We demonstrate that, in contrast to the single-component Abrikosov vortex, in two-component superconductors vortex solutions with exponentially screened magnetic field exist only in exceptional cases: in the case of vortices carrying an integer number of flux quanta, and in a special parameter limit for half-quantum vortices. For all other parameters the vortex solutions have delocalized magnetic field with a slowly decaying tail. Furthermore, we demonstrate a new effect which is generic in two-component systems but has no counterpart in single-component systems: on exactly half of the parameter space of the U (1) × U (1) Ginzburg-Landau model, the magnetic field of a generic fractional vortex inverts its direction at a certain distance from the vortex core.
The problem of constructing internally rotating solitons of fixed angular frequency ω in the Faddeev-Skyrme model is reformulated as a variational problem for an energylike functional, called pseudoenergy, which depends parametrically on ω. This problem is solved numerically using a gradient descent method, without imposing any spatial symmetries on the solitons, and the dependence of the solitons' energy on ω, and on their conserved total isospin J, studied. It is found that, generically, the shape of a soliton is independent of ω, and that its size grows monotonically with ω. A simple elastic rod model of time-dependent hopfions is developed which, despite having only one free parameter, accounts well for most of the numerical results.
We investigate the behaviour of parallel Faddeev-Hopf vortices under energy
minimization in a system with physically relevant, but unusual boundary
conditions. The homotopy classification is no longer provided by the Hopf
invariant, but rather by the set of integer homotopy invariants proposed by
Pontrjagin. The nature of these invariants depends on the boundary conditions.
A set of tightly wound parallel vortices of the usual Hopfion structure is
observed to form a bunch of intertwined vortices or unwind completely,
depending on the boundary conditions.Comment: 6 pages, 9 figures, minor clarifications of text and corrected the
final energy of the vortices section IV.B. To be published in Phys.Rev.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.