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Our results enable a better understanding and explanation of the physical phenomena associated with strong trapping of vortex lattice in superconducting wires. These measurements showed that dislocations oriented perpendicular to the external magnetic field most strongly trapped the vortex lattice in 8 T and much weaker in the 6 T magnetic field. Further research showed that dislocations situated in the angle of 45° to the external magnetic field most strongly trap the vortexes lattice in 7 T magnetic field. Subsequent results showed that dislocations oriented parallel to the external magnetic field trap the vortex lattice most strongly in the 6 T magnetic field and much weaker in the 8 T magnetic field. Previous studies have not reported these results and pinning analyses. Our results are also important for pinning centers created by irradiation for columnar defects. [ABSTRACT FROM AUTHOR]

In the framework of the London model, computer modeling has been carried out and the distribution of the magnetic field in a massive superconductor of the II kind has been found, taking into account changes in the inhomogeneity of the magnetic field of an irregular vortex lattice. It is shown that the line shape changes significantly depending on the vortex lattice irregularity. This change should be taken into account when interpreting experimental data on the observation of the local magnetic field, the consideration of this circumstance can change the conclusions concerning the type of vortex lattice and the parameters of the superconductor. [ABSTRACT FROM AUTHOR]

We investigate the vortex lattice configuration in a rotating spin orbit-coupled spin-2 Bose–Einstein condensate confined in a quasi-two-dimensional harmonic trap. By considering the interplay between rotation frequency, spin–orbit couplings, and interatomic interactions, we explore a variety of vortex lattice structures emerging as a ground state solution. Our study focuses on the combined effects of spin–orbit coupling and rotation, analyzed by using the variational method for the single-particle Hamiltonian. We observe that the interplay between rotation and Rashba spin–orbit coupling gives rise to different effective potentials for the bosons. Specifically, at higher rotation frequencies, isotropic spin–orbit coupling leads to an effective toroidal potential, while fully anisotropic spin–orbit coupling results in a symmetric double-well potential. To obtain these findings, we solve the five coupled Gross–Pitaevskii equations for the spin-2 BEC with spin–orbit coupling under rotation. Notably, we find that the antiferromagnetic, cyclic, and ferromagnetic phases exhibit similar behavior at higher rotation. [ABSTRACT FROM AUTHOR]

One of the main issues concerning the standard Vortex Lattice Method is its application to partially or fully detached flow conditions, where non-linear aerodynamic characteristics appear as the angle of attack increases and/or the aspect ratio decreases. In order to solve such limitations, a pure numerical approach based entirely on the Vortex Lattice Method concepts has been developed. The so-called steady "Full Multi-wake Vortex Lattice Method" comes from the main hypothesis that each discretized element on the body's surface detaches their own wakes downstream. The obtained results match for lift, drag and moment coefficients for the entire aspect ratio range configurations (under straight wakes and inviscid assumptions). Future unsteady versions of such a multi-wake approach could improve the current results obtained through Vortex Element Methods (as vortons or isolated vortex filaments). [ABSTRACT FROM AUTHOR]

Following some prehistory, we discuss the steps leading to the Abrikosov vortex lattice and type-II superconductivity. Dissipation due to flux flow and flux creep represented an important discovery and leads to the strong interest in magnetic flux pinning. High-temperature superconductors and pancake vortices started the new concepts of vortex matter. Nonlinear effects at high vortex velocities, flux-flow instabilities, and some resulting open questions are discussed. [ABSTRACT FROM AUTHOR]

In the framework of the London model, a computer simulation has been performed and the magnetic field distribution in a thin film of type II superconductor has been found, taking into account changes in the magnetic field inhomogeneity of the irregular vortex lattice. It is shown that the line shape changes significantly depending on the vortex lattice irregularity. This change should be taken into account when interpreting the experimental data on the observation of the local magnetic field; consideration of this circumstance can change the conclusions regarding the type of vortex lattice and the parameters of the superconductor. [ABSTRACT FROM AUTHOR]

A hallmark of unconventional superconductors is a complex electronic phase diagram where intertwined orders of charge-spin-lattice degrees of freedom compete and coexist. While the kagome metals such as CsV3Sb5 also exhibit complex behavior, involving coexisting charge density wave order and superconductivity, much is unclear about the microscopic origin of the superconducting pairing. We study the vortex lattice in the superconducting state of Cs(V0.86Ta0.14)3Sb5, where the Ta-doping suppresses charge order and enhances superconductivity. Using small-angle neutron scattering, a strictly bulk probe, we show that the vortex lattice exhibits a strikingly conventional behavior. This includes a triangular symmetry with a period consistent with 2e-pairing, a field dependent scattering intensity that follows a London model, and a temperature dependence consistent with a uniform superconducting gap. Our results suggest that optimal bulk superconductivity in Cs(V1−xTax)3Sb5 arises from a conventional Bardeen-Cooper-Schrieffer electron-lattice coupling, different from spin fluctuation mediated unconventional copper- and iron-based superconductors. The mechanism of superconductivity in layered kagome metals remains unclear, however its coexistence with charge order suggests exotic interpretations. Here the authors study the vortex lattice in the superconducting state of Ta-doped CsV3Sb5 with suppressed charge order, suggesting conventional pairing. [ABSTRACT FROM AUTHOR]

The Monte Carlo method was used in a 2D model of layered HTSC to explore the dynamics of a vortex lattice in the presence of a nonuniform temperature field. Vortex configurations in a superconductor with a "thermal spot" have been found. The characteristic size of the region in which melting of the vortex lattice is observed is shown to exceed the characteristic size of the thermal spot. The possibility of directional movement of vortices by means of a temperature gradient is demonstrated in a numerical calculation. [ABSTRACT FROM AUTHOR]

We investigate the thermodynamics of two-flavor quark matter in presence of nonzero isospin chemical potential and external magnetic field. It is known that at sufficiently high isospin chemical potential, charged pions undergo Bose–Einstein condensation (BEC). The condensate behaves as a superconductor, exhibiting Meissner effect in weak external magnetic fields. Stronger fields stress the superconducting state, turning it first into an Abrikosov lattice of vortices, and eventually destroying the condensate altogether. On the other hand, for sufficiently strong magnetic fields and low-to-moderate isospin chemical potential, the ground state of quantum chromodynamics (QCD) is expected to be a spatially modulated condensate of neutral pions, induced by the chiral anomaly: the chiral soliton lattice (CSL). We map the phase diagram of QCD as a function of isospin chemical potential and magnetic field in the part of the parameter space accessible to a low-energy effective field theory description of QCD. Our main result is an explicit account of the competition between the CSL and the Abrikosov vortex lattice. This is accomplished by adopting a fast numerical algorithm for finding the vortex lattice solution of the equation of motion and the corresponding Gibbs energy. We find that the Abrikosov vortex lattice phase persists in the phase diagram, separating the uniform charged pion BEC phase from the CSL phase. The precise layout of the phase diagram depends sensitively on the choice of the vacuum pion mass. [ABSTRACT FROM AUTHOR]

The present hybrid vortex tube-vorton method is based entirely on the Full Multi-wake Vortex Lattice Method (FMVLM) concepts, which means detaching vorticity with precise vortex strength and orientation along all separation lines between each discretized element of a shell-body, including all external edges. Since the classic Vortex Particle Method (VPM) is unstable by itself because it does not conserve the total amount of circulation as time evolves (Kelvin's circulation theorem), an isolated Vortex (regularized) Filament Method (VFM) approach is implemented to obtain advection of vorticity, while the induced velocity field is obtained through its corresponding full vorton cloud. Further, a novel vortex squeezing/stretching scheme for such a vortex cylinder-sphere approach is proposed based on variation in time for vortex volumes in order to precisely (zero residual) conserve both circulation and vorticity at each time step (for each detached vortex element), while the viscous effect can be accounted for via the Core Spreading Method (CSM). [ABSTRACT FROM AUTHOR]

Time-dependent equations of the two-band Ginzburg-Landau model are simulated numerically. Calculations are performed for square thin films of the LiFeAs two-band superconductor in the vicinity of the superconducting transition temperature in the transverse magnetic field; the quasi-hexagonal nature of the vortex lattice in the intermediate state is demonstrated. [ABSTRACT FROM AUTHOR]

Many superconducting materials are composed of weakly coupled conducting layers. Such a layered structure has a very strong influence on the properties of vortex matter in a magnetic field. This review focuses on the properties of the Josephson vortex lattice generated by the magnetic field applied in the direction of the layers. The theoretical description is based on the Lawrence-Doniach model in the London limit, which takes only the phase degree of freedom of the superconducting order parameter into account. In spite of its simplicity, this model leads to an amazingly rich set of phenomena. We review in detail the structure of an isolated vortex line and various properties of the vortex lattice, in both dilute and dense limits. In particular, we extensively discuss the influence of the layered structure and thermal fluctuations on the selection of lattice configurations at different magnetic fields. [ABSTRACT FROM AUTHOR]

Evolution of the excess conductivity in optimally doped YBa 2 Cu 3 O 7 - δ single crystals is investigated after their irradiation with fast electrons at T ≲ 10 K at energies of 0.5–2.5 MeV and a dose of 3 × 10 18 cm - 2 . The measurements were performed in a magnetic field of 15 kOe applied at various angles with respect to the basal plane of the crystals. The temperature dependences of the paraconductivity were analyzed within the framework of the Aslamazov–Larkin theoretical model of fluctuation conductivity and revealed two major effects of the electron irradiation. Namely, (i) the vortex-lattice-melting kinks in the resistivity temperature dependences vanish after electron irradiation and (ii) the resistivity data in the irradiated state allow for a Kouvel-Fisher-type scaling pointing to the presence of a irradiation-induced vortex Bragg-glass phase. These effects are discussed in terms of a competition between intrinsic pinning due to point defects and volume pinning induced by electron irradiation. In all, our findings are relevant for YBCO-based circuitry which is exposed to fast electrons in moderately strong magnetic fields. [ABSTRACT FROM AUTHOR]

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. [ABSTRACT FROM AUTHOR]

We introduce a 'Coulombian renormalized energy' W which is a logarithmic type of interaction between points in the plane, computed by a 'renormalization.' We prove various of its properties, such as the existence of minimizers, and show in particular, using results from number theory, that among lattice configurations the triangular lattice is the unique minimizer. Its minimization in general remains open. Our motivation is the study of minimizers of the two-dimensional Ginzburg-Landau energy with applied magnetic field, between the first and second critical fields H and H. In that regime, minimizing configurations exhibit densely packed triangular vortex lattices, called Abrikosov lattices. We derive, in some asymptotic regime, W as a Γ-limit of the Ginzburg-Landau energy. More precisely we show that the vortices of minimizers of Ginzburg-Landau, blown-up at a suitable scale, converge to minimizers of W, thus providing a first rigorous hint at the Abrikosov lattice. This is a next order effect compared to the mean-field type results we previously established. The derivation of W uses energy methods: the framework of Γ-convergence, and an abstract scheme for obtaining lower bounds for '2-scale energies' via the ergodic theorem, that we introduce. [ABSTRACT FROM AUTHOR]

We investigate vortex lattice solutions in a holographic superconductor model in asymptotically AdS4 spacetime which includes the gravitational backreaction of the vortex. The circular cell approximation, which is known to give a good result for several physical quantities in the Ginzburg-Landau model, is used. The critical magnetic fields and the magnetization curve are computed. The vortex lattice profiles are compared to expectations from the Abrikosov solution in the regime nearby the upper critical magnetic field H2c for which superconductivity is lost. [ABSTRACT FROM AUTHOR]

Penetration of a vorticity lattice formed by waves propagating on the surface at an angle to each other into the bulk of a liquid is studied experimentally. It is shown that along with the Stokes drift it is necessary to regard nonlinear wave interaction in order to explain experimental time dependences of average vorticity. Vorticity distribution over the depth of a liquid is described by a sum of two exponents considering the contribution of both mechanisms. It is determined that formation of large-scale vortex flows leads to deformation of a vortex lattice and a decrease in an average value of the amplitude of lattice vorticity as a result of its drift. [ABSTRACT FROM AUTHOR]

We show that the Landau vortex-free state in rotating container may give rise to the lattice of spin vortices. We consider this effect on example of spin vortices in magnon Bose-Einstein condensate (the phase coherent spin precession) in the B-phase of superfluid 3He, and on example of spin vortices in the polar phase of 3He. [ABSTRACT FROM AUTHOR]

This work reports magnetic field direction dependent second magnetisation peak (SMP) anomaly in single crystals of oxygenated for ab. Detailed investigations on crystal A revealed the direction dependence of SMP anomaly at temperatures below 25 K, above which the direction dependence vanishes. The state of spatial order of the vortex lattice was found to be correlated to the vortex lattice symmetry that underwent a change at certain fields and was captured via single flux jumps observed in the third and fifth quadrant of magnetisation hysteresis loops. Bean's critical state profiles drawn to explain the flux jumps required the presence of clusters of in the basal plane of with closely lying binding energies. Large full width at half maximum observed in Cu, O, Y and Ba photoelectron spectra confirmed the validity of the proposed cluster model. A vortex phase diagram incorporating all features in the magnetisation hysteresis loops has been made for oxygenated for || ab depicting various phases. [ABSTRACT FROM AUTHOR]

Ratchet devices allow turning an ac input signal into a dc output signal. A ratchet device is set by moving particles driven by zero averages forces on asymmetric potentials. Hybrid nanostructures combining artificially fabricated spin ice nanomagnet arrays with superconducting films have been identified as a good choice to develop ratchet nanodevices. In the current device, the asymmetric potentials are provided by charged Néel walls located in the vertices of spin ice magnetic honeycomb array, whereas the role of moving particles is played by superconducting vortices. We have experimentally obtained ratchet effect for different spin ice I configurations and for vortex lattice moving parallel or perpendicular to magnetic easy axes. Remarkably, the ratchet magnitudes are similar in all the experimental runs; i. e. different spin ice I configurations and in both relevant directions of the vortex lattice motion. We have simulated the interplay between vortex motion directions and a single asymmetric potential. It turns out vortices interact with uneven asymmetric potentials, since they move with trajectories crossing charged Néel walls with different orientations. Moreover, we have found out the asymmetric pair potentials which generate the local ratchet effect. In this rocking ratchet the particles (vortices) on the move are interacting each other (vortex lattice); therefore, the ratchet local effect turns into a global macroscopic effect. In summary, this ratchet device benefits from interacting particles moving in robust and topological protected type I spin ice landscapes. [ABSTRACT FROM AUTHOR]

Electric vertical take-off and landing (eVTOL) aircraft with multiple lifting rotors or prop-rotors have received significant attention in recent years due to their great potential for next-generation urban air mobility (UAM). Numerical models have been developed and validated as predictive tools to analyze rotor aerodynamics and wake dynamics. Among various numerical approaches, the vortex method is one of the most suitable because it can provide accurate solutions with an affordable computational cost and can represent vorticity fields downstream without numerical dissipation error. This paper presents a brief review of the progress of vortex methods, along with their principles, advantages, and shortcomings. Applications of the vortex methods for modeling the rotor aerodynamics and wake dynamics are also described. However, the vortex methods suffer from the problem that it cannot deal with the nonlinear aerodynamic characteristics associated with the viscous effects and the flow behaviors in the post-stall regime. To overcome the intrinsic drawbacks of the vortex methods, recent progress in a numerical method proposed by the authors is introduced, and model validation against experimental data is discussed in detail. The validation works show that nonlinear vortex lattice method (NVLM) coupled with vortex particle method (VPM) can predict the unsteady aerodynamic forces and complex evolution of the rotor wake. [ABSTRACT FROM AUTHOR]

It is well known that the interaction between defect-induced strain field and vortex lattice (VL) gives rise to vortex pinning behaviors. Likewise, magneto-elastic (ME) interaction is caused by the difference between specific volumes of normal phase and superconducting (SC) phase. Acting as inhomogeneous strain sources, the normal-state vortex cores produce local deformation in the surrounding SC matter and thus affect VL energy. ME interaction belongs to the fundamental physics of interdependences between vortex matter and crystal lattice. The review starts with the effects of ME interaction on magnetization, vortex morphology and intervortex interaction. In Sect. 2, theoretical descriptions of ME interaction are classified in terms of different simplifications. The core ideas and outstanding results of these theories are given. It is followed by Sect. 3, where the correlation and difference between ME and pinning interaction are outlined. Although pinning differs from ME interaction in their formation mechanisms, the pinning interaction is established upon the vortex-induced strain field from Ginzburg-Landau (GL) viewpoint. Section 4 goes further with the GL treatment for solving ME and pinning problem; the general thoughts and steps can be found in this section. The last section gives some outlooks which involve pressure dependence of Tc and anisotropy. [ABSTRACT FROM AUTHOR]

Recent experiments have shown that the complex spatio-temporal vortex structures emerging in active fluids are susceptible to weak geometrical constraints. This observation poses the fundamental question of how boundary effects stabilize a highly ordered pattern from seemingly turbulent motion. Here we show, by a combination of continuum theory and experiments on a bacterial suspension, how artificial obstacles guide the flow profile and reorganize topological defects, which enables the design of bacterial vortex lattices with tunable properties. To this end, the continuum model is extended by appropriate boundary conditions. Beyond the stabilization of square and hexagonal lattices, we also provide a striking example of a chiral, antiferromagnetic lattice exhibiting a net rotational flow, which is induced by arranging the obstacles in a Kagome-like array. Recent experiments showed that weak geometrical constraints can organize topological defects in turbulent bacterial suspensions. Here, the authors use a continuum model to study the connection between symmetry and stability of emergent vortex patterns and the geometry of constraining pillar arrays. [ABSTRACT FROM AUTHOR]

Long-range correlations in two-dimensional (2D) systems are significantly altered by disorder potentials. Theory has predicted the existence of disorder-induced phenomena, such as Anderson localization or the emergence of a Bose glass. More recently, it has been shown that when disorder breaks 2D continuous symmetry, long-range correlations can be enhanced. Experimentally, developments in quantum gases have allowed the observation of the effects of competition between interaction and disorder. However, experiments exploring the effect of symmetry-breaking disorder are lacking. Here, we create a 2D vortex lattice at 0.1 K in a superconducting thin film with a well-defined 1D thickness modulation-the symmetry-breaking disorder-and track the field-induced modification using scanning tunnelling microscopy. We find that the 1D modulation becomes incommensurate with the vortex lattice and drives an order-disorder transition, behaving as a scale-invariant disorder potential. We show that the transition occurs in two steps and is mediated by the proliferation of topological defects. The resulting critical exponents determining the loss of positional and orientational order are far above theoretical expectations for scale-invariant disorder and follow instead the critical behaviour describing dislocation unbinding melting. Our data show that randomness disorders a 2D crystal, with enhanced long-range correlations due to the presence of a 1D modulation. [ABSTRACT FROM AUTHOR]

It has been predicted that superconducting vortices should be electrically charged and that this effect is particularly enhanced for high-temperature superconductors. Hall effect and nuclear magnetic resonance (NMR) experiments suggest the existence of charge accumulation in the vortex core, but the effects are small and the interpretation controversial. Here we show that the Abrikosov vortex lattice, characteristic of the mixed state of superconductors, will become unstable at a sufficiently high magnetic field if there is charge trapped on the vortex core. Our NMR measurements of the magnetic fields generated by vortices in Bi2Sr2CaCu2O8+y single crystals provide evidence for an electrostatically driven vortex lattice reconstruction with the magnitude of charge on each vortex pancake of ∼2×10−3e, depending on doping, in line with theoretical estimates. [ABSTRACT FROM AUTHOR]

Abstract   We study vortex lattice structures of a trapped Bose-Einstein condensate in a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. By rotating the lattice potential, we observe the transition from the Abrikosov vortex lattice to the pinned vortex lattice. We investigate the transition of the vortex lattice structure by changing conditions such as angular velocity, strength, and lattice constant of the rotating lattice potential. [ABSTRACT FROM AUTHOR]

Aircraft design has become increasingly complex since it depends on technological advances and integration between modern engineering systems. These systems are multidisciplinary, i.e., any process or division of any aircraft design produces effects in all others, making the definition of each parameter a significant challenge. In this context, this work presents a general multidisciplinary design optimization method for the conceptual design of general aviation and hybrid-electric aircraft. The framework uses efficient computational methods comprising modules of engineering that include aerodynamics, flight mechanics, structures, and performance, and the integration of all of them. The aerodynamic package relies on a Nonlinear Vortex Lattice Method solver, while the flight mechanics package is based on an analytical procedure with minimal dependence on historical data. Moreover, the structural module adopts an analytical sizing approach using boom idealization, and the performance of the aircraft is computed based on energy and power required to accomplish a specific mission. The objective functions are to minimize the fuel consumption and to minimize the takeoff weight. The Pareto-optimal front encompasses aircraft with different propulsive architectures: turboelectric, hybrid electric, and fully electric. The degrees of hybridization defined by the optimization and the mission requirements chosen in this study directly affect the final weight breakdown of the aircraft, which is related to the sizing of the wings, propulsive system, and horizontal and vertical tails. [ABSTRACT FROM AUTHOR]

The equilibrium shape and the orientation of the vortex lattice are studied for an s-wave tetrahedral superconductor in the vicinity of the upper critical field. The phase diagram, which includes transitions between rhombic and rectangular lattices, is constructed in the parameter space of the Ginzburg-Landau functional. The developed theory is applied to the heavy-fermion superconductor PrOs4Sb12. In a wide range of parameters, the shape of the vortex lattice is only weakly dependent on the temperature. The neutron scattering measurements of the vortex lattice in PrOs4Sb12 can be explained by particularities of the tetrahedral symmetry group and are further supported by analysis of the appropriate band structure calculations. [ABSTRACT FROM AUTHOR]

We studied the commensurate semifluxon oscillations of Josephson flux-flow in Bi-2212 stacked structures near Tc as a probe of melting of a Josephson vortex lattice. We found that oscillations exist above 0.5 T. The amplitude of the oscillations is found to decrease gradually with the temperature and to turn to zero without any jump at T = T0 (3.5 K below the resistive transition temperature Tc), thus, indicating a phase transition of the second order. This characteristic temperature T0 is identified as the Berezinskii–Kosterlitz–Thouless (BKT) transition temperature, TBKT, in the elementary superconducting layers of Bi-2212 at zero magnetic field. On the basis of these facts, we infer that melting of a triangular Josephson vortex lattice occurs via the BKT phase with formation of characteristic flux loops containing pancake vortices and antivortices. The B–T phase diagram of the BKT phase found from our experiment is consistent with theoretical predictions. © 2005 Pleiades Publishing, Inc. [ABSTRACT FROM AUTHOR]

Focuses on a study which analyzed the complex impedance measurements in an untwinned YBaCuO crystal. Ways to measure the dynamic response of a vortex lattice; Description of the untwinned crystal used in the study; Main features of the linear response of a vortex lattice.

Nb films have been fabricated on top of array of Ni nanodots. The array of periodic pinning potentials modifies the vortex lattice for specific values of the external applied magnetic field. By means of an implemented code developed from scratch, computer simulations based only on the vortex-vortex and the vortex-nanodot interactions provide the total interaction between vortices and pinning sites as well as the position of the vortices in the array unit cell. This simulation approach could be performed on square, rectangular or triangular arrays of nanodefects of different size. [ABSTRACT FROM AUTHOR]

Collective elastic oscillations of a lattice of nonabelian quark semisuperfluid vortex filaments in the superfluid core of a rotating neutron star are examined. It is shown that in the incompressible fluid approximation, transverse long wavelength oscillations (Tkachenko oscillations) owing to shear deformation of the vortex lattice propagate in a plane perpendicular to the axis of rotation. The periods of these oscillations are consistent with rotational variations on the order of 100-1000 days observed in the pulsars PSR B0531+21 and PSR B1828-11. [ABSTRACT FROM AUTHOR]

Abstract   We study dynamics of quantized vortex lattice formation in a rotating Bose-Einstein condensate with a square blue-detuned optical lattice by solving the Gross-Pitaevskii equation. This dynamics depends on the depth of the optical lattice. Vortices tend to form a triangular lattice under the rotation, while an optical lattice likes to pin vortices at their peaks. Such a competition of two effects makes this system more interesting and complicated. [ABSTRACT FROM AUTHOR]

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas. [ABSTRACT FROM AUTHOR]

The nuclear magnetic resonance line shapes within a primitive cell of the vortex lattice of the type II anisotropic superconductors in a case when a vortex is displaced on small distance a from a regular position in a primitive cell are constructed. The results of the numerical calculations show that displacement of the flux line lattice essentially changes the NMR lineshape. The derivative of the power of the absorption energy with respect to the magnetic field is calculated. It allows to obtain more detailed information about the real vortex lattice of a superconductor. [ABSTRACT FROM AUTHOR]

The structure of the vortex lattice in anisotropic superconductors at an arbitrary temperature in magnetic fields close to critical was studied. Generally, a rhombohedral structure with a vertex angle depending on temperature, magnetic field, and material constants is formed. An important factor is the small (2%) difference of the free energies of the triangular and square lattices in the Ginzburg–Landau approximation. This factor also persists in anisotropic superconductors. © 2001 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

Experiments with the crossover superconductors between standard types I and II revealed exotic magnetic flux patterns where Meissner domains coexist with islands of the vortex lattice as well as with vortex clusters and chains. Until now a comprehensive theory for such configurations has not been presented. We solve this old-standing fundamental problem by developing an approach which combines the perturbation expansion of the microscopic theory with statistical simulations and which requires no prior assumption on the vortex distribution. Our study offers the most complete picture of the interchange of the superconductivity types available so far. The mixed state in this regime reveals a rich manifold of exotic configurations, which reproduce available experimental results. Our work introduces a pattern formation mechanism that originates from the self-duality of the theory that is universal and not sensitive to the microscopic details. Classification into type I and II reflects different responses of a superconductor to an applied magnetic field, however, there are intertype materials with unique properties and atypical vortex configurations. The authors study vortex patterns in this regime revealing that their properties are governed by a universal material independent mechanism, which amends the dual classification. [ABSTRACT FROM AUTHOR]

The vortex lattice in a Type II superconductor provides a versatile model system to investigate the order-disorder transition in a periodic medium in the presence of random pinning. Here, using scanning tunnelling spectroscopy in a weakly pinned Co0.0075NbSe2 single crystal, we show that the vortex lattice in a 3-dimensional superconductor disorders through successive destruction of positional and orientational order, as the magnetic field is increased across the peak effect. At the onset of the peak effect, the equilibrium quasi-long range ordered state transforms into an orientational glass through the proliferation of dislocations. At a higher field, the dislocations dissociate into isolated disclination giving rise to an amorphous vortex glass. We also show the existence of a variety of additional non-equilibrium metastable states, which can be accessed through different thermomagnetic cycling. [ABSTRACT FROM AUTHOR]

We study the dynamics of a rotating trapped Bose-Einstein condensate (BEC) at finite temperatures. Using the Zaremba-Nikuni-Griffin formalism, based on a generalized Gross-Pitaevskii equation for the condensate coupled to a semiclassical kinetic equation for a thermal cloud, we numerically simulate vortex lattice formation in the presence of a time-dependent rotating trap potential. At low rotation frequency, the thermal cloud undergoes rigid body rotation, while the condensate exhibits irrotational flow. Above a certain threshold rotation frequency, vortices penetrate into the condensate and form a vortex lattice. Our simulation result clearly indicates a crucial role for the thermal cloud, which triggers vortex lattice formation in the rotating BEC. [ABSTRACT FROM AUTHOR]

This report describes symmetry properties of tetragonal vortex lattice solutions of the Bogoliubov–de Gennes equation in a two-dimensional square lattice in a uniform magnetic field. The invariance group of a tetragonal vortex lattice solution is expressed in a form of G( l) = ( e + tC2 x) $$\widetilde C_4^l L$$ ( l = 0, 2, ± 1), where tC2 x is a space π rotation around the x-axis accompanied with time reversal, $$\widetilde C_4^l$$ is a kind of fourfold rotation group, and L is the magnetic translational group of the vortex lattice state. We give a new, refined definition of local symmetric order parameters (OPs) ( s-wave, d-wave, and p-wave), which have a well-defined nature such that the OP (e.g., s-wave OP) at the translated site by a lattice vector (of the vortex lattice) from a site ( m, n) is expressed by the OP (e.g., s-wave) at the site ( m, n) times a phase factor. Winding numbers around the origin of s-wave and d-wave OPs are obtained for four types of solutions G( l) ( l = 0, 2, ± 1). It is shown that all energy bands of quasiparticles of a vortex lattice state are doubly degenerate. [ABSTRACT FROM AUTHOR]

We study the spatial distribution of supercurrent circulated around an Abrikosov vortex in an SF bilayer in perpendicular magnetic field. Within the dirty limit regime and circular cell approximation for the vortex lattice, we derive the conditions when the Usadel equations the F-layer can be solved analytically. Using the obtained solutions, we demonstrate the possibility of reversal of direction of proximity induced supercurrents around the vortex in the F-layer compared to that in the S-layer. The direction of currents can be controlled either by varying transparency of the SF interface or by changing an exchange field in a ferromagnet. We argue that the origin of this effect is due the phase shift between singlet and triplet order parameter components induced in the F-layer. Possible ways of experimental detection of the predicted effect are discussed. [ABSTRACT FROM AUTHOR]

Spontaneous collective motion, as in some flocks of bird and schools of fish, is an example of an emergent phenomenon. Such phenomena are at present of great interest and physicists have put forward a number of theoretical results that so far lack experimental verification. In animal behaviour studies, large-scale data collection is now technologically possible, but data are still scarce and arise from observations rather than controlled experiments. Multicellular biological systems, such as bacterial colonies or tissues, allow more control, but may have many hidden variables and interactions, hindering proper tests of theoretical ideas. However, in systems on the subcellular scale such tests may be possible, particularly in in vitro experiments with only few purified components. Motility assays, in which protein filaments are driven by molecular motors grafted to a substrate in the presence of ATP, can show collective motion for high densities of motors and attached filaments. This was demonstrated recently for the actomyosin system, but a complete understanding of the mechanisms at work is still lacking. Here we report experiments in which microtubules are propelled by surface-bound dyneins. In this system it is possible to study the local interaction: we find that colliding microtubules align with each other with high probability. At high densities, this alignment results in self-organization of the microtubules, which are on average 15?µm long, into vortices with diameters of around 400?µm. Inside the vortices, the microtubules circulate both clockwise and anticlockwise. On longer timescales, the vortices form a lattice structure. The emergence of these structures, as verified by a mathematical model, is the result of the smooth, reptation-like motion of single microtubules in combination with local interactions (the nematic alignment due to collisions)-there is no need for long-range interactions. Apart from its potential relevance to cortical arrays in plant cells and other biological situations, our study provides evidence for the existence of previously unsuspected universality classes of collective motion phenomena. [ABSTRACT FROM AUTHOR]

The phase transition "triangular lattice-vortex liquid" in layered high-T[sub c] superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T[sub c] Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (... 3 K) into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (... 8 K for T[sub c] = 84 K), the boundaries of the "islands" become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point "triangular lattice-rotating lattice" decreases slightly (to ... 2 K) and the temperature of the phase transition "rotating lattice-vortex liquid" increases substantially (...70 K). [ABSTRACT FROM AUTHOR]

The results of an experimental investigation of the dependence of the dissipation in a vortex lattice on the magnetic field strength and orientation of a Bi 2212 crystal at a temperature of ∼15 K are presented. A sharp peak, whose width depends on the orientation of the superconductor relative to the field, is observed in the dissipation. The results can be explained qualitatively by the appearance of a geometrical barrier that leads to a substantial redistribution of the magnetic field in the bulk of the sample. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Topological defects such as dislocations are predicted to determine the two-dimensional (2D) melting transition. In 2D superconducting vortex lattices, macroscopic measurements provide evidence for melting close to the transition to the normal state. However, the direct observation at the scale of individual vortices of the melting sequence has never been carried out. Here, we use scanning tunnelling spectroscopy (STS) to provide step-by-step imaging of a 2D system of vortices up to the melting transition in a W-based superconducting thin film. We show directly the transition into an isotropic liquid below the superconducting critical temperature. Before that, we find a hexatic phase, characterized by the appearance of free dislocations, and a smectic-like phase, possibly formed through partial disclination unbinding. These results represent a significant step in the understanding of the melting of 2D systems, with an impact across several research fields, such as liquid-crystal molecules or lipids in membranes. [ABSTRACT FROM AUTHOR]

Describes the first-order inverse melting of lattice formed by magnetic flux lines in a high-temperature superconductor. Application of microscopic Hall sensors in local magnetization measurements; Details on the first-order melting transition; Mechanism of the first-order phase transition.

Presents a study in which a differential magneto-optical technique is used to obtain direct experimental visualization of the melting process in a disordered superconductor. Complex behavior in nucleation, pattern formation, and solid-liquid interface coarsening and pinning which the images reveal; The melting, which is found to be a first-order phase transition; Evaluation of the sold-liquid surface tension.

The theory of scanning tunneling spectroscopy of low-energy quasiparticle (QP) states in vortex lattices of d-wave superconductors is developed taking account of the effects caused by an extremely large extension of QP wavefunctions in the nodal directions and the band structure in the QP spectrum. The oscillatory structures in STM spectra, which correspond to van Hove singularities, are analyzed. Theoretical calculations carried out for finite temperatures and scattering rates are compared with recent experimental data for high-T[sub c] cuprates. © 2000 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

Order-disorder transitions of a vortex lattice transfer type-II superconductors from a low critical current state to a high one. The similar transition between different current states can be caused by electromagnetic granularity. A sigmoid curve is proposed to describe the corresponding peak in a field dependence of the macroscopic critical density. Using the extended critical state model, analytic expressions are obtained for the field dependencies of the local critical current density, the depth of equilibrium surface region, and the macroscopic critical current density. The expressions are well fit to published data. [ABSTRACT FROM AUTHOR]