Broken planar Skyrmions — statics and dynamics

Jennings, Paul; Winyard, Thomas

doi:10.1007/jhep01(2014)122

Cited by 17 publications

(9 citation statements)

References 15 publications

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“…This would suggest that local minima should appear for each of the various polyominoes in the London model. Similar types of interaction and corresponding minimal soliton configurations have been studied before in the baby Skyrme model 37 , where it appears for different reasons.…”

Section: Vortex Bound Statessupporting

confidence: 57%

Non-London electrodynamics in a multiband London model: Anisotropy-induced nonlocalities and multiple magnetic field penetration lengths

2018

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The London model describes strongly type-2 superconductors as massive vector field theories, where the magnetic field decays exponentially at the length scale of the London penetration length. This also holds for isotropic multi-band extensions, where the presence of multiple bands merely renormalises the London penetration length. We show that, by contrast, the magnetic properties of anisotropic multi-band London models are not this simple, and the anisotropy leads to the interband phase differences becoming coupled to the magnetic field. This results in the magnetic field in such systems having N + 1 penetration lengths, where N is the number of field components or bands. That is, in a given direction, the magnetic field decay is described by N + 1 modes with different amplitudes and different decay length scales. For certain anisotropies we obtain magnetic modes with complex masses. That means that magnetic field decay is not described by a monotonic exponential increment set by a real penetration length but instead is oscillating. Some of the penetration lengths are shown to diverge away from the superconducting phase transition when the mass of the phase-difference mode vanishes. Finally the anisotropy-driven hybridization of the London mode with the Leggett modes can provide an effectively non-local magnetic response in the nominally local London model. Focusing on the two-component model, we discuss the magnetic field inversion that results from the effective non-locality, both near the surface of the superconductor and around vortices. In the regime where the magnetic field decay becomes non-monotonic, the multiband London superconductor is shown to form weakly-bound states of vortices. arXiv:1710.09907v2 [cond-mat.supr-con]

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Section: Vortex Bound Statessupporting

confidence: 57%

Non-London electrodynamics in a multiband London model: Anisotropy-induced nonlocalities and multiple magnetic field penetration lengths

2018

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“…Numerous potentials have been proposed [7,19,24,[29][30][31][32][33] and studied extensively in the literature. However, there are two choices of potential that we are particularly interested in: the standard potential and the easy plane potential.…”

Section: A Standard Baby Skyrmionsmentioning

confidence: 99%

Baby Skyrmion crystals

Leask

2021

Preprint

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This paper describes a model for baby Skyrme crystal chunks with arbitrary potential by considering energy contributions from the bulk and surface of a crystal chunk. We focus on two potentials which yield distinct Skyrme lattices: the standard potential V = m 2 (1 − ϕ 3 ) and the easy plane potential V = 1 2 m 2 (ϕ 1 ) 2 . In both models, the static energy functional is minimized over all 2dimensional period lattices, yielding the minimal energy crystal structure(s). For the standard potential, the Skyrmions form a hexagonal crystal structure, whereas, for the easy plane potential, the minimal energy crystal structure is a square lattice of half-charge lumps. We find that square crystal chunks are the global minima in the easy plane model for charges B > 6 with 2B a perfect square (m 2 = 1). In contrast, we observe that hexagonal crystal chunks in the standard model become the global minima for surprisingly large charges, B > 954 (m 2 = 0.1).

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“…It is known, however that the structure of the multisoliton solution of the planar Skyrme model is very sensitive to the choice of the potential [47,48,[51][52][53]. In particular, it was proposed to consider the potential [54,55], which explicitly breaks the O(3) symmetry of the planar Skyrme model to the dihedral group D 3 . In the baby Skyrme model with the potential V = m 2 (φ 1 − c) 2 a single Skyrmion is splitted into two partons with the same topological charge Q 1/2, as c = 0 and into constituents with fractional charges Q = 1/3, 2/3, as c = 1/3.…”

Section: Multisoliton Configurations 431 Degrees 3 Andmentioning

confidence: 99%

Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential

Samoilenka

Shnir

2017

J. High Energ. Phys.

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Abstract:We construct new solutions of the Faddeev-Skyrme model with a symmetry breaking potential admitting S 1 vacuum. It includes, as a limiting case, the usual SO(3) symmetry breaking mass term, another limit corresponds to the potential m 2 φ 2 1 , which gives a mass to the corresponding component of the scalar field. However we find that the spacial distribution of the energy density of these solutions has more complicated structure, than in the case of the usual Hopfions, typically it represents two separate linked tubes with different thicknesses and positions. In order to classify these configurations we define a counterpart of the usual position curve, which represents a collection of loops C 1 , C −1 corresponding to the preimages of the points φ = (±1, 0, 0), respectively. Then the Hopf invariant can be defined as Q = link(C 1 , C −1 ). In this model, in the sectors of degrees Q = 5, 6, 7 we found solutions of new type, for which one or both of these tubes represent trefoil knots. Further, some of these solutions possess different types of curves C 1 and C −1 .

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Broken planar Skyrmions — statics and dynamics

Cited by 17 publications

References 15 publications

Non-London electrodynamics in a multiband London model: Anisotropy-induced nonlocalities and multiple magnetic field penetration lengths

Non-London electrodynamics in a multiband London model: Anisotropy-induced nonlocalities and multiple magnetic field penetration lengths

Baby Skyrmion crystals

Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential

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