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  • 1. Agterberg, Daniel F.
    et al.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics. University of Massachusetts, USA.
    Garaud, Julien
    KTH, School of Engineering Sciences (SCI), Theoretical Physics. University of Massachusetts, USA.
    Microscopic prediction of skyrmion lattice state in clean interface superconductors2014In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 90, no 6, p. 064509-Article in journal (Refereed)
    Abstract [en]

    When an in-plane field is applied to a clean interface superconductor, a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like phase is stabilized. This phase has a U(1)xU(1) symmetry and, in principle, this symmetry allows for flux carrying topological excitations different from Abrikosov vortices (which are the simplest defects associated with S-1 --> S-1 maps). However, in practice, largely due to electromagnetic and other intercomponent interactions, such topological excitations are very rare in superconducting systems. Here, we demonstrate that a realistic microscopic theory for interface superconductors, such as SrTiO3/LaAlO3, predicts an unconventional magnetic response where the flux-carrying objects are skyrmions, characterized by homotopy invariants of S-2 --> S-2 maps. Additionally, we show that this microscopic theory predicts that stable fractional vortices form near the boundary of these superconductors. It also predicts the appearance of type-1.5 superconductivity for some range of parameters. Central to these results is the assumption that the Rashba spin-orbit coupling is much larger than the superconducting gap.

  • 2. Babaev, Egor
    Andreev-Bashkin effect and knot solitons in an interacting mixture of a charged and a neutral superfluid with possible relevance for neutron stars2004In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 70, no 4Article in journal (Refereed)
    Abstract [en]

    We discuss a mixture of interacting neutral and charged Bose condensates, which is supposed being realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonic superconductor. We show that in this system, besides ordinary vortices of the S-1-->S-1 map, the neutron condensate also allows for (meta)stable finite-length knotted solitons, which are characterized by a nontrivial Hopf invariant and in some circumstances may be stabilized by a Faddeev-Skyrme term induced by the drag effect. We also consider a helical protonic flux tube in this system and show that, in contrast, it does not induce a Faddeev-Skyrme term.

  • 3. Babaev, Egor
    Characteristic length scales and formation of vortices in the Ginzburg-Landau-Higgs model in the presence of a uniform background charge2001In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 6317, no 17Article in journal (Refereed)
    Abstract [en]

    In this Brief Report we consider a nonlocal Ginzburg-Landau-Higgs model in the presence of a neutralizing uniform background charge. We show that such a system possesses vortices that feature a strong radial electric field. We estimate the basic properties of such an object and characteristic length scales in this model.

  • 4. Babaev, Egor
    Dual neutral variables and knot solitons in triplet superconductors2002In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 88, no 17Article in journal (Refereed)
    Abstract [en]

    We derive a dual presentation of a free energy functional for spin-triplet superconductors in terms of gauge-invariant variables. The resulting equivalent model in ferromagnetic phase has a form of a version of the Faddeev model. This allows one, in particular, to conclude that spin-triplet superconductors allow formation of stable finite-length closed vortices (knotted solitons).

  • 5. Babaev, Egor
    Fractional-flux vortices and spin superfluidity in triplet superconductors2005In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 94, no 13Article in journal (Refereed)
    Abstract [en]

    We discuss a novel type of fractional-flux vortices along with integer flux vortices in Kosterlitz-Thouless transitions in a triplet superconductor. We show that under certain conditions a spin-triplet superconductor should exhibit a novel state of spin superfluidity without superconductivity.

  • 6. Babaev, Egor
    Mass generation without symmetry breakdown in the chiral Gross-Neveu model at finite temperature and finite N in 2+1 dimensions2001In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 497, no 04-mar, p. 323-327Article in journal (Refereed)
    Abstract [en]

    The chiral Gross-Neveu model is one of the most popular toy models for QCD being a generic testing field for many ideas in particle physics. It has been studied in the past in detail in the limit of infinite number of flavors of fermions. Quite astonishingly, the study of this model was not carried through in all its facets. The most important omission is the study of the onset of quasi-long-range order in the decoupled massless phase field. The present work eliminates this deficiency. In this paper we derive behavior of the Kosterlitz-Thouless transition in this model at finite temperature in 2 + 1 dimensions in the regime when the number N of field components is large but finite. We also prove the anticipated before key feature of the model, namely, that in the regime of infinite N the temperature of the Kosterlitz-Thouless transition merges with the critical temperature T*, given by a mean-field equation for the gap modulus, thus recovering the BCS-like scenario [(T* - T-KT)/T* --> 0] of the phase transition at N --> infinity.

  • 7. Babaev, Egor
    Nonlinear sigma model approach for chiral fluctuations and symmetry breakdown in the Nambu-Jona-Lasinio model2000In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 6207, no 7Article in journal (Refereed)
    Abstract [en]

    Tills paper is organized in two parts. We start with the observation that the recent claim that the chiral symmetry in the Nambu-Jona-Lasinio (NJL) model is necessarily restored by violent chiral fluctuations at N-c = 3 [H. Kleinert and B. Van den Bossche, Phys. Lett. B 474, 336 (2000)] appears to be incorrect since the critical stiffness of the effective nonlinear sigma model used in the above reference is not a universal quantity in 3 + 1 dimensions. In the second part we discuss a modified Nn model, where the critical stiffness is expressed via an additional cutoff parameter. This model displays a symmetry breakdown, and also under certain conditions the chiral fluctuations give rise to a phase analogous to pseudogap phase of superconductors with strong coupling or low carrier density.

  • 8. Babaev, Egor
    Nonlinear sigma model approach for phase disorder transitions in chiral Gross-Neveu, Nambu-Jona-Lasinio models and strong-coupling superconductors2001In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 16, no 7, p. 1175-1197Article, review/survey (Refereed)
    Abstract [en]

    We briefly review the nonlinear sigma model approach for the subject of increasing interest: two-step phase transitions in the Gross-Neveu and the modified Nambu-Jona-Lasinio models at low N and condensation from pseudogap phase in strong-coupling superconductors. Recent success in describing of Bose-type superconductors that possess two characteristic temperatures and a pseudogap above T, is the develop ment approximately comparable with the BCS theory. One can expect that it should have influence on high-energy physics, similar to impact of the BCS theory on this subject. Although first generalizations of this concept to particle physics were made recently, these results were not systematized. In this review we summarize this development and discuss similarities and differences of the appearance of the pseudogap phase in superconductors and the Gross-Neveu and Nambu-Jona-Lasinio-like models. We discuss its possible relevance for chiral phase transition in QCD and color superconductors. This paper is organized in three parts. In the first part, we briefly review the separation of temperatures of pair formation and pair condensation in strong-coupling and low carrier density superconductors (i.e. the formation of the pseudogap phase). The second part is a review of nonlinear sigma model approach to an analogous phenomenon in the chiral Gross-Neveu model at small N. In the third part we discuss the modified Nambu-Jona-Lasinio model where the chiral phase transition is accompanied by a formation of a phase analogous to the pseudogap phase.

  • 9.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Non-Meissner electrodynamics and knotted solitons in two-component superconductors2009In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 79, no 10Article in journal (Refereed)
    Abstract [en]

    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 remain an outstandingly difficult question both for analytical and numerical treatment. Here I propose a special 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 in stark contrast to the Meissner electrodynamics of single-component systems. I also show that at certain short length scales knotted solitons in the 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 high topological charge may be more stable in these systems than low-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 the stability of knotted solitons. With this argument it is demonstrated that Ginzburg-Landau models possess stable knotted solitons.

  • 10. Babaev, Egor
    Phase diagram of planar U(l) x U(l) superconductor - Condensation of vortices with fractional flux and a superfluid state2004In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 686, no 3, p. 397-412Article in journal (Refereed)
    Abstract [en]

    We discuss a phase diagram of two-dimensional U(1) x U(l) superconductor in the field theoretic formalizm of [Phys. Rev. Lett. 89 (2002) 067001]. In particular we discuss that when penetration length is short the system exhibit a quasi-neutral quasi-superfluid state which is a state when quasi-long range order sets in only in phase difference while individually the phases are disordered.

  • 11. Babaev, Egor
    Thermodynamics of the crossover from weak- to strong-coupling superconductivity2001In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 6318, no 18Article in journal (Refereed)
    Abstract [en]

    In this paper we study an evolution of low-temperature thermodynamical quantities for an electron gas with a delta -function attraction as the system crosses over from weak-coupling (BCS-type) to strong-coupling (Bose-type) superconductivity in three and two dimensions.

  • 12.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Unconventional Rotational Responses of Hadronic Superfluids in a Neutron Star Caused by Strong Entrainment and a Sigma(-) Hyperon Gap2009In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 103, no 23Article in journal (Refereed)
    Abstract [en]

    I show that the usual model of the rotational response of a neutron star, which predicts rotation-induced neutronic vortices and no rotation-induced protonic vortices, does not hold (i) beyond a certain threshold of entrainment interaction strength nor (ii) in the case of nonzero Sigma(-) hyperon gap. I show that in both of these cases the rotational response involves the creation of phase windings in an electrically charged condensate. Lattices of bound states of vortices which result from these phase windings can (for a range of parameters) strongly reduce the interaction between rotation-induced vortices with magnetic-field carrying superconducting components.

  • 13. Babaev, Egor
    Vortex matter, effective magnetic charges, and generalizations of the dipolar superfluidity concept in layered systems2008In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 77, no 5Article in journal (Refereed)
    Abstract [en]

    In the first part of this paper, we discuss electrodynamics of an excitonic condensate in a bilayer. We show that under certain conditions, the system has a dominant energy scale and is described by the effective electrodynamics with "planar magnetic charges." In the second part of the paper, we point out that a vortex liquid state in bilayer superconductors also possesses dipolar superfluid modes and establish equivalence mapping between this state and a dipolar excitonic condensate. We point out that a vortex liquid state in a N-layer superconductor possesses multiple topologically coupled dipolar superfluid modes and therefore represents a generalization of the dipolar superfluidity concept.

  • 14. Babaev, Egor
    Vortices carrying an arbitrary fraction of magnetic flux quantum, neutral superfluidity and knotted solitons in two-gap Ginzburg-Landau model2004In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 404, no 04-jan, p. 39-43Article in journal (Refereed)
    Abstract [en]

    We show that in two-gap superconductors there exist vortices which carry an arbitrary fraction of magnetic flux quantum and in two dimensions under certain conditions these vortices undergo a BKT transition which marks onset of quasi-long-range order only in a difference of phases of the two order parameters. In the second part of the talk we show that an U(1) x U(1) Ginzburg-Landau model or a GL model where U(1) x U(1) symmetry is weakly broken to U(1) is exactly equivalent to a version of the Faddeev's the nonlinear O(3) sigma model. This implies in particular that such a system possesses a hidden O(3) symmetry and besides that allows for the formation of knotted solitons. The second part of the talk is based on a joint work with L.D. Faddeev and A. Niem: Phys. Rev. B 65 (2002) 100512.

  • 15. Babaev, Egor
    Vortices with fractional flux in two-gap superconductors and in extended Faddeev model2002In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 89, no 6Article in journal (Refereed)
    Abstract [en]

    We discuss linear topological defects allowed in two-gap superconductors and equivalent extended Faddeev model. We show that, in these systems, there exist vortices which carry an arbitrary fraction of magnetic flux quantum. Besides that, we discuss topological defects which do not carry magnetic flux and describe features of ordinary one-magnetic-flux-quantum vortices in the two-gap system. The results could be relevant for the newly discovered two-band superconductor MgB2.

  • 16.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Ashcroft, N. W.
    Violation of the London law and Onsager-Feynman quantization in multicomponent superconductors2007In: Nature Physics, ISSN 1745-2473, E-ISSN 1745-2481, Vol. 3, no 8, p. 530-533Article in journal (Refereed)
    Abstract [en]

    Non-classical response to rotation is a hallmark of quantum ordered states such as superconductors and superfluids. The rotational responses of all currently known single-component 'super' states of matter (superconductors, superfluids and supersolids) are largely described by two fundamental principles and fall into two categories according to whether the systems are composed of charged or neutral particles: the London law relating the angular velocity to a subsequently established magnetic field and the Onsager-Feynman quantization of superfluid velocity. These laws are theoretically shown to be violated in a two-component superconductor such as the projected liquid metallic states of hydrogen and deuterium at high pressures. The rotational responses of liquid metallic hydrogen or deuterium identify them as a new class of dissipationless states; they also directly point to a particular experimental route for verification of their existence.

  • 17. Babaev, Egor
    et al.
    Carlstrom, J.
    Silaev, Mihail
    KTH, School of Engineering Sciences (SCI), Physics, Statistical Physics.
    Speight, J. M.
    Type-1.5 superconductivity in multicomponent systems2017In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 533, p. 20-35Article in journal (Refereed)
    Abstract [en]

    In general a superconducting state breaks multiple symmetries and, therefore, is characterized by several different coherence lengths i = 1,..., N. Moreover in multiband material even superconducting states that break only a single symmetry are nonetheless described, under certain conditions by multi component theories with multiple coherence lengths. As a result of that there can appear a state where some coherence lengths are smaller and some are larger than the magnetic field penetration length A: xi(1) <= xi(2)...<root 2 lambda < xi(M) <=... (N). That state was recently termed "type-1.5" superconductivity. This breakdown of type-1/type-2 dichotomy is rather generic near a phase transition between superconducting states with different symmetries. The examples include the transitions between U(1) and U(1) x U(1) states or between U(1) and U(1) x Z(2) states. The later example is realized in systems that feature transition between s-wave and s + is states. The extra fundamental length scales have many physical consequences. In particular in these regimes vortices can attract one another at long range but repel at shorter ranges. Such a system can form vortex clusters in low magnetic fields. The vortex clustering in the type 1.5 regime gives rise to many physical effects, ranging from macroscopic phase separation in domains of different broken symmetries, to unusual transport properties. Prepared for the proceedings of Vortex IX conference, Rhodes 12-17 September 2015.

  • 18.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Statistical Physics.
    Carlström, J.
    Silaev, Mihail
    KTH, School of Engineering Sciences (SCI), Physics, Statistical Physics.
    Speight, J. M.
    Type-1.5 superconductivity2017In: Superconductors at the Nanoscale: From Basic Research to Applications, Walter de Gruyter GmbH , 2017, p. 133-164Chapter in book (Other academic)
  • 19.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Carlström, Johan
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Type-1.5 superconductivity in two-band systems2010In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 470, no 19, p. 717-721Article in journal (Refereed)
    Abstract [en]

    In the usual Ginzburg-Landau theory the critical value of Ginzburg-Landau parameter kappa(c) = 1/root 2 separates regimes of type-I and type-II superconductivity. The latter regime possess thermodynamically stable vortex excitations which interact with each other repulsively and tend to form vortex lattices. It was shown in [5] that this dichotomy in broken in U(1) x U(1) Ginzburg-Landau models which possess a distinct phase with vortex excitations which interact attractively at large length scales and repulsively at shorter distances. Here we discuss the influence of the Josephson coupling and that similar kind of superconductivity can also arise for entirely different reasons in superconductors where only one band is superconducting if this band interacting via a proximity effect with another band (the report is partially based on [1]).

  • 20.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Carlström, Johan
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Garaud, J.
    Silaev, Mihail
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Speight, J. M.
    Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory - A brief overview2012In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 479, p. 2-14Article in journal (Refereed)
    Abstract [en]

    A conventional superconductor is described by a single complex order parameter field which has two fundamental length scales, the magnetic field penetration depth lambda and the coherence length xi. Their ratio kappa determines the response of a superconductor to an external field, sorting them into two categories as follows; type-I when kappa < 1/root 2 and type-II when kappa > 1/root 2. We overview here multicomponent systems which can possess three or more fundamental length scales and allow a separate "type-1.5" superconducting state when, e. g. in two-component case xi(1) < root 2 lambda < xi(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. As a consequence the system should form an additional Semi-Meissner state which properties we discuss below. In that state vortices form clusters in low magnetic fields. Inside the cluster one of the component is depleted and the superconductor-to-normal interface has negative energy. In contrast the current in second component is mostly concentrated on the cluster's boundary, making the energy of this interface positive. Here we briefly overview recent developments in Ginzburg-Landau and microscopic descriptions of this state.

  • 21.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Carlström, Johan
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Speight, Martin
    Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors2010In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 105, no 6, p. 067003-Article in journal (Refereed)
    Abstract [en]

    We show that in multiband superconductors, even an extremely 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 an unusual response to low magnetic fields leading to phase separation into domains of two-component Meissner states and vortex droplets.

  • 22. Babaev, Egor
    et al.
    Faddeev, L. D.
    Niemi, A. J.
    Hidden symmetry and knot solitons in a charged two-condensate Bose system2002In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 65, no 10Article in journal (Refereed)
    Abstract [en]

    We show that a charged two-condensate Ginzburg-Landau model or equivalently a Gross-Pitaevskii functional for two charged Bose condensates, can be mapped onto a version of the nonlinear O(3) sigma model. This implies in particular that such a system possesses a hidden O(3) symmetry and allows for the formation of stable knotted solitons.

  • 23.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Jaykka, Juha
    Speight, Martin
    Magnetic Field Delocalization and Flux Inversion in Fractional Vortices in Two-Component Superconductors2009In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 103, no 23Article in journal (Refereed)
    Abstract [en]

    We demonstrate that, in contrast with the single-component Abrikosov vortex, in two-component superconductors vortex solutions with an exponentially screened magnetic field exist only in exceptional cases: in the case of vortices carrying an integer number of flux quanta and in a special parameter limit for half-quantum vortices. For all other parameters, the vortex solutions have a delocalized magnetic field with a slowly decaying tail. Furthermore, we demonstrate a new effect which is generic in two-component systems but has no counterpart in single-component systems: on exactly half of the parameter space of the U(1)xU(1) Ginzburg-Landau model, the magnetic field of a generic fractional vortex inverts its direction at a certain distance from the vortex core.

  • 24.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Silaev, Mihail
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Comment on "Ginzburg-Landau theory of two-band superconductors: Absence of type-1.5 superconductivity"2012In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 86, no 1, p. 016501-Article in journal (Other academic)
    Abstract [en]

    The recent paper by V. G. Kogan and J. Schmalian [Phys. Rev. B 83, 054515 (2011)] argues that the widely used two-component Ginzburg-Landau (GL) models are not correct, and further concludes that in the regime which is described by a GL theory there could be no disparity in the coherence lengths of two superconducting components. This would in particular imply that [in contrast to U(1) x U(1) superconductors] there could be no "type-1.5" superconducting regime in U(1) multiband systems for any finite interband coupling strength. We point out that these claims are incorrect and based on an erroneous scheme of reduction of a two-component GL theory.

  • 25.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Silaev, Mihail
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Type-1.5 Superconductivity in Multiband and Other Multicomponent Systems2013In: Journal of Superconductivity and Novel Magnetism, ISSN 1557-1939, E-ISSN 1557-1947, Vol. 26, no 5, p. 2045-2055Article in journal (Refereed)
    Abstract [en]

    Usual superconductors are classified into two categories: of type-1 when the ratio of the magnetic field penetration length (lambda) to coherence length (xi) kappa = lambda/xi < 1/root 2 and of type-2 when kappa > 1/root 2. The boundary case kappa = 1/root 2 is also considered to be a special situation, frequently termed as "Bogomolnyi limit". Here we discuss multicomponent systems which can possess three or more fundamental length scales and allow a separate superconducting state, which was recently termed "type-1.5". In that state, a system has the following hierarchy of coherence and penetration lengths xi(1) < root 2 lambda < xi(2). We also briefly overview the works on single-component regime kappa approximate to 1/root 2 and comment on recent discussion by Brandt and Das in the proceedings of the previous conference in this series.

  • 26. Babaev, Egor
    et al.
    Speight, M.
    Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors2005In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 72, no 18Article in journal (Refereed)
    Abstract [en]

    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 classification into types I and II 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 nonmonotonic ratio E(n)/n where E(n) is the energy per unit length, (iv) energetic preference for nonaxisymmetric 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.

  • 27. Babaev, Egor
    et al.
    Sudbo, A.
    Ashcroft, N. W.
    A superconductor to superfluid phase transition in liquid metallic hydrogen2004In: Nature, ISSN 0028-0836, E-ISSN 1476-4687, Vol. 431, no 7009, p. 666-668Article in journal (Refereed)
    Abstract [en]

    Although hydrogen is the simplest of atoms, it does not form the simplest of solids or liquids. Quantum effects in these phases are considerable (a consequence of the light proton mass) and they have a demonstrable and often puzzling influence on many physical properties(1), including spatial order. To date, the structure of dense hydrogen remains experimentally elusive(2). Recent studies of the melting curve of hydrogen(3,4) indicate that at high (but experimentally accessible) pressures, compressed hydrogen will adopt a liquid state, even at low temperatures. In reaching this phase, hydrogen is also projected to pass through an insulator-to-metal transition. This raises the possibility of new state of matter: a near ground-state liquid metal, and its ordered states in the quantum domain. Ordered quantum fluids are traditionally categorized as superconductors or superfluids; these respective systems feature dissipationless electrical currents or mass flow. Here we report a topological analysis of the projected phase of liquid metallic hydrogen, finding that it may represent a new type of ordered quantum fluid. Specifically, we show that liquid metallic hydrogen cannot be categorized exclusively as a superconductor or superfluid. We predict that, in the presence of a magnetic field, liquid metallic hydrogen will exhibit several phase transitions to ordered states, ranging from superconductors to superfluids.

  • 28. Babaev, Egor
    et al.
    Sudbo, A.
    Ashcroft, N. W.
    Observability of a projected new state of matter: A metallic superfluid2005In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 95, no 10Article in journal (Refereed)
    Abstract [en]

    Dissipationless quantum states, such as superconductivity and superfluidity, have attracted interest for almost a century. A variety of systems exhibit these macroscopic quantum phenomena, ranging from superconducting electrons in metals to superfluid liquids, atomic vapors, and even large nuclei. It was recently suggested that liquid metallic hydrogen could form two new and unusual dissipationless quantum states, namely, the metallic superfluid and the superconducting superfluid. Liquid metallic hydrogen is projected to occur only at an extremely high pressure of about 400 GPa, with pressures on hydrogen of 320 GPa having already been reported. The issue to be addressed is whether this state could be experimentally observable in principle. We propose four experimental probes for detecting it.

  • 29.
    Babaev, Egor
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Svistunov, Boris
    Rotational response of superconductors: Magnetorotational isomorphism and rotation-induced vortex lattice2014In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 89, no 10, p. 104501-Article in journal (Refereed)
    Abstract [en]

    The analysis of nonclassical rotational response of superfluids and superconductors was performed by Onsager [Onsager, Nuovo Cimento, Suppl. 6, 279 (1949)] and London [Superfluids (Wiley, NewYork, 1950)] and crucially advanced by Feynman [Prog. Low Temp. Phys. 1, 17 (1955)]. It was established that, in the thermodynamic limit, neutral superfluids rotate by forming-without any threshold-a vortex lattice. In contrast, the rotation of superconductors at angular frequency Omega-supported by uniform magnetic field B-L proportional to Omega due to surface currents-is of the rigid-body type (London law). Here we show that, neglecting the centrifugal effects, the behavior of a rotating superconductor is identical to that of a superconductor placed in a uniform fictitious external magnetic field (H) over tilde = -B-L. In particular, the isomorphism immediately implies the existence of two critical rotational frequencies in type-2 superconductors.

  • 30. Bojesen, Troels Arnfred
    et al.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Sudbø, Asle
    Phase transitions and anomalous normal state in superconductors with broken time-reversal symmetry2014In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 89, no 10, p. 104509-Article in journal (Refereed)
    Abstract [en]

    Using Monte Carlo simulations, we explore the phase diagram and the phase transitions in U(1) x Z(2) n-band superconductors with spontaneously broken time-reversal symmetry (also termed s + is superconductors), focusing on the three-band case. In the limit of infinite penetration length, the system under consideration can, for a certain parameter regime, have a single first-order phase transition from a U(1) x Z(2) broken state to a normal state due to a nontrivial interplay between U(1) vortices and Z(2) domain walls. This regime may also apply to multicomponent superfluids. For other parameters, when the free energy of the domain walls is low, the system undergoes a restoration of broken Z(2) time-reversal symmetry at temperatures lower than the temperature of the superconducting phase transition. We show that inclusion of fluctuations can strongly suppress the temperature of the Z(2) transition when frustration is weak. The main result of our paper is that for relatively short magnetic field penetration lengths, the system has a superconducting phase transition at a temperature lower than the temperature of the restoration of the broken Z(2) symmetry. Thus, there appears a new phase that is U(1) symmetric, but breaks Z(2) time-reversal symmetry, an anomalous dissipative (metallic) state.

  • 31. Bojesen, Troels Arnfred
    et al.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Sudbø, Asle
    Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems2013In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 88, no 22, p. 220511-Article in journal (Refereed)
    Abstract [en]

    We discuss the phase diagram and phase transitions in U(1) x Z(2) three-band superconductors with broken time reversal symmetry. We find that beyond mean-field approximation and for sufficiently strong frustration of interband interactions there appears an unusual metallic state precursory to a superconducting phase transition. In that state, the system is not superconducting. Nonetheless, it features a spontaneously broken Z(2) time reversal symmetry. By contrast, for weak frustration of interband coupling the energy of a domain wall between different Z(2) states is low and thus fluctuations restore broken time reversal symmetry in the superconducting state at low temperatures.

  • 32.
    Carlström, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics. University of Massachusetts, United States.
    Entropy- and Flow-Induced Superfluid States2014In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 113, no 5, p. 055301-Article in journal (Refereed)
    Abstract [en]

    Normally the role of phase fluctuations in superfluids and superconductors is to drive a phase transition to the normal state. This happens due to proliferation of topologically nontrivial phase fluctuations in the form of vortices. Here we discuss a class of systems where, by contrast, nontopological phase fluctuations can produce superfluidity. Here we understand superfluidity as a phenomenon that does not necessarily arises from a broken U(1) symmetry, but can be associated with a certain class of (approximate or exact) degeneracies of the system's energy landscape giving raise to a U(1)-like phase.

  • 33.
    Carlström, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Spontaneous breakdown of time-reversal symmetry induced by thermal fluctuations2015In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 91, no 14, article id 140504Article in journal (Refereed)
    Abstract [en]

    In systems with broken U(1) symmetry, such as superfluids, superconductors, or magnets, the symmetry restoration is driven by the proliferation of topological defects in the form of vortex loops (unless the phase transition is strongly first order). Here we discuss that the proliferation of topological defects can, by contrast, lead to the breakdown of an additional symmetry. We demonstrate that this effect should take place in s + is superconductors, which are widely discussed in connection with iron-based materials (although the mechanism is much more general). In these systems a vortex excitation can create a "bubble" of fluctuating Z(2) order parameter. The thermal excitation of vortices then leads to the breakdown of Z(2) time-reversal symmetry when the temperature is increased.

  • 34.
    Carlström, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Speight, Martin
    Type-1.5 superconductivity in multiband systems: Effects of interband couplings2011In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 83, no 17, p. 174509-Article in journal (Refereed)
    Abstract [en]

    In contrast to single-component superconductors, which are described at the level of Ginzburg-Landau theory by a single parameter kappa and are divided in type-I kappa < 1/root 2 and type-II kappa > 1/root 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. 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.

  • 35.
    Carlström, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Garaud, Julien
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Length scales, collective modes, and type-1.5 regimes in three-band superconductors2011In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 84, no 13, p. 134518-Article in journal (Refereed)
    Abstract [en]

    The recent discovery of iron pnictide superconductors has resulted in a rapidly growing interest in multiband models with more than two bands. In this work we specifically focus on the properties of three-band Ginzburg-Landau models which do not have direct counterparts in more studied two-band models. First we derive normal modes and characteristic length scales in the conventional U(1) three-band Ginzburg-Landau model as well as in its time-reversal symmetry-broken counterpart with U(1) x Z(2) symmetry. We show that, in the latter case, the normal modes are mixed phase-density collective excitations. A possibility of the appearance of a massless mode associated with fluctuations of the phase difference is also discussed. Next we show that gradients of densities and phase differences can be inextricably intertwined in vortex excitations in three-band models. This can lead to very long-range attractive intervortex interactions and the appearance of type-1.5 regimes even when the intercomponent Josephson coupling is large. In some cases it also results in the formation of a domainlike structure in the form of a ring of suppressed density around a vortex across which one of the phases shifts by p. We also show that field-induced vortices can lead to a change of broken symmetry from U(1) to U(1) x Z(2) in the system. In the type-1.5 regime, it results in a semi-Meissner state where the system has a macroscopic phase separation in domains with broken U(1) and U(1) x Z(2) symmetries.

  • 36.
    Carlström, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Garaud, Julien
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Semi-Meissner state and nonpairwise intervortex interactions in type-1.5 superconductors2011In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 84, no 13, p. 134515-Article in journal (Refereed)
    Abstract [en]

    We demonstrate the existence of nonpairwise interaction forces between vortices in multicomponent and layered superconducting systems. That is, in contrast to most common models, the interaction in a group of such vortices is not a universal superposition of Coulomb or Yukawa forces. Next, we consider the properties of vortex clusters in a semi-Meissner state of type-1.5 two-component superconductors. We show that under certain conditions nonpairwise forces can contribute to the formation of very complex vortex states in type-1.5 regimes.

  • 37. Dahl, E. K.
    et al.
    Babaev, Egor
    Kragset, S.
    Sudbo, A.
    Preemptive vortex-loop proliferation in multicomponent interacting Bose-Einstein condensates2008In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 77, no 14Article in journal (Refereed)
    Abstract [en]

    We use analytical arguments and large-scale Monte Carlo calculations to investigate the nature of the phase transitions between distinct complex superfluid phases in a two-component Bose-Einstein condensate when a nondissipative drag between the two components is being varied. We focus on understanding the role of topological defects in various phase transitions and develop vortex-matter arguments, allowing an analytical description of the phase diagram. We find the behavior of fluctuation induced vortex matter to be much more complex and substantially different from that of single-component superfluids. We propose and numerically investigate a drag-induced "preemptive vortex loop proliferation" scenario. Such a transition may be a quite generic feature in many multicomponent systems where symmetry is restored by a gas of several kinds of competing vortex loops.

  • 38. Dahl, E. K.
    et al.
    Babaev, Egor
    Sudbo, A.
    Hidden vortex lattices in a thermally paired superfluid2008In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 78, no 14Article in journal (Refereed)
    Abstract [en]

    We study the evolution of rotational response of a statistical mechanical model of two-component superfluid with a nondissipative drag interaction as the system undergoes a transition into a paired superfluid phase at finite temperature. The transition manifests itself in a change of (i) vortex-lattice symmetry and (ii) nature of the 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 translation symmetry.

  • 39. Dahl, E. K.
    et al.
    Babaev, Egor
    Sudbo, A.
    Unusual States of Vortex Matter in Mixtures of Bose-Einstein Condensates on Rotating Optical Lattices2008In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 101, no 25Article in journal (Refereed)
    Abstract [en]

    In a single-component superfluid under rotation a broken symmetry in the order parameter space results in a broken translational symmetry in real space: a vortex lattice. If translational symmetry is restored, the phase of the order parameter disorders and thus the broken symmetry in the order parameter space is also restored. We show that for Bose-Einstein condensate mixtures in optical lattices with negative dissipationless drag, a new situation arises. This state is a modulated vortex liquid which breaks translational symmetry in the direction transverse to the rotation vector.

  • 40. Diaz-Mendez, Rogelio
    et al.
    Mezzacapo, Fabio
    Lechner, Wolfgang
    Cinti, Fabio
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Pupillo, Guido
    Glass Transitions in Monodisperse Cluster-Forming Ensembles: Vortex Matter in Type-1.5 Superconductors2017In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 118, no 6, article id 067001Article in journal (Refereed)
    Abstract [en]

    At low enough temperatures and high densities, the equilibrium configuration of an ensemble of ultrasoft particles is a self-assembled, ordered, cluster crystal. In the present Letter, we explore the out-of-equilibrium dynamics for a two-dimensional realization, which is relevant to superconducting materials with multiscale intervortex forces. We find that, for small temperatures following a quench, the suppression of the thermally activated particle hopping hinders the ordering. This results in a glass transition for a monodispersed ensemble, for which we derive a microscopic explanation in terms of an "effective polydispersity" induced by multiscale interactions. This demonstrates that a vortex glass can form in clean systems of thin films of "type-1.5" superconductors. An additional setup to study this physics can be layered superconducting systems, where the shape of the effective vortex-vortex interactions can be engineered.

  • 41.
    Diaz-Mendez, Rogelio
    et al.
    KTH, School of Engineering Sciences (SCI), Physics.
    Pupillo, Guido
    Univ Strasbourg, IPCMS, UMR 7504, IcFRC,ISIS,UMR 7006, F-67000 Strasbourg, France.;CNRS, F-67000 Strasbourg, France..
    Mezzacapo, Fabio
    ENS Lyon, CNRS, UMR 5672, Lab Phys, F-69364 Lyon 07, France..
    Wallin, Mats
    KTH, School of Engineering Sciences (SCI), Physics.
    Lidmar, Jack
    KTH, School of Engineering Sciences (SCI), Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Physics.
    Phase-change switching in 2D via soft interactions2019In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 15, no 3, p. 355-358Article in journal (Refereed)
    Abstract [en]

    We present a new type of phase-change behavior relevant for information storage applications, that can be observed in 2D systems with cluster-forming ability. The temperature-based control of the ordering in 2D particle systems depends on the existence of a crystal-to-glass transition. We perform molecular dynamics simulations of models with soft interactions, demonstrating that the crystalline and amorphous structures can be easily tuned by heat pulses. The physical mechanism responsible for this behavior is a self-assembled polydispersity, that depends on the cluster-forming ability of the interactions. Therefore, the range of real materials that can perform such a transition is very wide in nature, ranging from colloidal suspensions to vortex matter. The state of the art in soft matter experimental setups, controlling interactions, polydispersity and dimensionality, makes it a very fertile ground for practical applications.

  • 42. Galteland, Peder Notto
    et al.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Sudbo, Asle
    Fluctuation effects in rotating Bose-Einstein condensates with broken SU(2) and U(1) x U(1) symmetries in the presence of intercomponent density-density interactions2015In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 91, no 1, p. 013605-Article in journal (Refereed)
    Abstract [en]

    Thermal fluctuations and melting transitions for rotating single-component superfluids have been intensively studied and are well understood. In contrast, the thermal effects on vortex states for two-component superfluids with density-density interaction, which have a much richer variety of vortex ground states, have been much less studied. Here, we investigate the thermal effects on vortex matter in superfluids with U(1) x U(1) broken symmetries and intercomponent density-density interactions, as well as the case with a larger SU(2) broken symmetry obtainable from the [U(1) x U(1)]-symmetric case by tuning scattering lengths. In the former case we find that, in addition to first-order melting transitions, the system exhibits thermally driven phase transitions between square and hexagonal lattices. Our main result, however, concerns the case where the condensate exhibits SU(2) symmetry, and where vortices are not topological. At finite temperature, the system exhibits effects which do not have a counterpart in single-component systems. Namely, it has a state where thermally averaged quantities show no regular vortex lattice, yet the system retains superfluid coherence along the axis of rotation. In such a state, the thermal fluctuations result in transitions between different (nearly) degenerate vortex states without undergoing a melting transition. Our results apply to multicomponent Bose-Einstein condensates, and we suggest how to detect some of these unusual effects experimentally in such systems.

  • 43. Galteland, Peder Notto
    et al.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Sudbo, Asle
    Thermal remixing of phase-separated states in two-component bosonic condensates2015In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 17, article id 103040Article in journal (Refereed)
    Abstract [en]

    We consider a two-component interacting bosonic condensate with dominating intra-species repulsive density-density interactions. We study the phase diagram of the system at finite temperature with rotation, using large-scale Monte Carlo simulations of a two-component Ginzburg-Landau model of the system. In the presence of rotation, the system features a competition between long-range vortex-vortex interactions and short-range density-density interactions. This leads to a rotation-driven 'mixing' phase transition in a spatially inhomogeneous state with a broken U(1) symmetry. Thermal fluctuations in this state lead to nematic two-component sheets of vortex liquids. At sufficiently strong inter-component interaction, we find that the superfluid and Z(2) phase transitions split. This results in the formation of an intermediate state which breaks only Z(2) symmetry. It represents two phase separated normal fluids with a difference in their densities.

  • 44.
    Garaud, Julien
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Agterberg, Daniel F.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Vortex coalescence and type-1.5 superconductivity in Sr2RuO42012In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 86, no 6, p. 060513-Article in journal (Refereed)
    Abstract [en]

    Recently vortex coalescence was reported in superconducting Sr2RuO4 by several experimental groups for fields applied along the c axis. We argue that Sr2RuO4 is a type-1.5 superconductor with long-range attractive, short-range repulsive intervortex interaction. The type-1.5 behavior stems from an interplay of the two orbital degrees of freedom describing this chiral superconductor together with the multiband nature of the superconductivity. These multiple degrees of freedom give rise to multiple coherence lengths, some larger and some smaller than the magnetic field penetration length, resulting in nonmonotonic intervortex forces.

  • 45.
    Garaud, Julien
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Domain walls and their experimental signatures in s + i s superconductors2014In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 112, no 1, p. 017003-Article in journal (Refereed)
    Abstract [en]

    Arguments were recently advanced that hole-doped Ba1-xKxFe2As2 exhibits the s+is state at certain doping. Spontaneous breaking of time-reversal symmetry in the s+is state dictates that it possess domain wall excitations. Here, we discuss what are the experimentally detectable signatures of domain walls in the s+is state. We find that in this state the domain walls can have a dipolelike magnetic signature (in contrast to the uniform magnetic signature of domain walls p+ip superconductors). We propose experiments where quench-induced domain walls can be stabilized by geometric barriers and observed via their magnetic signature or their influence on the magnetization process, thereby providing an experimental tool to confirm the s+is state.

  • 46.
    Garaud, Julien
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Properties of skyrmions and multi-quanta vortices in chiral p-wave superconductors2015In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 5, article id 17540Article in journal (Refereed)
    Abstract [en]

    Chiral p-wave superconducting state supports a rich spectrum of topological excitations different from those in conventional superconducting states. Besides domain walls separating different chiral states, chiral p-wave state supports both singular and coreless vortices also interpreted as skyrmions. Here, we present a numerical study of the energetic properties of isolated singular and coreless vortex states as functions of anisotropy and magnetic field penetration length. In a given chiral state, single quantum vortices with opposite winding have different energies and thus only one kind is energetically favoured. We find that with the appropriate sign of the phase winding, two-quanta (coreless) vortices are always energetically preferred over two isolated single quanta (singular) vortices. We also report solutions carrying more flux quanta. However those are typically more energetically expensive/metastable as compared to those carrying two flux quanta.

  • 47.
    Garaud, Julien
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Skyrmionic state and stable half-quantum vortices in chiral p-wave superconductors2012In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 86, no 6, p. 060514-Article in journal (Refereed)
    Abstract [en]

    Observability of half-quantum vortices and skyrmions in p-wave superconductors is an outstanding open question. Under the most common conditions, fractional flux vortices are not thermodynamically stable in bulk samples. Here we show that in chiral p-wave superconductors, there is a regime where, in contrast, lattices of integer-flux vortices are not thermodynamically stable. Instead, skyrmions made of spatially separated half-quantum vortices are the topological defects produced by an applied external field.

  • 48.
    Garaud, Julien
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Topological defects in mixtures of superconducting condensates with different charges2014In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 89, no 21, p. 214507-Article in journal (Refereed)
    Abstract [en]

    We investigate the topological defects in phenomenological models describing mixtures of charged condensates with commensurate electric charges. Such situations are expected to appear for example in liquid metallic deuterium. This is modeled by a multicomponent Ginzburg-Landau theory where the condensates are coupled to the same gauge field by different coupling constants whose ratio is a rational number. We also briefly discuss the case where electric charges are incommensurate. Flux quantization and finiteness of the energy per unit length dictate that the different condensates have different winding and thus different number of (fractional) vortices. Competing attractive and repulsive interactions lead to molecule-like bound states between fractional vortices. Such bound states have finite energy and carry integer flux quanta. These can be characterized by the CP1 topological invariant that motivates their denomination as skyrmions.

  • 49.
    Garaud, Julien
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Vortex chains due to nonpairwise interactions and field-induced phase transitions between states with different broken symmetry in superconductors with competing order parameters2015In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 91, no 1, p. 014510-Article in journal (Refereed)
    Abstract [en]

    We study superconductors with two order components and phase separation driven by intercomponent densitydensity interaction, focusing on the phase where only one condensate has nonzero ground-state density and a competing order parameter exists only in vortex cores. We demonstrate there that multibody intervortex interactions can be strongly nonpairwise, leading to some unusual vortex patterns in an external field, such as vortex pairs and vortex chains. We demonstrate that in an external magnetic field such a system undergoes a field-driven phase transition from (broken) U(1) to (broken) U(1) x U(1) symmetries when a subdominant order parameter in the vortex cores acquires global coherence. Observation of these characteristic ordering patterns in surface probes may signal the presence of a subdominant condensate in the vortex core.

  • 50.
    Garaud, Julien
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Babaev, Egor
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Bojesen, Troels Arnfred
    Sudbo, Asle
    Lattices of double-quanta vortices and chirality inversion in p(x) + i p(y) superconductors2016In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 94, no 10, article id 104509Article in journal (Refereed)
    Abstract [en]

    We investigate the magnetization processes of a standard Ginzburg-Landau model for chiral p-wave superconducting states in an applied magnetic field. We find that the phase diagram is dominated by triangular lattices of doubly quantized vortices. Only in close vicinity to the upper critical field the lattice starts to dissociate into a structure of single-quanta vortices. The degeneracy between states with opposite chirality is broken in a nonzero field. If the magnetization starts with an energetically unfavorable chirality, the process of chirality inversion induced by the external magnetic field results in the formation of a sequence of metastable states with characteristic magnetic signatures that can be probed by standard experimental techniques.

12 1 - 50 of 89
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