Vortex Excitations Research Articles

Transverse Meissner physics of planar superconductors with columnar pins

The statistical mechanics of thermally excited vortex lines with columnar defects can be mapped onto the physics of interacting quantum particles with quenched random disorder in one less dimension. The destruction of the Bose glass phase in type-II superconductors, when the external magnetic field is tilted sufficiently far from the column direction, is described by a poorly understood non-Hermitian quantum phase transition. We present here exact results for this transition in $(1+1)$ dimensions, obtained by mapping the problem in the hard core limit onto one-dimensional fermions described by a non-Hermitian tight binding model. Both site randomness and the relatively unexplored case of bond randomness are considered. Analysis near the mobility edge and near the band center in the latter case is facilitated by a real space renormalization group procedure used previously for Hermitian quantum problems with quenched randomness in one dimension.

Lower pseudogap phase of Mott insulators: A spin/vortex liquid state

The pseudogap phase is considered to be a new state of matter in the phase string model of the doped Mott insulator, which is composed of two distinct regimes known as the upper and lower pseudogap phases, respectively. The former corresponds to the formation of spin-singlet pairing, the magnetic characterizations of which have been recently studied [Phys. Rev. B 72, 104520 (2005)]. The latter, as a low-temperature regime of the pseudogap phase, is systematically explored in this work, which is characterized by the formation of the Cooper pair amplitude and described by a generalized Ginzburg-Landau theory. Elementary excitation in this phase is a charge-neutral object carrying spin-$1∕2$ and locking with a supercurrent vortex, known as a spinon-vortex composite. Such a lower pseudogap phase can be regarded as a vortex liquid state due to the presence of free spinon vortices. Here thermally excited spinon vortices destroy the phase coherence and are responsible for the nontrivial Nernst effect and diamagnetism. The transport entropy and core energy associated with a spinon vortex are determined by the spin degrees of freedom. Such a spontaneous vortex liquid phase can be also considered as a spin liquid with a finite correlation length and gaped $S=1∕2$ excitations, where a resonancelike nonpropagating spin mode emerges at the antiferromagnetic wavevector $(\ensuremath{\pi},\ensuremath{\pi})$ with a doping-dependent characteristic energy. The superconducting phase is closely related to the lower pseudogap phase by a topological transition with spinon vortices and antivortices forming bound pairs and the emergence of fermionic quasiparticles as holon-spinon-vortex bound objects. A quantitative phase diagram in the parameter space of doping, temperature, and magnetic field is determined. Comparisons with experiments are also made.

Laboratory model of generation of a large-scale spiral vortex in a convectively unstable rotating fluid

Laboratory experiments have been carried out to investigate conditions for the generation of a large- scale spiral vortex from a localized heat source in a rotating fluid. It is shown that there is a threshold for the excitation of a vortex rotating much more rapidly than the cuvette. The influence of the intensities of convection and background rotation on the excitation threshold of a spiral vortex has been investigated for various liquids in cuvettes of different geometry. In all experiments, the threshold of vortex excitation corresponds to turbulent convection states and a relatively slow background rotation and practically does not depend on the Prandtl num- ber. The influence of the spatial distribution of temperature in the heating area on the threshold of vortex gen- eration has been revealed.

Characteristics of fluctuating lift forces of a circular cylinder during generation of vortex excitation

This paper describes the characteristics of the fluctuating lift forces when a circular cylinder vibrates in the cross-flow direction. The response characteristics on elastically supported the circular cylinder was first examined by a free-vibration test. Next, flow-induced vibrations obtained by the free-vibration test were reproduced by a forced-vibration test, and then the characteristics of the fluctuating lift forces, the work done by the fluctuating lift, the behavior of the rolling-up of the separated shear layers were investigated on the basis of the visualized flow patterns. The main findings were that (i) the fluctuating lift forces become considerably large than those of a stationary circular cylinder, (ii) negative pressure generates on the surface of the circular cylinder when the rolling-up of separated shear layer begins, (iii) the phase between the fluctuating lift force and the cylinder displacement changes abruptly as the reduced velocity <TEX>$U_r$</TEX> increases, and (iv) whether the generating cross-flow vibration becomes divergent or convergent can be described based on the work done by the fluctuating lift force. Furthermore, it was found that the generation of cross-flow vibration can be perfectly suppressed when the small tripping rods are installed on the surface of the circular cylinder.

Superradiance from hydrodynamic vortices: A numerical study

The scattering of sound-wave perturbations from vortex excitations in hydrodynamic systems with typical Bose-Einstein-condensate (BEC) parameters is investigated by numerical integration of the associated Klein-Gordon equation. The simulations indicate that at sufficiently high angular speeds, in the perturbative limit where back-reaction effects can be neglected, sound wave packets can extract a sizable fraction of the vortex energy through a mechanism of superradiant scattering. It is conjectured that this superradiant regime may be detectable in BEC experiments.

Response characteristics and suppression of torsional vibration of rectangular prisms with various width-to-depth ratios

The response characteristics and suppression of flow-induced vibrations of rectangular prisms with various width-to-depth ratios were experimentally investigated. The prisms were rigid and elastically mounted at both ends to enable constrained torsional vibrations only. The present study focused on torsional vibrations, one of the three types of flow-induced vibrations generated in a rectangular prism. First, the response characteristics of torsional vibrations generated in rectangular prisms were investigated by free-vibration tests. It was found that the response characteristics of torsional vibrations generated in rectangular prisms could be classified into six patterns depending on the width-to-depth ratio. Next, the response characteristics of torsional vibrations observed in the free-vibration tests were reproduced by forced-vibration tests, and the mechanisms by which the three types of flow-induced vibrations, low-speed torsional flutter, vortex excitation and high-speed torsional flutter, are generated in the rectangular prisms were elucidated on the basis of characteristics of fluid forces and visualized flow patterns. Experiments were also carried out to establish an effective method for suppressing flow-induced vibrations generated in the rectangular prisms, and it was found that low-speed torsional flutter and high-speed torsional flutter could be suppressed by placing a small normal plate upstream of the prism, which results in suppression of the alternating rolling-up of the shear layers separating from the leading edges of the prism. It was also found that vortex excitation could be suppressed by placing a splitter plate downstream of the prism, which results in suppression of the generation of wake vortices.

Magnetic field induced suppression of vortex flow resistance in superconductors with periodic pinning centers

We study vortex flow resistance (VFR) in films of Pb with holes as periodic pinning centers (PPCs) and of Nb with PPCs in the form of Ni dots, as function of temperature, dc current and constant applied magnetic field. The experimental resolution is better than 10−5 of the normal state resistance. At high temperatures near to Tc and high drive currents the resistance shows local minima both at matching fields and zero field. For lower temperatures, however, in a narrow temperature range before the vortex system becomes completely frozen, we observe suppression of the VFR with increasing magnetic field. In the Pb film with PPCs these phenomena show up as a clear zero field resistance excess, which is gradually suppressed by the applied magnetic field. We attribute this unusual feature in the magnetoresistance to thermally excited vortex–antivortex pairs. In the Nb superconducting film with PPCs we observe a gradual suppression of the VFR near integer matching fields up to n=3 at the lowest accessible dc currents and relevant temperatures. This anomalous behaviour is followed by the observation of negligible VFL for higher fields (H3<H<H4) and a strong enhancement of VFR for H>H4. We tentatively explain this observation as due to the moving vortex glass.

Nernst effect in high-Tcsuperconductors

The observation of a large Nernst signal ${e}_{N}$ in an extended region above the critical temperature ${T}_{c}$ in hole-doped cuprates provides evidence that vortex excitations survive above ${T}_{c}$. The results support the scenario that superfluidity vanishes because long-range phase coherence is destroyed by thermally created vortices (in zero field) and that the pair condensate extends high into the pseudogap state in the underdoped (UD) regime. We present a series of measurements to high fields $H$ which provide strong evidence for this phase-disordering scenario. Measurements of ${e}_{N}$ in fields $H$ up to $45\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ reveal that the vortex Nernst signal has a characteristic ``tilted-hill'' profile, which is qualitatively distinct from that of quasiparticles. The hill profile, which is observed above and below ${T}_{c}$, underscores the continuity between the vortex-liquid state below ${T}_{c}$ and the Nernst region above ${T}_{c}$. The upper critical field (depairing field) ${H}_{c2}$ determined by the hill profile (in slightly UD to overdoped samples) displays an anomalously weak $T$ dependence, which is consistent with the phase-disordering scenario. We contrast the Nernst results and ${H}_{c2}$ behavior in hole-doped and electron-doped cuprates. Contour plots of ${e}_{N}(T,H)$ in the $T$-$H$ plane clearly bring out the continuous extension of the low-$T$ vortex liquid state into the high-$T$ Nernst region in hole-doped cuprates (but not in the electron-doped cuprate). The existence of an enhanced diamagnetic magnetization $M$ that survives to intense $H$ above ${T}_{c}$ is obtained from torque magnetometry. The observed $M$ scales accurately like ${e}_{N}$ above ${T}_{c}$, confirming that the large Nernst signal is associated with local diamagnetic supercurrents that persist above ${T}_{c}$. We emphasize implications of the new features in the phase diagram implied by the high-field results and discuss relevant theories.

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

We study the rotational properties of an attractively interacting Bose gas in a quadratic + quartic potential. The low-lying modes of both rotational ground state configurations, namely the vortex and the center of mass rotating states, are solved. The vortex excitation spectrum is positive for weak interactions but the lowest modes decrease rapidly to negative values when the interactions become stronger. The broken rotational symmetry involved in the center of mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center of mass rotational state also demonstrate the coupling between the center of mass and relative motions.

Non-power-law I–V characteristics inCa-doped polycrystalline Y1−xCaxBa2Cu3O7−δ

Experiments reveal that there is a non-ohmic dissipation behaviour in the Ca-doped polycrystallineY1−xCaxBa2Cu3O7−δ even attemperature T = 20 K. This non-ohmic dissipation seems to come from the vortexexcitation along the grain boundaries and appears in anomalousI–V characteristics with a non-power-law behaviour at temperatures below60 K, and then with a power-law behaviour as the temperature approachesTc. This abnormal behaviour cannot be explained by the thermal flux creepmodel. We suppose that a giant flux motion along the grain boundaries mightbe responsible for this anomalous non-ohmic dissipation behaviour. A modifiedI–V relation was worked out based on Larkin’s collective pinning model, and the analyticalI–V curves were found to be coincident with the experimental curves quite well. This confirmedthat the vortex excitation process along the grain boundaries in Ca-doped polycrystallineY1−xCaxBa2Cu3O7−δ might be described with a modified collective pinning model.

Influence of Cross-Sectional Configuration on the Longitudinal Vortex Excitation of the Upstream Cylinder in Cruciform Two-Cylinder System

In earlier works by the present authors, it was shown that a large cross-flow excitation is induced to a circular cylinder by setting another cylinder downstream in a cruciform arrangement with a certain gap between them, caused by longitudinal vortices shedding periodically around the crossing. In this work, influence of the cross-sectional configuration of cylinders forming a cross on the longitudinal vortex excitation was investigated by wind tunnel experiments. Three systems, i.e. a two-circular-cylinder, a circular-cylinder/strip-plate and a square-cylinder/strip-plate system, with essentially equal structural parameters were compared. In the case of the circular-cylinder/strip-plate system, the trailing vortex excitation occurs over much wider velocity region, while the necklace vortex excitation is indefinite, as compared with the two-circular-cylinder system. In the case of the square-cylinder/strip-plate system, vortex excitation occurs in a certain velocity region of the galloping of single cylinder attributed to the necklace vortex.

Vortex Excitation Caused by Longitudinal Vortices Shedding from Cruciform Cylinder System in Water Flow

Wind tunnel experiments by the present authors have shown that a large crossflow oscillation can be induced on the upstream cylinder in cruciform cylinder system by two types of longitudinal vortices, i.e. trailing and necklace vortices. In this study, experiments on this phenomenon are carried out in a water tunnel over a Reynolds number range comparable with that of the wind tunnel experiments to investigate the effects of the mass ratio M R and the Scruton number Sc. The alternating lift coefficient C LR for Karman vortex excitation in water flow agrees well with that in air flow in spite of the large differences in M R and Sc between them. However, the value of C LR for the trailing vortex excitation is much lower in water flow and no definite excitation due to the necklace vortex is observed.

Response Characteristics and Suppression of Flow-Induced Vibrations of Rectangular Prisms with Cross-Flow Vibration

This study was to experimentally investigate on response characteristics and suppression of flow-induced vibrations of rectangular prisms with various width-to-height ratios. The present study focused on cross-flow vibration, which is one of flow-induced vibrations generated in the prism. At first, the response characteristics on elastically supported prisms were examined in detail by the free-vibration test. Next, the generation mechanism of flow-induced vibrations was examined on the basis of the visualized flow patterns. Furthermore, the suppression of flow-induced vibrations of the prisms with cross-flow vibration was attempted. The main findings were that (i) there are four types of flow-induced vibrations with cross-flow vibrations, i.e., low-speed galloping, vortex excitation, wake breathing and high-speed galloping, (ii) flow-induced vibrations can be classified into four patterns depending on the width-to-height ratio, and (iii) the generation of flow-induced vibrations of the prisms is completely suppressed by the semicircle fairings attached on front and rear surface of the prism.

Vortex fractionalization in a Josephson ladder

We show numerically that, in a Josephson ladder with periodic boundary conditions and subject to a suitable transverse magnetic field, a vortex excitation can spontaneously break up into two or more fractional excitations. If the ladder has N plaquettes, and N is divisible by an integer q, then in an applied transverse field of 1/q flux quanta per plaquette the ground state is a regular pattern of one fluxon every q plaquettes. When one additional fluxon is added to the ladder, it breaks up into q fractional fluxons, each carrying 1/q units of vorticity. The fractional fluxons are basically walls between different domains of the ground state of the underlying 1/q lattice. The fractional fluxons are all depinned at the same applied current and move as a unit. For certain applied fields and ladder lengths, we show that there are isolated fractional fluxons. It is shown that the fractional fluxons would produce a time-averaged voltage related in a characteristic way to the ac voltage frequency.

Single vortex states in a confined Bose-Einstein condensate

It has been demonstrated experimentally that non-axially symmetric vortices precess around the centre of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S-vortex and the U-vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S-vortex has higher energy than the U-vortex in a rotating elongated condensate. We show that the S-vortex is related to the solitonic vortex which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S-vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.

Non-equilibrium Higgs transition in classical scalar electrodynamics

Real time rearrangement of particle spectra is studied numerically in a U(1) Gauge+Higgs system, in the unitary gauge and in three spatial dimensions. The cold system starts from the symmetric phase. Evolution of the partial energy densities and pressures reveal well-defined equations of state for the longitudinal and transversal gauge fields very early. Longitudinal modes are excited more efficiently and thermalize the slowest. Hausdorff-dimension of the Higgs-defect manifold, eventually seeding vortex excitations is thoroughly discussed. Scaling dependence of the vortex density on the characteristic time of the symmetry breaking transition is established.

Front aggregation in multiarmed excitation vortices

Using the Belousov-Zhabotinsky reaction, we study the pinning of multiarmed spiral waves to nonexcitable obstacles. With increasing obstacle size, the individual arms switch from a repulsive to an attractive state. This transition yields densely aggregated spiral arms and is caused by anomalous dispersion. A kinematic model reproduces the measurements quantitatively and identifies the transition as a supercritical pitchfork bifurcation.

Macroscopic quantum tunnelling of Bose–Einstein condensates in a finite potential well

Bose–Einstein condensates are studied in a potential of finite depth which supports both bound and quasi-bound states. This potential, which is harmonic for small radii and decays as a Gaussian for large radii, models experimentally relevant optical traps. The nonlinearity, which is proportional to both the number of atoms and the interaction strength, can transform bound states into quasi-bound ones. The latter have a finite lifetime due to tunnelling through the barriers at the borders of the well. We predict the lifetime and stability properties for repulsive and attractive condensates in one, two and three dimensions, for both the ground state and excited soliton and vortex states. We show, via a combination of the variational and WKB approximations, that macroscopic quantum tunnelling in such systems can be observed on time scales of 10 ms to 10 s.

Magnetic vortex resonance in patterned ferromagnetic dots

We report a high-resolution experimental detection of the resonant behavior of magnetic vortices confined in small disk-shaped ferromagnetic dots. The samples are magnetically soft Fe-Ni disks of diameter 1.1 and 2.2 um, and thickness 20 and 40 nm patterned via electron beam lithography onto microwave co-planar waveguides. The vortex excitation spectra were probed by a vector network analyzer operating in reflection mode, which records the derivative of the real and the imaginary impedance as a function of frequency. The spectra show well-defined resonance peaks in magnetic fields smaller than the characteristic vortex annihilation field. Resonances at 162 and 272 MHz were detected for 2.2 and 1.1 um disks with thickness 40 nm, respectively. A resonance peak at 83 MHz was detected for 20-nm thick, 2-um diameter disks. The resonance frequencies exhibit weak field dependence, and scale as a function of the dot geometrical aspect ratio. The measured frequencies are well described by micromagnetic and analytical calculations that rely only on known properties of the dots (such as the dot diameter, thickness, saturation magnetization, and exchange stiffness constant) without any adjustable parameters. We find that the observed resonance originates from the translational motion of the magnetic vortex core.

Quasi-One-dimensional Spin-Density-Wave States in Presence of Two Commensurate Potentials and Interchain Misfit

The spin-density-wave (SDW) states of a quasi-one-dimensional system with an incommensurate wave vector perpendicular to the chain have been studied in the presence of two kinds of commensurate potential, which originate in a quarter-filled band and under dimerization along the chain. For the phase variance phase of the SDW order parameter, we classically treat a two-dimensional Hamiltonian, which includes both acoustic excitation with a long wavelength and a vortex excitation with a short wavelength. A phase diagram on the plane of temperature and chemical potential (where the latter corresponds to the deviation of the transverse wave vector from the commensurate one) exhibits a variety of states given by the commensurate SDW state without charge density, the commensurate SDW state with charge density, the incommensurate SDW state, and the disordered state.