huse, D. Thermal fluctuations, quenched disorder, phase transitions, and transport in type II superconductors. Phys. Rev. B 43, 130–159 ( 1991).

    CAS  Article  Google Scholar 

  11. 11

    Nelson, D.R. & Vinokur, V.M. Bose glass scaling for superconducting vortex arrays revisited. Phys. Rev. B 61, 5917–5919 ( 2000).

    CAS  Article  Google Scholar 

  12. 12

    Giamarchi, T. & Le Doussal, P. Elastic theory of flux lattices in the presence of weak disorder. Phys. Rev. B 52, 1242–1270 ( 1995).

    CAS  Article  Google Scholar 

  13. 13

    Klein, T. et al. A Bragg glass phase in the vortex lattice of a type II superconductor. Nature 413, 404–406 ( 2001).

    CAS  Article  Google Scholar 

  14. 14

    Giamarchi, T. & Le Doussal, P. Moving glass theory of driven lattices with disorder. Phys. Rev. B 57, 11356–11403 ( 1998).

    Article  Google Scholar 

  15. 15

    Crabtree, G.W., Lopez, D., Kwok, W.K., Safar, H. & Paulius, L.M. Dynamic correlation in driven vortex phases. J. Low Temp. Phys. 117, 1313–1322 ( 1999).

    CAS  Article  Google Scholar 

  16. 16

    Bhattacharya, S. & Higgins, M.J. Dynamics of a disordered flux line lattice. Phys. Rev. Lett. 70, 2617–2620 ( 1993).

    CAS  Article  Google Scholar 

  17. 17

    Marchevsky, M., Aarts, J., Kes, P.H., & Indenbom, M.V. Observation of the correlated vortex flow in NbSe2 with magnetic decoration. Phys. Rev. Lett. 78, 531–534 ( 1997).

    CAS  Article  Google Scholar 

  18. 18

    Paltiel, Y. et al. Dynamic instabilities and memory effects in vortex matter. Nature 403, 398–401 ( 2000).

    CAS  Article  Google Scholar 

  19. 19

    Paltiel, Y. et al. Instabilities and disorder-driven first-order transition of the vortex lattice. Phys. Rev. Lett. 85, 3712–3715 ( 2000).

    CAS  Article  Google Scholar 

  20. 20

    D'Anna, G. et al. Evidence of surface superconductivity in 2H-NbSe2 single crystals. Phys. Rev. B 54, 6583–6586 ( 1996).

    CAS  Article  Google Scholar 

  21. 21

    López, D. et al. Spatially resolved dynamic correlation in the vortex state of high temperature superconductors. Phys. Rev. Lett. 82, 1277–1280 ( 1999).

    Article  Google Scholar 

  22. 22

    Marchetti, M.C. & Nelson, D.R. Vortex physics in confined geometries. Physica C 330, 105–129 ( 2000).

    CAS  Article  Google Scholar 

  23. 23

    Benetatos, P. & Marchetti, M.C. Plasticity in current-driven vortex lattices. Phys. Rev. B 65, 134517 ( 2002).

    Article  Google Scholar 

  24. 24

    Jensen, H.J., Brass, A. & Berlinsky, A.J. Lattice deformations and plastic flow through bottlenecks in a two-dimensional model for flux pinning in type-II superconductors. Phys. Rev. Lett. 60, 1676–1679 ( 1988).

    CAS  Article  Google Scholar 

  25. 25

    Fangohr, H., Cox, S.J. & de Groot, P.A.J. Vortex dynamics in two-dimensional systems at high driving forces. Phys. Rev. B 64, 064505 ( 2001).

    Article  Google Scholar 

  26. 26

    Chen, Q.-H. & Hu, X. Nonequilibrium phase transitions of vortex matter in three-dimensional layered superconductors. Phys. Rev. Lett. 90, 117005 ( 2003).

    Article  Google Scholar 

  27. 27

    Miguel, M.-C., Vespignani, A., Zapperi, S., Weiss, J. & Grasso, J.R. Intermittent dislocation flow in viscoplastic deformation. Nature 410, 667–671 ( 2001).

    CAS  Article  Google Scholar 

  28. 28

    Hirth, J.P. & Lothe, J. Theory of Dislocations (Krieger, Malabar, Florida, 1992).

    Google Scholar 

  29. 29

    Miguel, M.-C. & Kardar, M. Elasticity and melting of vortex crystals in anisotropic superconductors: Beyond the continuum regime. Phys. Rev. B 62, 5942–5956 ( 2000).

    CAS  Article  Google Scholar 

  30. 30

    de Gennes, P.-G. Superconductivity of Metals and Alloys (Benjamin, New York, 1966).

    Google Scholar 

  31. 31

    Chaikin, P.M. & Lubensky, T.C. Principles of Condensed Matter Physics (Cambridge Univ. Press, Cambridge, 1995).

    Google Scholar 

  32. 32

    Veje, C.T., Howell, D.W. & Behringer, R.P. Kinematics of a two-dimensional granular Couette experiment at the transition to shearing. Phys. Rev. E 59 739–745 ( 1999).

    CAS  Article  Google Scholar 

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We thank G. Jung, M. Zaiser, R. Pastor-Satorras, and J. S. Andrade Jr. for useful remarks. This work is supported by an Italy–Spain Integrated Action. M.C.M. is supported by the Ministerio de Ciencia y Tecnología (Spain).

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Correspondence to Stefano Zapperi.

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Supplementary information

Supplementary Information, Fig. S1

Supplementary Information, Fig. S2 (PDF 234 kb)

Supplementary Information, Movie 1The onset of plastic flow (I =0.04) in a system of radius D = 18 with N = 1032 vortices. (GIF 1230 kb)

Supplementary Information, Movie 2The onset of plastic flow (I = 0.04) in a system of radius D = 36 with N = 1032 vortices. (GIF 1246 kb)

Supplementary Information, Movie 3The laminar phase (I = 0.3) when defects are arranged into grain boundaries, in a system of radius D = 18 with N = 1-32 vortices. (GIF 1422 kb)

Supplementary Information, Movie 4The laminar phase (I = 0.3) when defects are arranged into grain boundaries, in a system of radius D = 36 with N = 2064 vortices. (GIF 1775 kb)

Supplementary Information, Movie 5The first transient steps before reaching the laminar phase corresponding (I = 0.3) in a system of radius D = 36 with N = 2064 vortices. In this animation each snapshot is separated by dt = 3 timesteps and the sequence is cycled. (GIF 1396 kb)

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Miguel, MC., Zapperi, S. Tearing transition and plastic flow in superconducting thin films. Nature Mater 2, 477–481 (2003). https://doi.org/10.1038/nmat909

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