Non-Meissner electrodynamics and knotted solitons in two-component superconductors

I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ago. However their basic properties and stability in these systems remains an outstandingly difficult question both for analytical and numerical treatment. Here I propose a new perturbative approach to treat self-consistently all the degrees of freedom in the problem. I show that there exists a length scale for a Hopfion texture where the electrodynamics of a two-component superconductor is dominated by a self-induced Faddeev term, which is a stark contrast to the Meissner electrodynamics of single-component systems. I also show that at certain short length scales knotted solitons in two-component Ginzburg-Landau model are not described by a Faddeev-Skyrme-type model and are unstable. However these solitons can be stable at some intermediate length scales. I argue that configurations with a high topological charge may be more stable in this system than low-topological-charge configurations. In the second part of the paper I discuss qualitatively different physics of the stability of knotted solitons in a more general Ginzburg-Landau model and point out the physically relevant terms which enhance or suppress stability of the knotted solitons. With this argument it is demonstrated that the generalized Ginburg-Landau model possesses stable knotted solitons.Comment: In print in Phys. Rev. B. v2: a typo (missing factor) fixed. v3: discussion of some aspects made more detailed following a referee reques

Hidden vortex lattices in a thermally paired superfluid

We study the evolution of rotational response of a hydrodynamic model of a two-component superfluid with a non-dissipative drag interaction, as the system undergoes a transition into a paired phase at finite temperature. The transition manifests itself in a change of (i) vortex lattice symmetry, and (ii) nature of vortex state. Instead of a vortex lattice, the system forms a highly disordered tangle which constantly undergoes merger and reconnecting processes involving different types of vortices, with a "hidden" breakdown of translational symmetry.Comment: 4 pages, 5 figs. Submitted to Physical Review. Online suppl. material available; Ref. 6. V2: Fig. 1 re-sent, URL in Ref. 6 correcte

Encoding and Decoding Procedures for Arrangements

This article discusses an algorithm based on the encoding procedure for representing a set of arrangement elements as a single number. Also the author provides the procedure for the inverse transformation of the code into arrangement elements. In addition the Article includes recommendations on the use of the above procedures in combinatorial algorithms of optimization

Phase structure and phase transitions in a three dimensional SU(2) superconductor

We study the three dimensional SU(2)-symmetric noncompact CP1 model, with two charged matter fields coupled minimally to a noncompact Abelian gauge-field. The phase diagram and the nature of the phase transitions in this model have attracted much interest after it was proposed to describe an unusual continuous transition associated with deconfinement of spinons. Previously, it has been demonstrated for various two-component gauge theories that weakly first-order transitions may appear as continuous ones of a new universality class in simulations of relatively large, but finite systems. We have performed Monte-Carlo calculations on substantially larger systems sizes than those in previous works. We find that in some area of the phase diagram where at finite sizes one gets signatures consistent with a single first-order transition, in fact there is a sequence of two phase transitions with an O(3) paired phase sandwiched in between. We report (i) a new estimate for the location of a bicritical point and (ii) the first resolution of bimodal distributions in energy histograms at relatively low coupling strengths. We perform a flowgram analysis of the direct transition line with rescaling of the linear system size in order to obtain a data collapse. The data collapses up to coupling constants where we find bimodal distributions in energy histograms.Comment: 16 pages, 11 figures. Submitted to Physical Review

Skyrmions induced by dissipationless drag in U(1)xU(1) superconductors

Rather generically, multicomponent superconductors and superfluids have intercomponent current-current interaction. We show that in superconductors with substantially strong intercomponent drag interaction, the topological defects which form in external field are characterized by a skyrmionic topological charge. We then demonstrate that they can be distinguished from ordinary vortex matter by a very characteristic magnetization process due to the dipolar nature of inter-skyrmion forces. The results provide an experimental signature to confirm or rule out the formation $p$-wave state with reduced spin stiffness in $p$-wave superconductors.Comment: Replaced with a version in print in Physical Review B; Improved and extended as compared to the first version; 13 pages; 12 figure

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

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 short-range 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.Comment: in print in Phys. Rev. B Rapid Communications. v2: presentation is made more accessible for a general reader. Latest updates and links to related papers are available at the home page of one of the authors: http://people.ccmr.cornell.edu/~egor