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Magnetic flux lines in type-II superconductors and the 'hairy ball' theorem

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  • Mark Laver

    (Laboratory for Neutron Scattering, Paul Scherrer Institut
    Risø DTU, Technical University of Denmark
    Nano-Science Center, Niels Bohr Institute, University of Copenhagen)

  • Edward. M. Forgan

    (School of Physics and Astronomy, The University of Birmingham)

Abstract

Many prominent phenomena originate from geometrical effects rather than from local physics. For example, the 'hairy ball' (HB) theorem asserts that a hairy sphere cannot be combed without introducing at least one singularity, and is fulfilled by the atmospheric circulation with the existence of stratospheric polar vortices and the fact that there is always at least one place on Earth where the horizontal wind is still. In this study, we examine the consequences of the HB theorem for the lattice of flux lines that form when a magnetic field is applied to a type-II superconducting crystal. We find that discontinuities must exist in lattice shape as a function of field direction relative to the crystal. Extraordinary, 'unconventional' flux line lattice shapes that spontaneously break the underlying crystal symmetry are thus remarkably likely across all type-II superconductors, both conventional and unconventional.

Suggested Citation

  • Mark Laver & Edward. M. Forgan, 2010. "Magnetic flux lines in type-II superconductors and the 'hairy ball' theorem," Nature Communications, Nature, vol. 1(1), pages 1-4, December.
    • Handle: RePEc:nat:natcom:v:1:y:2010:i:1:d:10.1038_ncomms1047
    DOI: 10.1038/ncomms1047
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