Scattering of knotted vortices (Hopfions) in the Faddeev-Skyrme model

Abstract

Several materials, such as ferromagnets, spinor Bose-Einstein condensates, and some topological insulators, are now believed to support knotted structures. One of the most successful base-models having stable knots is the Faddeev-Skyrme model and it is expected to be contained in some of these experimentally relevant models. The taxonomy of knotted topological solitons (Hopfions) of this model is known. In this paper we describe some aspects of the dynamics of Hopfions and show that they do indeed behave like particles: during scattering the Hopf charge is conserved and bound states are formed when the dynamics allows it. We have also investigated the dynamical stability of a pair of Hopfions in stacked or side-by-side configurations, whose theoretical stability has been recently discussed by Ward.

24 pages, 11 figures

References in corpus (7)

• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Spontaneous Skyrmion Ground States in Magnetic Metals
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Topological surface states in three-dimensional magnetic insulators
• Knots in the Skyrme-Faddeev model
• Vortex rings in ferromagnets
• Hopf solitons and elastic rods

Cited by in corpus (11)

• Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures
• Three-dimensional crystals of adaptive knots
• Three-dimensional dynamics of magnetic hopfion driven by spin transfer torque
• Vortex knots in a Bose-Einstein condensate
• Vortices in the extended Skyrme-Faddeev model
• Leapfrogging vortex rings in the Landau-Lifshitz equation
• Hopfions interaction from the viewpoint of the product ansatz
• Creation of electrical knots and observation of DNA topology
• Topological transition from a hopfion to a toron via flexoelectric self-polarization in chiral liquid crystals
• Coherence simplices
• Interaction of hopfions of charge 1 and 2 from product ansatz