Hidden symmetry and knot solitons in a charged two-condensate Bose system

Babaev, Egor; Faddeev, L. D.; Niemi, Antti J.

doi:10.1103/physrevb.65.100512

Cited by 267 publications

(329 citation statements)

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“…In the model (1), vortices with phase winding in only one field have logarithmically divergent energy per unit length if η = 0 and linearly divergent if η = 0 [9]. Here we do not consider the effect of thermal fluctuations, so we can, without loss of generality, restrict attention to vortices with φ 1 − φ 2 = const in the case η = 0.…”

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confidence: 99%

“…Recently, multicomponent superconducting systems have attracted increasing interest in areas ranging through metallic superconductors, hydrogen in extreme conditions and color superconductivity in dense QCD [9,10,11]. Below we consider a generic two-component superconductor (TCS), showing that it allows a novel type of thermodynamically stable vortices, whose electrodynamics is of Pippard type with respect to one of the order parameters and which have non-monotonic interaction energy for a wide range of parameters as an intrinsic feature.…”

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Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors

2005

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Traditionally, superconductors are categorized as type-I or type-II. Type-I superconductors support only Meissner and normal states, while type-II superconductors form magnetic vortices in sufficiently strong applied magnetic fields. Recently there has been much interest in superconducting systems with several species of condensates, in fields ranging from Condensed Matter to High Energy Physics. Here we show that the type-I/type-II classification is insufficient for such multicomponent superconductors. We obtain solutions representing thermodynamically stable vortices with properties falling outside the usual type-I/type-II dichotomy, in that they have the following features: (i) Pippard electrodynamics, (ii) interaction potential with long-range attractive and shortrange repulsive parts, (iii) for an n-quantum vortex, a non-monotonic ratio E(n)/n where E(n) is the energy per unit length, (iv) energetic preference for non-axisymmetric vortex states, "vortex molecules". Consequently, these superconductors exhibit an emerging first order transition into a "semi-Meissner" state, an inhomogeneous state comprising a mixture of domains of two-component Meissner state and vortex clusters.The formation of vortices in type-II superconductors subjected to a magnetic field is one of the most remarkable phenomena occuring in condensed matter. In all type-II superconductors (i.e. superconductors where the GL parameter, which is the ratio of the magentic field penetration length to the coherence lenth, is κ > 1/ √ 2 [1]) these vortices share a set of properties: an n-quantum vortex is unstable with respect to decay into n onequantum vortices, two vortices have purely repulsive interaction, and invasion of vortices under normal conditions is a second order phase transition characterised by a critical value of the external magnetic field H c1 .Vortices as solutions of the GL equations also exist formally in a type-I superconductor (κ < 1/ √ 2), but these vortices are thermodynamically unstable. The special case κ = 1/ √ 2 is also very interesting since, at this value of κ, vortices do not interact [2,3]. One should note, however, that in real life systems the situation is more complicated; experiments [4] show that in certain materials with κ ≈ 1/ √ 2 there might exist a tiny attractive force between vortices at a certain distance. Such an interaction was reproduced in a modified one-component GL model with additional terms in the regime κ ≈ 1/ √ 2 [5]. We should also mention a long range van der Waals -type vortex attraction in layered systems produced by thermal fluctuations or disorder [6].Besides superconductivity, the vortex concept has a direct counterpart in High Energy Physics, called the Nielsen-Olesen string. Such strings have been considered in cosmology [7] where they are expected to form during a symmetry breaking phase transition in the early universe. There also exists a similar type-I/type-II division of semilocal cosmic strings in the Higgs doublet model [8].Recently, multicomponent superconducting systems hav...

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Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors

2005

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“…The relative linking number of these two closed constituent egorons coincides with the self-linking number of the knotted composite egoron. This double-stranded structure of egorons has also been observed in numerical simulations [11]; see [14] for a detailed analysis.…”

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confidence: 64%

“…The r.h.s. of (5) and (6) admit a direct interpretation in terms of the Landau-Ginzburg free energy of a two-gap superconductor, employed to describe high-T c materials [7], [8] such as the widely studied MgB 2 [9]. Indeed, the first two terms in the r.h.s.…”

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Dual Superconductors And Su(2) Yang-Mills

Niemi

2004

J. High Energy Phys.

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We propose that the SU(2) Yang-Mills theory can be interpreted as a two-band dual superconductor with an interband Josephson coupling. We discuss various consequences of this interpretation including electric flux quantization, confinement of vortices with fractional flux, and the possibility that a closed vortex loop exhibits exotic exchange statistics. PACS numbers:Color confinement remains one of the great mysteries of modern high energy physics [1]. Several approaches have been proposed to explain why and how a SU(N) Yang-Mills theory supports confining colored strings, including a variety of dual superconductor and central vortex models [2]. But until now the relevant dynamical string degrees of freedom have not been identified.Recently it has been proposed [3] that the string variables in a Yang-Mills theory could relate to an appropriate decomposion of the gauge field. In the simplest case of SU(2) considered here, we start by separating A a µ (a = 1, 2, 3) into its U(1) Cartan component A 3 µ ≡ A µ while the off-diagonal A i µ (i = 1, 2) we combine into the complex variableWe introduce the U(1) covariant derivativesHere we have explicitely displayed a gauge fixing and Faddeev-Popov ghost (P, η) [4] only for the off-diagonal A 1,2 µ components. The remaining Cartan U(1) gauge invariance can be fixed similarly. But we shall find that this U(1) invariance can also be eliminated directly, by casting the Lagrangian in a form that involves only manifestly U(1) invariant variables. In the following we shall mostly exclude the ghosts from explicit equations. Their inclusion has very little if any conceptual impact. For the present purposes it is important to note that the sole effect of the fourth term in the r.h.s. of (1) is a redefinition of the gauge parameter ξ → ξ − 1 in the gauge fixing (fifth) term. Thus these terms can be combined. In particular, in the ξ → ∞ limit the fourth term becomes entirely immaterial. This limit yields the Landau version of the maximal abelian gaugewhich we shall assume has been imposed. We note that this gauge condition appears as the variational equation when one locates the extrema of the functionalwith respect to the full SU(2) gauge transformations. Thus, even though the field ρ is in general a gauge dependent quantity, its extremum values with respect to gauge transformations are manifestly gauge independent when the theory is subject to the Landau version of maximal abelian gauge. Recent numerical investigations indicate that in strong coupling regime the extrema of ρ are nonvanishing [5] The antisymmetric tensor

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Topology in Magnetism

Wang

2021

Topics in Applied Physics

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Hidden symmetry and knot solitons in a charged two-condensate Bose system

Cited by 267 publications

References 30 publications

Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors

Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors

Dual Superconductors And Su(2) Yang-Mills

Topology in Magnetism

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