Dual neutral variables and knot solitons in triplet superconductors

Abstract

In this paper we derive a dual presentation of free energy functional for spin-triplet superconductors in terms of gauge-invariant variables. The resulting equivalent model in ferromagnetic phase has a form of a version of the Faddeev model. This allows one in particular to conclude that spin-triplet superconductors allow formation of stable finite-length closed vortices (the knotted solitons).

Replaced with version published in PRL (added a discussion of the effect of the coupling of the fields {\vec s} and {\vec C} on knot stability). Latest updates of the paper and miscellaneous links related to knotted solitons are also available at the homepage of the author http://www.teorfys.uu.se/PEOPLE/egor/ . Animations of knotted solitons by Hietarinta and Salo are available at http://users.utu.fi/h/hietarin/knots/c45_p2.mpg

References in corpus (6)

• Hidden symmetry and knot solitons in a charged two-condensate Bose system
• Aspects of Electric and Magnetic Variables in SU(2) Yang-Mills Theory
• QCD versus Skyrme-Faddeev Theory
• Faddeev-Niemi Conjecture and Effective Action of QCD
• The (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry at non-zero temperature
• Possible Pseudogap Phase in QCD

Cited by in corpus (66)

• Vortices with fractional flux in two-gap superconductors and in extended Faddeev model
• Stationary ring solitons in field theory - knots and vortons
• Vortex solitons: Old results and new perspectives
• Tying knots in light fields
• Stable Solitons in Three Dimensional Free Space: Self-Trapped Bose-Einstein Condensates with Spin-Orbit Coupling
• Knots in a Spinor Bose-Einstein Condensate
• Current-Driven Dynamics of Magnetic Hopfions
• Multidimensional solitons: Well-established results and novel findings
• Topological Transformation and Free-Space Transport of Photonic Hopfions
• Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
• Phase diagram of planar U(1)xU(1) superconductors: condensation of vortices with fractional flux and a superfluid state
• Three-dimensional dynamics of magnetic hopfion driven by spin transfer torque
• Vortex knots in a Bose-Einstein condensate
• Soliton gyroscopes in media with spatially growing repulsive nonlinearity
• Skyrmionic state and stable half-quantum vortices in chiral p-wave superconductors
• Weaving knotted vector fields with tunable helicity
• Three-dimensional hybrid vortex solitons
• Torus knots as Hopfions
• Non-Meissner electrodynamics and knotted solitons in two-component superconductors
• Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion
• Exact vortex solutions in an extended Skyrme-Faddeev model
• Andreev-Bashkin effect and knot solitons in interacting mixture of a charged and a neutral superfuids with possible releveance for neutron stars
• Stable Cosmic Vortons
• Relaxation of twisted vortices in the Faddeev-Skyrme model
• Excitation of knotted vortex lines in matter waves
• Winding Hopfions on R^2 x S^1
• Reinterpretation of Faddeev-Niemi Knot in Skyrme Theory
• Fractional-flux vortices and spin superfluidity in triplet superconductors
• Formation and Controlling of Optical Hopfions in High Harmonic Generation
• Kelvin knots in superconducting state
• Low temperature electronic properties of Sr_2RuO_4 II: Superconductivity
• Inner topological structure of Hopf invariant
• Magnetic monopoles in a charged two-condensate Bose-Einstein system
• Knotlike Cosmic Strings in The Early Universe
• Discovery of parity-violating Majorana fermions in a chiral superconductor Sr2RuO4
• Vortices in the extended Skyrme-Faddeev model
• $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model
• Static Hopfions in the extended Skyrme-Faddeev model
• Knot soliton in Weinberg-Salam model
• Knotted Solitons in a Charged Two-Condensate Bose System
• Collision of two Hopfions
• Energy Bounds of Linked Vortex States
• New Interpretation of Skyrme Theory
• Parity Violation in a Single Domain of Spin-Triplet Sr2RuO4 Superconductors
• Dynamics of dipoles and vortices in nonlinearly-coupled three-dimensional harmonic oscillators
• Linked and knotted synthetic magnetic fields
• Topological aspects of dual superconductors
• The phases of deuterium at extreme densities
• Strongly coupled Skyrme-Faddeev-Niemi hopfions
• Knotted Topological Phase Singularities of Electromagnetic Field
• Hopf Solitons in the AFZ Model
• Low temperature electronic properties of Sr_2RuO_4 III: Magnetic fields
• Entangled multi-knot lattice model of anyon current
• Flux quantization for a vortex in two-gap superconductor
• Knots in Physics
• Symmetry induced pairing in dark excitonic condensate at finite temperature
• Topological Soliton with Nonzero Hopf Invariant in Yang-Mills-Higgs Model
• Structures of Order Parameters in Inhomogeneous Phase States of Strongly Correlated Systems
• Vector and Spinor Decomposition of SU(2) Gauge Potential, their quivalence and Knot Structure in SU(2) Chern-Simons Theory
• Finite temperature phases and excitations of bosons on a square lattice: A cluster mean field study
• Self-dual Vortices in the Abelian Chern-Simons Model with Two Complex Scalar Fields
• Novel Topological Invariant in the U(1) Gauge Field Theory
• Magnetic Monopoles in Ferromagnetic Spin-Triplet Superconductors
• Some vortex solutions in the extended Skyrme-Faddeev model
• Topological Excitation in Skyrme Theory
• From Hopf fibrations to exotic causal replacements