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Suprafroth in type-I superconductors

Nature Physics volume 4, pages 327–332 (2008)Cite this article

Abstract

The structure and dynamics of froths have been subjects of intense interest owing to the desire to understand the behaviour of complex systems where topological intricacy prohibits exact evaluation of the ground state. The dynamics of a traditional froth involves drainage and drying at the cell boundaries; thus, it is irreversible. Here, we report a new member of the froth family: suprafroth, in which the cell boundaries are superconducting and the cell interior is normal, or non-superconducting. Despite having a very different microscopic origin, topological analysis of the structure of the suprafroth shows that the same statistical laws, such as those of von Neumann and of Lewis apply to a suprafroth. Furthermore, for the first time in the analysis of froths, there is a global measurable property, the magnetic moment, which can be directly related to the suprafroth structure. We propose that this suprafroth is a model system for the analysis of the complex physics of two-dimensional froths—with magnetic field and temperature as external (reversible) control parameters.

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Figure 1: Phase diagram of a superconducting lead disc.
Figure 2: Suprafroth coarsening and cell analysis.
Figure 3: Structural evolution of the suprafroth.
Figure 4: Distribution of the number of n-sided cells.
Figure 5: Lewis’ and generalized von Neumann’s laws in suprafroth.
Figure 6: Parameters of Lewis’ law.

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References

  1. Weaire, D. & Hutzler, S. The Physics of Foams (Oxford Univ. Press, New York, 1999).

    Google Scholar 

  2. Elias, F., Flament, C., Bacri, J.-C. & Francer, F. in Foams and Emulsions (eds Sadoc, J. F. & Rivier, N.) 91–104 (NATO ASI Series, Series E: Applied Sciences, Vol. 354, Kluwer, Dordrecht, 1999).

    Google Scholar 

  3. Elias, F., Drikis, I., Cebers, A., Flament, C. & Bacri, J.-C. Undulation instability in two-dimensional foams of magnetic fluid. Eur. Phys. J. B 3, 203–209 (1998).

    Article  ADS  Google Scholar 

  4. Weaire, D., Bolton, F., Molho, P. & Glazier, J. A. Investigation of an elementary model for magnetic froth. J. Phys. Condens. Matter 3, 2101–2114 (1990).

    Article  ADS  Google Scholar 

  5. Prozorov, R. Equilibrium topology of the intermediate state in type-I superconductors of different shapes. Phys. Rev. Lett. 98, 257001 (2007).

    Article  ADS  Google Scholar 

  6. Prozorov, R., Giannetta, R. W., Polyanskii, A. A. & Perkins, G. K. Topological hysteresis in the intermediate state of type-I superconductors. Phys. Rev. B 72, 212508 (2005).

    Article  ADS  Google Scholar 

  7. Landau, L. The intermediate state of superconductors. Nature 141, 688 (1938).

    Article  ADS  Google Scholar 

  8. Cēbers, A., Gourdon, C., Jeudy, V. & Okada, T. Normal-state bubbles and lamellae in type-I superconductors. Phys. Rev. B 72, 014513 (2005).

    Article  ADS  Google Scholar 

  9. Huebener, R. P. Magnetic Flux Structures of Superconductors 2nd edn (Springer, New York, 2001).

    Book  Google Scholar 

  10. Lewis, F. T. The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of cucumis. Anat. Rec. 38, 341–362 (1928).

    Article  Google Scholar 

  11. Rivier, N. in Foams and Emulsions (eds Sadoc, J. F. & Rivier, N.) 105–125 (NATO ASI Series, Series E: Applied Sciences, Vol. 354, Kluwer, Dordrecht, 1999).

    Book  Google Scholar 

  12. Poole, C. J., Farach, H., Creswick, R. & Prozorov, R. Superconductivity 2nd edn (Elsevier (Imprint: Academic Press), Amsterdam, 2007).

    Google Scholar 

  13. MacPherson, R. D. & Srolovitz, D. J. The von Neumann relation generalized to coarsening of three-dimensional microstructures. Nature 446, 1053–1055 (2007).

    Article  ADS  Google Scholar 

  14. Von Neumann, J. Metal Interfaces 108–110 (American Society for Metals, Cleveland, 1952).

    Google Scholar 

  15. Elias, F., Flament, C., Glazier, J. A., Graneri, F. & Jiang, Y. Foams out of stable equilibrium: Cell elongation and side swapping. Phil. Mag. B 79, 729–751 (1999).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank J. Clem, N. Goldenfeld, R. Huebener, V. Kogan, R. Mints and J. Schmalian for helpful discussions. Work at the Ames Laboratory was supported by the Department of Energy, Basic Energy Sciences under Contract No. DE-AC02-07CH11358. R.P. acknowledges support from NSF Grant Number DMR-05-53285 and the Alfred P. Sloan Foundation.

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Authors and Affiliations

  1. Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

    Ruslan Prozorov, Andrew F. Fidler, Jacob R. Hoberg & Paul C. Canfield

  2. Permanent address: Department of Physics, Albion College, Albion, Michigan 59224, USA,

    Andrew F. Fidler

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  1. Ruslan Prozorov
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  2. Andrew F. Fidler
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Contributions

R.P. idea, measurements, data analysis; A.F.F. measurements, data analysis; J.R.H. measurements; P.C.C. idea, data analysis.

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Correspondence to Ruslan Prozorov.

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Prozorov, R., Fidler, A., Hoberg, J. et al. Suprafroth in type-I superconductors. Nature Phys 4, 327–332 (2008). https://doi.org/10.1038/nphys888

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