Investigation of the stability of Hopfions in the two-component Ginzburg-Landau model

Details Investigation of the stability of Hopfions in the two-component Ginzburg-Landau model Investigation of the stability of Hopfions in the two-component Ginzburg-Landau model

2006-08-18

arxiv.org/abs/cond-mat/0608424v5

Phys.Rev.B77:094509,2008

Physics

Condensed Matter

Superconductivity

v5: Enhanced figure resolution. v4: Additional numerical simulations, new figures, and some smaller revisions, 9 pages, 2 figu

Scientific paper

10.1103/PhysRevB.77.094509

We study the stability of Hopfions embedded in the Ginzburg-Landau (GL) model of two oppositely charged components. It has been shown by Babaev et al. [Phys. Rev. B 65, 100512 (2002)] that this model contains the Faddeev-Skyrme (FS) model, which is known to have topologically stable configurations with a given Hopf charge, the so-called Hopfions. Hopfions are typically formed from a unit-vector field that points to a fixed direction at spatial infinity and locally forms a knot with a soft core. The GL model, however, contains extra fields beyond the unit-vector field of the FS model and this can in principle change the fate of topologically non-trivial configurations. We investigate the stability of Hopfions in the two-component GL model both analytically (scaling) and numerically (first order dissipative dynamics). A number of initial states with different Hopf charges are studied; we also consider various different scalar potentials, including a singular one. In all the cases studied, we find that the Hopfions tend to shrink into a thin loop that is too close to a singular configuration for our numerical methods to investigate.

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