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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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]).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous superconducting and superfluid ground states, spontaneously breaking translation symmetries. In this Letter, we demonstrate that the transition from the FFLO to the normal state as a function of temperature or increased Fermi surface splitting is not a direct one. Instead, the system has an additional phase transition to a different state where pair-density-wave superconductivity (or superfluidity) exists only on the boundaries of the system, while the bulk of the system is normal. The surface pair-density-wave state is very robust and exists for much larger fields and temperatures than the FFLO state.
We consider the interface between a Bardeen-Cooper-Schrieffer superconductor and nonsuperconducting band insulator. We show that under certain conditions, such interfaces can have an elevated superconducting critical temperature, without increasing the strength of the pairing interaction at the interface. We identify the regimes where the interface critical temperature exceeds the critical temperature associated with a superconductor vacuum interface.
We show that in superfluids with fermionic imbalance and uniform ground state, there are stable solitons. These solutions are formed of radial density modulations resulting in nodal rings. We demonstrate that these solitons exhibit nontrivial soliton-soliton and soliton-vortex interactions and can form complicated bound states in the form of "soliton sacks." In a phase-modulating (Fulde-Ferrell) background, we find different solitonic states, in the form of stable vortex-antivortex pairs.
Larkin-Ovchinnikov superconducting state has spontaneous modulation of Cooper pair density, while Fulde-Ferrell state has a spontaneous modulation in the phase of the order parameter. We report that a quasi-two-dimensional Dirac metal, under certain conditions has principally different inhomogeneous superconducting states that by contrast have spontaneous modulation in a submanifold of a multiple-symmetries-breaking order parameter. The first state we find can be viewed as a nematic superconductor where the nematicity vector spontaneously breaks rotational and translational symmetries due to spatial modulation. The other demonstrated state is a chiral superconductor with spontaneously broken time-reversal and translational symmetries. It is characterized by an order parameter, which forms a lattice pattern of alternating chiralities.
We present a study of the basic microscopic model of a s-wave superconductor with frustrated interbandinteraction. When frustration is strong, such an interaction gives raise to a s + is state. This is a s-wave superconductor that spontaneously breaks time reversal symmetry. We show that in addition to the known s + is state,there is additional phase where the system’s bulk is a conventional s-wave state, but superconducting surfacestates break time reversal symmetry. Furthermore, we show that s + is superconductors can have spontaneousboundary currents and spontaneous magnetic fields. These arise at lower-dimensional boundaries, namely, thecorners in two-dimensional samples. This demonstrates that boundary currents effects in superconductors canarise in states which are not topological and not chiral according to the modern classification.
Topological defects, such as magnetic-flux-carrying quantum vortices, determine the magnetic response of superconductors and hence are of fundamental importance. Here, we show that stable CP2 skyrmions exist in three-band s + is superconductors as fully self-consistent solutions to a microscopic Bogoliubov-de Gennes model. This allows us to calculate microscopically the magnetic signatures of CP2 skyrmions and their footprint in the local density of states.
Topological defects, such as magnetic-flux-carrying quantum vortices determine the magnetic response of superconductors and hence are of fundamental importance. Here, we show that stable CP2 skyrmions exist in three-band s+is superconductors as fully self-consistent solutions to a microscopic Bogoluibov-de Gennes model. This allows us to calculate microscopically the magnetic signatures of CP2 skyrmions and their footprint in the local density of states.
One of the defining features of spontaneously broken time-reversal symmetry (BTRS) is the existence of domain walls, the detection of which would be strong evidence for such systems. There is keen interest in BTRS currently, in part, due to recent muon spin rotation experiments, which have pointed towards Ba1-xKxFe2As2 exhibiting a remarkable case of s-wave superconductivity with spontaneously broken time-reversal symmetry. A key question, however, is how to differentiate between the different theoretical models which describe such a state. Two particularly popular choices of model are s + is and s + id superconducting states. In this paper, we obtain solutions for domain walls in s + is and s + id systems, including the effects of lattice anisotropies. We show that, in general, both models exhibit spontaneous magnetic fields that extend along the entire length of the domain wall. We demonstrate the qualitative difference between the magnetic signatures of s + is and s + id domain walls and propose a procedure to extract the superconducting pairing symmetry from the magnetic-field response of domain walls.
The knowledge of vortex nucleation barriers is crucial for applications of superconductors, such as single-photon detectors and superconductor-based qubits. Contrarily to the problem of finding energy minima and critical fields, there are no controllable methods to explore the energy landscape, identify saddle points, and compute associated barriers. Similar problems exist in high-energy physics where the saddle-point configurations are called sphalerons. Here, we present a generalization of the string method to gauge field theories, which allows the calculation of energy barriers in superconductors. We solve the problem of vortex nucleation, assessing the effects of the nonlinearity of the model, complicated geometry, surface roughness, and pinning.
We present a microscopic study of the behavior of the order parameters near the boundaries of a two-band superconducting material, described by the standard tight-binding Bardeen-Cooper-Schrieffer model. We find superconducting surface states. The relative difference between bulk and surface critical temperatures is a nontrivial function of the interband coupling strength. For superconductors with weak interband coupling, boundaries induce variations of the gaps with the presence of multiple length scales, despite nonzero interband Josephson coupling.
Superconductors usually display either type-I or type-II superconductivity and the coexistence of these two types in the same material, for example, at different temperatures, is rare in nature. We employed the muon spin rotation (mu SR) technique to unveil the superconducting phase diagram of the dodecaboride ZrB12 and obtained clear evidence of both type-I and type-II characteristics. Most important, we found a region showing unusual behavior where the usually mutually exclusive mu SR signatures of type-I and type-II superconductivity coexist. We reproduced that behavior in theoretical modeling that required taking into account multiple bands and multiple coherence lengths, which suggests that material has one coherence length larger and another smaller than the magnetic field penetration length (the type-1.5 regime). At stronger fields, a footprint of the type-II mixed state showing square flux-line lattice was also obtained using neutron diffraction.
We demonstrate microscopically the existence of a new superfluid state of matter in a three-component Bose mixture trapped in an optical lattice. The superfluid transport involving coflow of all three components is arrested in that state, while counterflows between any pair of components are dissipationless. The presence of three components allows for three different types of counterflows with only two independent superfluid degrees of freedom.
We demonstrate microscopically the existence of a new superfluid state of matter in a three-component Bose mixture trapped in an optical lattice. In that state, the superfluid transport involving co-flow of all three components is arrested, while counter-flows between any pair of components are dissipationless. Due to the presence of the third component, the types of counterpropagating components are allowed to fluctuate.
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.
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.
Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes in semiconductor nanowires proximity coupled to a superconductor. We track the evolution of the induced superconducting gap in InSb nanowires coupled to a NbTiN superconductor in a large range of magnetic field strengths and orientations. Based on realistic simulations of our devices, we reveal SOI with a strength of 0.15-0.35 eV angstrom. Our approach identifies the direction of the spin-orbit field, which is strongly affected by the superconductor geometry and electrostatic gates.
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.
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.
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.
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.