Vortices with fractional flux in two-gap superconductors and in extended faddeev model

Two-gap topological superconductor LaB2 with high Tc = 30 K

Since two gap superconductivity was discovered in MgB2, research on multigap superconductors has attracted increasing attention because of its intriguing fundamental physics. In MgB2, the Mg atom donates two electrons to the borophene layer, resulting in a stronger gap from the σ band and a weaker gap from the π bond. First-principles calculations demonstrate that the two gap anisotropic superconductivity strongly enhances the transition temperature of MgB2 in comparison with that given by the isotropic model. In this work, we report a three-band (B-σ, B-π, and La-d) two-gap superconductor LaB2 with very high Tc = 30 K by solving the fully anisotropic Migdal-Eliashberg equation. Because of the σ and π-d hybridization on the Fermi surface, the electron-phonon coupling constant λ = 1.5 is significantly larger than the λ = 0.7 of MgB2. Our work paves a new route to enhance the electron-phonon coupling strength of multigap superconductors with d orbitals. On the other hand, our analysis reveals that LaB2 belongs to the weak topological semimetal category, leading to a possible topological superconductor with the highest Tc to date. Moreover, upon applying pressure and/or doping, the topology is tunable between weak and strong with Tc varying from 15 to 30 K, opening up a flexible platform for manipulating topological superconductors.

Energy spectrum of the ideal DNA knot on a torus

In this study, we consider DNA as a torus knot that is formed by an elastic string. In order to determine what kinds of knot could be formed, we present its energy spectrum by combining Euler rotation, DNA's mechanical properties, and the modified Faddeev-Skyrme model. Our results theoretically demonstrated that the flexural rigidity of DNA plays an important role. If it is smaller than a critical value, DNA is likely to form a coiled structure. Conversely, above the critical value, DNA forms a twisting structure. The energy spectrum provides a way to identify the types of knots that are most likely to be created by DNA, according to the principle of energy minimisation, and with implications for its functional and packaging states in the cell nucleus.

Superconducting vortices carrying a temperature-dependent fraction of the flux quantum

Magnetic field penetrates type-II bulk superconductors by forming quantum vortices that enclose a magnetic flux equal to the magnetic flux quantum. The flux quantum is a universal quantity that depends only on fundamental constants. Here we investigate isolated vortices in the hole-overdoped Ba_1-xK_xFe₂As₂ (x = 0.77) by using scanning superconducting quantum interference device (SQUID) magnetometry. In many locations, we observed vortices that carried only part of a flux quantum, with a magnitude that varied continuously with temperature. We interpret these features as quantum vortices with non-universally quantized (fractional) magnetic flux whose magnitude is determined by the temperature-dependent parameters of a multiband superconductor. The demonstrated mobility and manipulability of the fractional vortices may enable applications in fluxonics-based computing.

Measurements of Surface Impedance in MgB2 in DC Magnetic Fields: Insights in Flux-Flow Resistivity

We present the multifrequency measurements of the surface resistance of spark-plasma-sintered MgB2 performed through a dielectric loaded resonator operating at 16.5 and 26.7 GHz. By normally applying magnetic fields ≤1.2 T to the sample surface, we drove it in the mixed state. By means of data-rooted analysis, we found that the sample vortex dynamics could be fully described within a single-component approach. Pinning phenomena were present and characterized by a depinning frequency smaller than the measurement ones. The multiband nature of the superconductor emerged in the flux-flow resistivity, whose field dependence could be interpreted well within theoretical models. By exploiting them, the upper critical field was extracted in the low-temperature range, which exhibited a consistent temperature trend with the values obtained at the onset of the resistive transition near Tc, and was well in line with literature data on other polycrystalline samples.

Multiband Superconductors: Two Characteristic Lengths for Each Contributing Condensate

The interference of multiple condensates coexisting in one system may lead to unconventional coherent behavior. This is expected when the spatial lengths of the condensates are essentially different. Traditionally, the characteristic spatial length of a superconducting condensate is associated with the gap function. However, the broader readership is more familiar with the concept of the Cooper-pair wave function. For conventional single-band superconductors, the gap function coincides with the center-of-mass Cooper-pair wave function up to the coupling constant, and the corresponding gap and wave function characteristic lengths are the same. Surprisingly, we find that in two-band superconductors, these lengths are the same only near the critical temperature. At lower temperatures, they can significantly deviate from each other, and the fundamental question of which of these lengths should be preferred when specifying the spatial scale of a band-dependent condensate in multiband superconducting materials arises.

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

Dimensional interpolation for metallic hydrogen

We employ a simple and mostly accurate dimensional interpolation formula using dimensional limits D = 1 and D = ∞ to obtain D = 3 ground-state energy of metallic hydrogen. We also present results describing the phase transitions for different symmetries of three-dimensional structure lattices. The interpolation formula not only predicts fairly accurate energies but also predicts a correct functional form of the energy as a function of the lattice parameters. That allows us to calculate different physical quantities such as the bulk modulus, Debye temperature, and critical transition temperature, from the gradient and the curvature of the energy curve as a function of the lattice parameters. These theoretical calculations suggest that metallic hydrogen is a likely candidate for high temperature superconductivity. The dimensional interpolation formula is robust and might be useful to obtain the energies of complex many-body systems.

Effects of paramagnetic pair-breaking and spin-orbital coupling on multi-band superconductivity

The BCS picture of superconductivity describes pairing between electrons originating from a single band. A generalization of this picture occurs in multi-band superconductors, where electrons from two or more bands contribute to superconductivity. The contributions of the different bands can result in an overall enhancement of the critical field and can lead to qualitative changes in the temperature dependence of the upper critical field when compared to the single-band case. While the role of orbital pair-breaking on the critical field of multi-band superconductors has been explored extensively, paramagnetic and spin-orbital scattering effects have received comparatively little attention. Here we investigate this problem using thin films of Nd-doped SrTiO3. We furthermore propose a model for analyzing the temperature-dependence of the critical field in the presence of orbital, paramagnetic and spin-orbital effects, and find a very good agreement with our data. Interestingly, we also observe a dramatic enhancement in the out-of-plane critical field to values well in excess of the Chandrasekhar-Clogston (Pauli) paramagnetic limit, which can be understood as a consequence of multi-band effects in the presence of spin-orbital scattering.

Single-gap superconductivity in Mo8Ga41

In this paper, the potential existence of two-gap superconductivity in Mo₈Ga₄₁ is addressed in detail by means of thermodynamic and spectroscopic measurements. A combination of highly sensitive bulk and surface probes, specifically ac-calorimetry and scanning tunneling spectroscopy (STS), are utilized on the same piece of crystal and reveal the presence of only one intrinsic gap in the system featuring strong electron-phonon coupling. Minute traces of additional superconducting phases detected by STS and also in the heat capacity measured in high magnetic fields on a high-quality and seemingly single-phase crystal might mimic the multigap superconductivity of Mo₈Ga₄₁ suggested recently in several studies.

Berezinskii-Kosterlitz-Thouless Transition of Two-Component Bose Mixtures with Intercomponent Josephson Coupling

We study the Berezinskii-Kosterlitz-Thouless (BKT) transition of two-component Bose mixtures in two spatial dimensions. When phases of both components are decoupled, half-quantized vortex-antivortex pairs of each component induce two-step BKT transitions. On the other hand, when phases of both components are synchronized through the intercomponent Josephson coupling, two species of vortices of each component are bound to form a molecule, and, in this case, we find that there is only one BKT transition by molecule-antimolecule pairs. Our results can be tested by two weakly connected Bose systems such as two-component ultracold diluted Bose mixtures with the Rabi oscillation, and multiband superconductors.

Knot soliton in DNA and geometric structure of its free-energy density

In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.

Nematic Skyrmions in Odd-Parity Superconductors

We study topological excitations in two-component nematic superconductors, with a particular focus on Cu_{x}Bi_{2}Se_{3} as a candidate material. We find that the lowest-energy topological excitations are coreless vortices: a bound state of two spatially separated half-quantum vortices. These objects are nematic Skyrmions, since they are characterized by an additional topological charge. The inter-Skyrmion forces are dipolar in this model, i.e., attractive for certain relative orientations of the Skyrmions, hence forming multi-Skyrmion bound states.

Glass Transitions in Monodisperse Cluster-Forming Ensembles: Vortex Matter in Type-1.5 Superconductors

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.

Ground state, collective mode, phase soliton and vortex in multiband superconductors

This article reviews theoretical and experimental work on the novel physics in multiband superconductors. Multiband superconductors are characterized by multiple superconducting energy gaps in different bands with interaction between Cooper pairs in these bands. The discovery of prominent multiband superconductors MgB2 and later iron-based superconductors, has triggered enormous interest in multiband superconductors. The most recently discovered superconductors exhibit multiband features. The multiband superconductors possess novel properties that are not shared with their single-band counterpart. Examples include: the time-reversal symmetry broken state in multiband superconductors with frustrated interband couplings; the collective oscillation of number of Cooper pairs between different bands, known as the Leggett mode; and the phase soliton and fractional vortex, which are the main focus of this review. This review presents a survey of a wide range of theoretical exploratory and experimental investigations of novel physics in multiband superconductors. A vast amount of information derived from these studies is shown to highlight unusual and unique properties of multiband superconductors and to reveal the challenges and opportunities in the research on the multiband superconductivity.

Crossover between integer and fractional vortex lattices in coherently coupled two-component Bose-Einstein condensates

We study the effects of the internal coherent (Rabi) coupling in vortex lattices in two-component BECs under rotation. We find how the vortex lattices without the Rabi coupling known before are connected to the Abrikosov lattice of integer vortices with increasing the Rabi coupling. We find that (1) for small Rabi couplings, fractional vortices in a triangular or square lattice for small or large intercomponent coupling constitute hexamers or tetramers, namely multidimer bound states made of six or four vortices, respectively, (2) these bound states are broken into a set of dimers at intermediate Rabi couplings, and (3) vortices change their partners in various ways depending on the intercomponent coupling, to organize themselves for constituting the Abrikosov lattice of integer vortices at strong Rabi couplings.

Dissociation transition of a composite lattice of magnetic vortices in the flux-flow regime of two-band superconductors

In multiband superconductors, each superconducting condensate supports vortices with fractional quantum flux. In the ground state, vortices in different bands are spatially bounded together to form a composite vortex, carrying one quantum flux Φ(0). Here we predict dissociation of the composite vortices lattice in the flux flow state due to the disparity of the vortex viscosity and flux of the vortex in different bands. For a small driving current, composite vortices start to deform, but the constituting vortices in different bands move with the same velocity. For a large current, composite vortices dissociate and vortices in different bands move with different velocities. The dissociation transition shows up as an increase of flux flow resistivity. In the dissociated phase, Shapiro steps are developed when an ac current is superimposed with a dc current.

Topological defect-phase soliton and the pairing symmetry of a two-band superconductor: role of the proximity effect

We suggest a mechanism which promotes the existence of a phase soliton--a topological defect formed in the relative phase of superconducting gaps of a two-band superconductor with s(+-) type of pairing. This mechanism exploits the proximity effect with a conventional s-wave superconductor which favors the alignment of the phases of the two-band superconductor which, in the case of s(+-) pairing, are π shifted in the absence of proximity. In the case of a strong proximity such an effect can be used to reduce the soliton's energy below the energy of a soliton-free state, thus making the soliton thermodynamically stable. Based on this observation we consider an experimental setup, applicable for both stable and metastable solitons, which can be used to distinguish between ss(+-) and s(++) types of pairing in the iron-based multiband superconductors.

Massless Leggett mode in three-band superconductors with time-reversal-symmetry breaking

The Leggett mode associated with out-of-phase oscillations of the superconducting phase in multiband superconductors usually is heavy due to interband coupling, which makes its excitation and detection difficult. We report on the existence of a massless Leggett mode in three-band superconductors with time-reversal-symmetry breaking. The mass of this Leggett mode is small close to the time-reversal-symmetry-breaking transition and vanishes at the transition point, and thus locates within the smallest superconducting energy gap, which makes it stable and detectable, e.g., by means of the Raman spectroscopy. The thermodynamic consequences of this massless mode and possible realization in iron-based superconductors are also discussed.

Topological solitons in three-band superconductors with broken time reversal symmetry

We show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topological solitons. They can be induced by fluctuations or quenching the system through a phase transition. It can provide an experimental signature of the time reversal symmetry breakdown.

Magnetic field delocalization and flux inversion in fractional vortices in two-component superconductors

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) x U(1) Ginzburg-Landau model, the magnetic field of a generic fractional vortex inverts its direction at a certain distance from the vortex core.

Unconventional rotational responses of hadronic superfluids in a neutron star caused by strong entrainment and a Sigma- hyperon gap

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.

Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov vortex state of spin-singlet superconductors

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a nontrivial solution for the FFLO vortex phase that exists near the upper critical field in which the wave function has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of nonparallel line nodes. We show that these solutions arise from the decay of conventional Abrikosov vortices into pairs of fractional vortices. We propose that neutron scattering studies can observe these fractional vortex pairs through the observation of a lattice of 1/2 flux quanta vortices. We also consider related phases in noncentrosymmetric superconductors.

Stability of half-quantum vortices in p(x)+ip(y) superconductors

We consider the stability conditions for half-quantum vortices in a quasi-two-dimensional p{x}+ip{y} superconductor (such as Sr2RuO4 is believed to be). The predicted exotic nature of these excitations has recently attracted much attention, but they have not been observed yet. We emphasize that an isolated half-quantum vortex has a divergent energy cost in the bulk due to its unscreened spin current, which requires two half-quantum vortices with opposite spin winding to pair. We show that the stability of such a pair is enhanced when the ratio of spin superfluid density to superfluid density rho{sp}/rho{s} is small. We propose using various mesoscopic geometries to stabilize and observe these exotic excitations.

First-order phase transition in easy-plane quantum antiferromagnets

Quantum phase transitions in Mott insulators do not fit easily into the Landau-Ginzburg-Wilson paradigm. A recently proposed alternative to it is the so-called deconfined quantum criticality scenario, providing a new paradigm for quantum phase transitions. In this context it has recently been proposed that a second-order phase transition would occur in a two-dimensional spin 1/2 quantum antiferromagnet in the deep easy-plane limit. A check of this conjecture is important for understanding the phase structure of Mott insulators. To this end we have performed large-scale Monte Carlo simulations on an effective gauge theory for this system, including a Berry-phase term that projects out the S=1/2 sector. The result is a first-order phase transition, thus contradicting the conjecture.

Magnetic response of mesoscopic superconducting rings with two order parameters

The magnetic response and fluxoid transitions of superconducting aluminum rings of various sizes, deposited under conditions likely to generate a layered structure, show good agreement with a two-order-parameter Ginzburg-Landau model. For intermediate couplings, we find metastable states that have different phase winding numbers around the ring in each of the two order parameters. Those states, previously theoretically predicted, are analogous to fractional vortices in singly connected samples with two-order-parameter superconductivity. Larger coupling locks the relative phase so that the two order parameters are only manifest in the temperature dependence of the response. With increasing proximitization, this signature gradually disappears.

Phase textures induced by dc-current pair breaking in weakly coupled multilayer structures and two-gap superconductors

We predict the current-induced formation of equilibrium phase textures for a multicomponent superconducting order parameter. Using the two-component Ginzburg-Landau and Usadel equations, we show that, for weakly coupled comoving superconducting condensates, the dc current I first causes the breakdown of the phase-locked state at I>I{c1} followed by the formation of intrinsic phase textures well below the depairing current I{d}. These phase textures can manifest themselves in multilayer structures, atomic Bose condensate mixtures in optical lattices, and two-gap superconductors, particularly MgB(2), where they can result in oscillating and resistive switching effects.

Large anisotropic normal-state magnetoresistance in clean MgB2 thin films

We report a large normal-state magnetoresistance with temperature-dependent anisotropy in very clean epitaxial MgB2 thin films (residual resistivity much smaller than 1 microOmega cm) grown by hybrid physical-chemical vapor deposition. The magnetoresistance shows a complex dependence on the orientation of the applied magnetic field, with a large magnetoresistance (Delta(rho)/(rho)0=136%) observed for the field H perpendicular ab plane. The angular dependence changes dramatically as the temperature is increased, and at high temperatures the magnetoresistance maximum changes to H||ab. We attribute the large magnetoresistance and the evolution of its angular dependence with temperature to the multiple bands with different Fermi surface topology in MgB2 and the relative scattering rates of the sigma and pi bands, which vary with temperature due to stronger electron-phonon coupling for the sigma bands.

Field dependence of the vortex core size in a multiband superconductor

The magnetic field dependence of the vortex core size in the multiband superconductor NbSe2 has been determined from muon spin rotation measurements. The spatially extended nature of the quasiparticle core states associated with the smaller gap leads to a rapid field-induced shrinkage of the core size at low fields, while the more tightly bound nature of the states associated with the larger gap leads to a field-independent core size for fields greater than 4 kOe. A simple model is proposed for the density of delocalized core states that establishes a direct relationship between the field-induced reduction of the vortex core size and the corresponding enhancement of the electronic thermal conductivity. We show that this model accurately describes both NbSe2 and the single-band superconductor V3Si.

Observation of a metallic superfluid in a numerical experiment

We report the observation, in Monte Carlo simulations, of a novel type of quantum ordered state: the metallic superfluid. The metallic superfluid features Ohmic resistance to counterflows of protons and electrons, while featuring dissipationless coflows of electrons and protons. One of the candidates for a physical realization of this remarkable state of matter is hydrogen or its isotopes under high compression. This adds another potential candidate to the presently known quantum dissipationless states, namely, superconductors, superfluid liquids and vapors, and supersolids.

Observability of a projected new state of matter: a metallic superfluid

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.

Dissociation of vortex stacks into fractional-flux vortices

We discuss the zero field superconducting phase transition in a finite system of magnetically coupled superconducting layers. Transverse screening is modified by the presence of other layers resulting in topological excitations with fractional flux. Vortex stacks trapping a full flux and present at any finite temperature undergo a dissociation transition which corresponds to the depairing of fractional-flux vortices in individual layers. We propose an experiment with a bilayer system allowing us to identify the dissociation of bound vortex molecules.

Vortex sublattice melting in a two-component superconductor

We consider the vortices in a superconductor with two individually conserved condensates in a finite magnetic field. The ground state is a lattice of cocentered vortices in both order parameters. We find two phase transitions: (i) a "vortex sublattice melting" transition where vortices in the field with lowest phase stiffness ("light vortices") lose cocentricity with the vortices with large phase stiffness ("heavy vortices"), entering a liquid state (the structure factor of the light vortices vanishes continuously; this transition is in the 3Dxy universality class); (ii) a first-order melting transition of the lattice of heavy vortices, in a liquid of light vortices.

A superconductor to superfluid phase transition in liquid metallic hydrogen

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, including spatial order. To date, the structure of dense hydrogen remains experimentally elusive. Recent studies of the melting curve of hydrogen 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.

Critical properties of the N-color london model

The critical properties of the N-color London model are studied in d=2+1 dimensions. The model is dualized to a theory of N vortex fields interacting through a Coulomb and a screened potential. The model with N=2 shows two anomalies in the specific heat. From the critical exponents alpha and nu, the mass of the gauge field, and the vortex correlation functions, we conclude that one anomaly corresponds to an inverted 3Dxy fixed point, while the other corresponds to a 3Dxy fixed point. There are N fixed points, namely, one corresponding to an inverted 3Dxy fixed point, and N-1 corresponding to neutral 3Dxy fixed points. This represents a novel type of quantum fluid, where superfluid modes arise out of charged condensates.