title: Twisted toroidal vortex solitons in inhomogeneous media with repulsive nonlinearity.
abstract: Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis (m), appear in many fields, including field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multicomponent systems, or as trapped quasilinear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0, 1, 2 are produced. They are stable for m≤1, and do not exist for s>1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented in a Bose-Einstein condensate (BEC) by means of the Feshbach resonance controlled by inhomogeneous magnetic fields.
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain and Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, 142190 Moscow, Russia.
authors.forename: Yaroslav V
authors.initials: YV
authors.lastname: Kartashov
authors.affiliation: Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, 69978 Tel Aviv, Israel.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed
authors.affiliation: Bogoliubov Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia and Institute of Physics, Carl von Ossietzky University Oldenburg, Oldenburg D-26111, Germany.
authors.forename: Yasha
authors.initials: Y
authors.lastname: Shnir
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain.
authors.forename: Lluis
authors.initials: L
authors.lastname: Torner