Dynamics of vortices with magnetic impurities

Cockburn, Alexander; Krusch, Steffen; Muhamed, Abera A.

doi:10.1063/1.4984980

Cited by 23 publications

(39 citation statements)

References 28 publications

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“…In the first one, the impurity couples to a topological quantity (the topological charge density and the magnetic field, respectively) while in the second one it multiplies the square root of the potential. As numerical studies in (1+1) dimensions are much simpler, our paper may also be viewed as a guideline for numerics for this vortex model [32], [33]. In addition, we prove the existence of the zero mode (moduli space), which has not yet been completely achieved for the vortex model.…”

Section: Introductionmentioning

confidence: 90%

The ϕ4 model with the BPS preserving defect

Adam

Romańczukiewicz

Wereszczyński

2019

J. High Energ. Phys.

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The φ 4 model is coupled to an impurity in a way that preserves one-half of the BPS property. This means that the antikink-impurity bound state is still a BPS solution, i.e., a zero-pressure solution saturating the topological energy bound. The kink-impurity bound state, on the other hand, does not saturate the bound, in general.We found that, although the impurity breaks translational invariance, it is, in some sense, restored in the BPS sector where the energy of the antikink-impurity solution does not depend on their mutual distance. This is reflected in the existence of a generalised translational symmetry and a zero mode.We also investigate scattering processes. In particular, we compare the antikinkimpurity interaction close to the BPS regime, which presents a rather smooth, elastic like nature, with other scattering processes. However, even in this case, after exciting a sufficiently large linear mode on the incoming antikink, we can depart from the close-to-BPS regime. This results, for example, in a backward scattering.

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Section: Introductionmentioning

confidence: 90%

The ϕ4 model with the BPS preserving defect

Adam

Romańczukiewicz

Wereszczyński

2019

J. High Energ. Phys.

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“…We note that these solutions were also calculated in Ref. [19] using the Bogomolny equation (10). We have obtained the same solutions by solving the gradient flow equations (29).…”

Section: E Static Vortices and Impuritiesmentioning

confidence: 52%

“…The numerical evidence is compelling and encourages us to generalise the argument of Ref. [19] to any value of λ.…”

Section: B Delta Function Impuritiesmentioning

confidence: 59%

“…We have been particularly motivated by Ref. [19], in which the authors investigated the dynamics of vortices at critical coupling with magnetic impurities. They obtained solutions in flat space by numerically solving the Bogomolny equation for localised, axially symmetric impurities, and their numerics confirms the existence of a moduli space of vortex solutions.…”

Section: Introductionmentioning

confidence: 99%

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Vortices and magnetic impurities

Ashcroft

Krusch

2020

Phys. Rev. D

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Ginzburg-Landau vortices in superconductors attract or repel depending on whether the value of the coupling constant λ is less than 1 or larger than 1. At critical coupling λ = 1, it was previously observed that a strongly localised magnetic impurity behaves very similarly to a vortex. This remains true for axially symmetric configurations away from critical coupling. In particular, a delta function impurity of a suitable strength is related to a vortex configuration without impurity by singular gauge transformation. However, the interaction of vortices and impurities is more subtle and depends not only on the coupling constant λ and the impurity strength, but also on how broad the impurity is. Furthermore, the interaction typically depends on the distance and may be attractive at short distances and repulsive at long distances. Numerical simulations confirm moduli space approximation results for the scattering of one and two vortices with an impurity. However, a double vortex will split up when scattering with an impurity, and the direction of the split depends on the sign of the impurity. * jea29@kentforlife.net † S.Krusch@kent.ac.uk arXiv:1808.07441v1 [hep-th]

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“…A similar study has already been performed for the half-BPS impurity φ 4 model, where the scattering of the BPS antikink on the impurity has been shown to be very well described by the motion on moduli space [21]. It would be even more interesting to analyze the existence of solitons and their dynamics in the Abelian Higgs model with half-BPS impurities of both magnetic [22] and Higgs types.…”

Section: Discussionmentioning

confidence: 79%

BPS soliton-impurity models and supersymmetry

Adam

Queiruga

Wereszczyński

2019

J. High Energ. Phys.

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We find supersymmetric extensions of the half-BPS soliton-impurity models in (1+1) dimensions which preserve half of the N = 1 supersymmetry. This is related to the fact that in the bosonic sector (i.e., the half-BPS soliton-impurity model), only one soliton (for example, the kink) is a BPS configuration which solves the pertinent Bogomolnyi equation and saturates the topological energy bound. On the other hand, the topological charge conjugate state (the antikink) is not a BPS solution. This means that it obeys the full Euler-Lagrange equation and does not saturate the topological energy bound.The supersymmetric approach also allows us to construct half-BPS soliton-impurity models in (2+1) dimensions. Concretely, in the case of the CP 1 model, its BPS impurity generalisation preserves one-quarter of the N = 2 SUSY, while for the Abelian Higgs model at critical coupling both impurity generalisations preserving one-quarter (the case of a new, so-called Higgs impurity) as well as one-half of the N = 2 SUSY (the case of the previously known magnetic impurity) are possible.We also discuss a possible relation between the BPS CP 1 -impurity model and the Dzyaloshinskii-Moriya interaction energy.

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Dynamics of vortices with magnetic impurities

Cited by 23 publications

References 28 publications

The ϕ4 model with the BPS preserving defect

The ϕ4 model with the BPS preserving defect

Vortices and magnetic impurities

BPS soliton-impurity models and supersymmetry

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