Vortex Lattice Research Articles

Band-resolved Caroli-de Gennes-Matricon states of multiple-flux-quanta vortices in a multiband superconductor.

Superconductors are of type I or II depending on whether they form an Abrikosov vortex lattice. Although bulk lead (Pb) is classified as a prototypical type-I superconductor, we show that its two-band superconductivity allows for single-flux-quantum and multiple-flux-quanta vortices in the intermediate state at millikelvin temperature. Using scanning tunneling microscopy, the winding number of individual vortices is determined from the real space wave function of its Caroli-de Gennes-Matricon bound states. This generalizes the topological index theorem put forward by Volovik for isotropic electronic states to realistic electronic structures. In addition, the bound states due to the two superconducting bands of Pb can be separately detected and the two gaps close independently inside vortices. This yields strong evidence for a low interband coupling.

The Simulation of a Vortex Lattice in a Nanofilm of a Type-II Superconductor

The Simulation of a Vortex Lattice in a Nanofilm of a Type-II Superconductor

It’s About Time: Jet Interactions in an Asymmetrical Plenum

Hybrid Reynolds-Averaged Navier-Stokes–Large Eddy Simulation was used to reveal detailed flow information and timescales in an isothermal reactor cavity cooling system plenum four-jet configuration. Plenum asymmetry and nonuniformity work together to cause premature jet merging. Bulk stirring in the plenum causes lateral jet vortex shedding, strong jet-jet interactions, swirl, and premature confluence. Two dominant transient modes exist: a jet flow timescale and then a plenum circulation timescale that is nearly three orders of magnitude larger. A primary consequence is that frequencies far less than the presumed 10 Hz threshold for thermal striping are pervasive. A second result is that scale-resolved computational fluid dynamics (CFD) models (as well as experimental rigs) need hundreds of seconds of statistically stationary flow time (tens of thousands of jet timescales) to produce stationary time averages. Fluid typically arrives at positions on the laser sheet in less time than it spends at those positions fluctuating in the streamwise and lateral directions. Also, a previously undocumented, but experimentally confirmed, vortex trap was identified via CFD. Finally, two-point velocity correlation analyses demonstrated a few dozen strong correlations across positions on the laser sheet. Expected close-proximity correlations emerged, but others across larger spaces also were connected. Most of these correlated at timescales close to that of the jet.

Generation of discrete higher-order optical vortex lattice at focus.

Higher-order vortices (HOVs) extend the dimensions of optical vortex regulation, which is of great significance in optical communication and optical tweezers. Herein, we demonstrate an alternative scheme to produce a HOV in the focus plane using multiple Laguerre-Gaussian (LG) beam interference, termed a discrete higher-order optical vortex lattice (DHOVL). The modulation depth of the DHOVL exceeds 2π. In this case, the topological charge (TC) of the DHOVL is determined by the difference of the phase period between the innermost and the outermost interference beams. Compared with a conventional HOV (CHOV), the vortex exists in a form of multiple unit singularities sharing a dark core. In addition, the average orbital angular momentum per photon of the DHOVL increases with increasing TC, surpassing that of the CHOV. This work provides a novel, to the best of our knowledge, scheme to produce a HOV, which will facilitate several advanced applications, including optical micromanipulation, optical sensing and imaging, and optical fabrication.

Phase transitions in rotating binary Bose–Einstein condensates with Spin–orbit and Rabi couplings

We present the phase transition analysis of binary Bose–Einstein condensates (BECs) with spin–orbit (SO) and Rabi couplings in quasi-two-dimensional system under rotation. In particular, we investigate the superfluid properties induced by rotation and SO coupling within hydrodynamic theory which can explain the emergence of the domain wall. By calculating the evolution of angular momentum with respect to rotation frequency, we discover first-order phase transitions where the domain wall changes into the wall-vortex complex. On the other hand, the angular momentum changes continuously with SO coupling strength accompanying by the elongation of the domain wall along x-direction. When the Rabi coupling strength exceeds a critical value, we observe a transition from the domain wall to vortex lattice resulting from a significant change of angular momentum. A phase diagram demonstrating the boundary regime in the plane of SO and Rabi coupling strengths is obtained. Our result is not only motivated by the search for novel states of matter inaccessible to existing experiments, but also by the need to identify situations where the phase transitions can be benchmarked systematically.

The Full Multi-wake Vortex Lattice Method: a detached flow model based on Potential Flow Theory

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).

Wind Tunnel Study of a Grid Fin Stabilized Guided Projectile

There is a need for methods/techniques to analyze the aerodynamics of grid fins at high angle of attack. The existing methods to predict or compute the aerodynamic parameters for grid fins are inadequate at high angles of attack. The present study attempts to extend the understanding of the complex aerodynamics associated with grid fins. The analysis draws its conclusion from wind tunnel test results of five basic grid fin configurations. A vortex lattice solution was used to model the aerodynamics of the chosen grid fins. Next the analytical and empirical relations as discussed in open literature were applied to model grid fin aerodynamics at high angle of attack. The aerodynamic coefficients were computed. These coefficients were then compared with the experimental results obtained using the five grid fin configurations. To improve the matching at high angle of attack a proposed approach using Kirchoff’s theory along with vortex lattice method was applied. The results show that this approach can be a starting tool to model lattice/grid fin aerodynamics.

A Numerical Unsteady Analysis of a Plunging Wing

Numerical simulation of unsteady motion of wing through undisturbed fluid is formulated using Unsteady Vortex Lattice Method. A free-wake algorithm is developed using a fourth order Adam-Bashforth technique. Rankine vortex model is used to avoid numerical singularities and wake decay algorithm is used to model the viscous dissipation of the shed wake. The resulting MN x MN equations are solved for unknown Γwing using LU decomposition, where M and N are number of divisions of the wing along chord and span respectively. The aerodynamic coefficient of lift, CL, induced drag, CDi , distribution of circulation, Γ and wake geometry are calculated for unsteady plunging motion. Effect of cross-flow is studied. The results are found to be in good agreement with available literature.

Generating high-efficiency swimming kinematics using hydrodynamic eigenmode decomposition

This paper explores the use of hydrodynamic eigenmode decomposition as a means of generating optimal swimming kinematics of slender three-dimensional bodies. The eigenvectors of the unsteady hydrodynamic system are used as basis functions for the response to external forcing, such as perturbations generated by the deformation of the body. Exploiting the orthogonality of the modes, we show that swimming according to a single appropriately selected hydrodynamic eigenmode results in high-efficiency swimming. To demonstrate this result, we use an inviscid three-dimensional vortex lattice model to investigate the hydrodynamic eigenmodes of a selection of geometries. We find that for all of the body geometries tested, hydrodynamic efficiency far exceeding that of pure heaving or pitching can be achieved. All eigenmodes tested produce high-efficiency motion, as long as the beat frequency is higher than the mode's “cut-in” frequency for thrust generation. The eigenmodes show qualitative similarity to swimming patterns observed in nature and also correspond well to the existing classifications of undulatory and oscillatory swimming. This study demonstrates that the hydrodynamic eigenmode analysis can generate high-efficiency swimming kinematics based only on information about the body and wake geometry, and as such, this method has significant potential for further development and application to autonomous underwater vehicle design.

Numerical Evaluation of Hydrodynamic Coefficients in Roll Motion

The determination of ship motions in a seaway heavily depends on hydrodynamic coefficients. However, the coefficients related to roll-motion exhibit nonlinear behavior due to viscous effects and relatively small wave damping, which pose significant challenges. To overcome these challenges, several studies have employed computational fluid dynamics (CFD) to analyze hydrodynamic performance, leveraging the advancements in computational performance. Nevertheless, limited research has investigated the error and uncertainty of these numerical solutions. In this study, we conducted a forced oscillation test on a ship-like section that induces lateral vortex shedding using the OpenFOAM with overset grid method. We validated the numerical results of the roll hydrodynamic coefficients with experiments and the results of potential theory. We used the procedure proposed by the ITTC to perform uncertainty analysis on the grid size and time step size, which presented the overall uncertainty of the numerical analysis results. Our findings indicate that the grid uncertainty of the added moment of inertia was significant in the low frequency region, while the time step uncertainty was significant in the high frequency region.

Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating 4He.

Quantum vortices are a core element of superfluid dynamics and elusively hold the keys to our understanding of energy dissipation in these systems. We show that we are able to visualize these vortices in the canonical and higher-symmetry case of a stationary rotating superfluid bucket. Using direct visualization, we quantitatively verify Feynman's rule linking the resulting quantum vortex density to the imposed rotational speed. We make the most of this stable configuration by applying an alternative heat flux aligned with the axis of rotation. Moderate amplitudes led to the observation of collective wave mode propagating along the vortices, and high amplitudes led to quantum vortex interactions. When increasing the heat flux, this ensemble of regimes defines a path toward quantum turbulence in rotating 4He and sets a baseline to consolidate the descriptions of all quantum fluids.

Adherence of the rotating vortex lattice in the noncentrosymmetric superconductor Ru7B3 to the London model

The noncentrosymmetric superconductor Ru7B3 has in previous studies demonstrated remarkably unusual behaviour in its vortex lattice (VL), where the nearest neighbour directions of the vortices dissociate from the crystal lattice and instead show a complex field-history dependence, and the VL rotates as the field is changed. In this study, we look at the VL form factor of Ru7B3 during this field-history dependence, to check for deviations from established models, such as the London model. We find that the data is well described by the anisotropic London model, which is in accordance with theoretical predictions that the alterations to the structure of the vortices due to broken inversion symmetry should be small. From this, we also extract values for the penetration depth and coherence length.

Vortex-lattice structures in rotating Bose-Fermi superfluid mixtures

The system of Bose-Fermi superfluid mixture offers a playground to explore rich macroscopic quantum phenomena. In a recent experiment of Yao et al. (2016) [35], 41K-6Li superfluid mixture is implemented. Coupled quantized vortices are generated via rotating the superfluid mixture, and a few unconventional behaviors on the formations of vortex numbers are observed, which can be traced to boson-fermion interactions. Here we provide a theoretical insight into the unconventional behaviors observed in the experiment. To this end, the orbital-free density functional theory is hired, and its utility is validated by making comparison of the numerical results and a microscopic theory for vortex lattices in strongly interacting Fermi superfluids alone. We also predict interesting phenomena which can be readily explored experimentally, including the novel structures of bosonic-fermionic vortices, and attractive interactions between the bosonic and fermionic vortices.

Low temperature singularities of electron density in a two-gap superconductor ZrB12

Fine details of crystal structure of ZrB12 two-gap superconductor are studied at low temperatures by precise x-ray diffraction technique. Small static Jahn-Teller distortions of a face centered cubic lattice are observed in the range 30–70 K, leading to emergence of two types singularities of electron density (ED). These are: (i) dynamic charge stripes along selected directions <110> and <112> in the crystal and (ii) triangular lattice of the ED antinodes located in the interstices of the boron lattice in the {111} planes. The second anomaly was detected for the first time, and it is very pronounced for ZrB12, being intensified at low temperatures. The anisotropy of the two-gap superconductivity in ZrB12 is confirmed by measurements of the low temperature heat capacity in a magnetic field directed along three principal axes in the crystal, H || [100], H || [110] and H || [111]. We conclude in favor of the magnetic field-induced anisotropy arising from the interaction of vortex lattice in this superconductor with fluctuating ED (charge stripes) of a two-type filamentary structure.

Ginzburg-Landau equations on non-compact Riemann surfaces

We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less than that of the constant curvature (magnetic field) one. These solutions are the non-commutative generalizations of the Abrikosov vortex lattice of superconductivity. Conjecturally, they are (local) minimizers of the Ginzburg-Landau energy. We obtain precise asymptotic expansions of these solutions and their energies in terms of the curvature of the underlying Riemann surface. Among other things, our result shows the spontaneous breaking of the gauge-translational symmetry of the Ginzburg-Landau equations.

Strongly coupled fluid–structure interaction analysis of aquatic flapping wings based on flexible multibody dynamics and the modified unsteady vortex lattice method

Because of their superior efficiency and low detectability compared to conventional submarine-shaped vehicles, bionic underwater vehicles such as Mantabot are playing increasingly important roles in ocean exploration. However, current research on manta-inspired robots is limited to structural design and pure hydrodynamics analysis of pectoral fin performance, with other aspects such as hydroelasticity and optimal design of flapping wings rarely addressed. This work presents a novel method for analyzing aquatic flapping wings by coupling flexible multibody dynamics with a modified unsteady vortex lattice method. The flexible multibody system is solved by using the absolute nodal coordinate formulation, and the conventional unsteady vortex lattice method is modified to accommodate dynamic stall. Compactly supported radial basis functions are used to transfer the hydroelastic forces and structural displacements across the interface meshes while satisfying global energy conservation, and a predictor–corrector method is used to stabilize the iteration procedure. Three different experiments are used to validate the flexible multibody dynamics solver, the modified unsteady vortex lattice solver, and the proposed fluid–structure interaction framework, respectively. Finally, the hydroelastic framework is demonstrated for a fin-like wing, and how flexibility and movement affect the flapping wing dynamics is examined. Numerical examples show that reducing the structural stiffness of the aquatic flapping wing within a certain range improves the propulsive efficiency but also reduces the thrust coefficient, and how the stiffness distribution affects the thrust and propulsive efficiency remains consistent over a range of the Strouhal number.

Control of the vortex lattice formation in coupled atom-molecular Bose–Einstein condensate in a double well potential: role of atom-molecule coupling, trap rotation frequency and detuning parameter

We study the vortex formation in coupled atomic and molecular condensates in a rotating double well trap by numerically solving the coupled Gross–Pitaevskii like equations. Starting with the atomic condensate in the double well potential we considered two-photon Raman photo-association for coherent conversion of atoms to molecules. It is shown that the competition between atom-molecule coupling strength and repulsive atom-molecule interaction controls the spacings between atomic and molecular vortices and the rotation frequency of the trap is the key player for controlling the number of visible atomic and molecular vortices. Whereas the Raman detuning controls the spacing between atomic and molecular vortices as well as the number of atomic and molecular vortices in the trap. We have shown by considering the molecular lattices the distance between two molecular vortices can be controlled by varying the Raman detuning. In addition we have found that the Feynman rule relating the total number of vortices and average angular momentum both for atoms and molecules can be satisfied by considering the atomic and molecular vortices those are hidden in density distribution and seen as singularities in phase distribution of the coupled system except for the lattice structure where molecular vortices are overlapped with each other. It is found that although the number of visible/core vortices in atomic and molecular vortex lattices depends significantly on the system parameters the number of atomic and molecular hidden vortices remains constant in most of the cases.

Quantum Interference by Vortex Supercurrents

The origin of the parabolic background of magnetoresistance oscillations measured in finite‐width superconducting mesoscopic rings with input and output stubs and in patterned films is analyzed. The transmission model explaining the sinusoidal oscillation of magnetoresistance is extended to address the parabolic background as a function of the magnetic field. Apart from the interference mechanism activated by the ring, pinned superconducting vortices as topological defects introduce a further interference‐based distribution of supercurrents that affects, in turn, the voltmeter‐sensed quasiparticles. The onset of vortices changes the topology of the superconducting state in a mesoscopic ring in such a way that the full magnetoresistance dynamics can be interpreted due to the interference of the constituents of the order parameter induced by both the ring with its doubly connected topology and the vortex lattice in it.

The pairing symmetry in quasi-one-dimensional superconductor Rb[formula omitted]Mo[formula omitted]As[formula omitted

Quasi-one-dimensional electron systems display intrinsic instability towards long-range ordered phases at sufficiently low temperatures. The superconducting orders are of particular interest as they can possess either singlet or triplet pairing symmetry and frequently compete with magnetism. Here we report on muon spin rotation and relaxation (μSR) study of Rb2Mo3As3 characterised by one of the highest critical temperatures Tc=10.4 K among quasi-one-dimensional superconductors. The transverse-field μSR signal shows enhanced damping below Tc due to the formation of vortex lattice. Comparison of vortex lattice broadening against single gap s−, p− and d−wave models shows the best agreement for the s−wave scenario but with the anomalously small superconducting gap, Δ0, to Tc ratio of 2Δ0/kBTc=2.74(1). The alternative nodal p−wave or d−wave scenarios with marginally worse goodness of fit would yield more realistic 2Δ0/kBTc=3.50(2) and 2Δ0/kBTc=4.08(1), respectively, and thus they cannot be ruled out when accounting for the superconducting state in Rb2Mo3As3.

Generation of optical vortex lattices by in-line phase modulation with partially coherent light.

Of late, generation of different kinds of optical vortex lattices has been gaining much attention due to various applications. Several methods have been reported for the generation of optical vortex lattices using a coherent light source involving interferometric, diffractive, and pinhole phase plate methods. Owing to cost effectiveness and ease in optical implementation, these days use of incoherent or partially coherent light beams is becoming popular. In this study, we demonstrate generation of different kinds of optical vortex lattices through in-line modulation of phase distributions employing the phase concatenation approach and a light-emitting diode as a light source. It is a non-interferometric and flexible technique for the selection of the parameters that characterize the optical vortices and their arrays. The proposed method allows generation of an array of optical vortices of different topological charges with zero and non-zero radial indices having different symmetries.