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...
A spatially-discrete sine-Gordon system with some novel features is described. There is a topological or Bogomol'nyi lower bound on the energy of a kink, and an explicit static kink which saturates this bound. There is no Peierls potential barrier, and consequently the motion of a kink is simpler, especially at low speeds. At higher speeds, it radiates and slows down.
Nuclear binding energies are investigated in two variants of the Skyrme model: the first replaces the usual Skyrme term with a term that is sixth order in derivatives, and the second includes a potential that is quartic in the pion fields. Solitons in the first model are shown to deviate significantly from ans\"atze previously assumed in the literature. The binding energies obtained in both models are lower than those obtained from the standard Skyrme model, and those obtained in the second model are close to the experimental values.Comment: 22 pages, 11 figures v2: minor changes to text and one figur
In contrast to single-component superconductors, which are described at the level of GinzburgLandau theory by a single parameter κ and are divided in type-I κ < 1/ √ 2 and type-II κ > 1/ √ 2 classes, two-component systems in general possess three fundamental length scales and have been shown to possess a separate "type-1.5" superconducting state 1,2 . In that state, as a consequence of the extra fundamental length scale, vortices attract one another at long range but repel at shorter ranges, and therefore should form clusters in low magnetic fields. In this work we investigate the appearance of type-1.5 superconductivity and the interpretation of the fundamental length scales in the case of two active bands with substantial interband couplings such as intrinsic Josephson coupling, mixed gradient coupling and density-density interactions. We show that in the presence of substantial intercomponent interactions of the above types the system supports type-1.5 superconductivity with fundamental length scales being associated with the mass of the gauge field and two masses of normal modes represented by mixed combinations of the density fields.
We show that in multiband superconductors even small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vortices by producing long-range intervortex attraction. This type of vortex interaction results in unusual response to low magnetic fields leading to phase separation into domains of a two-component Meissner states and vortex droplets.
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