Thermal fluctuations of vortex matter in trapped bose-einstein condensates

We perform Monte Carlo studies of vortices in three dimensions in a cylindrical confinement, with uniform and nonuniform density. The former is relevant to rotating 4He; the latter is relevant to a rotating trapped Bose-Einstein condensate. In the former case, we find dominant angular thermal vortex fluctuations close to the cylinder wall. For the latter case, a novel effect is that at low temperatures the vortex solid close to the center of the trap crosses directly over to a tensionless vortex tangle near the edge of the trap. At higher temperatures an intermediate tensionful vortex liquid located between the vortex solid and the vortex tangle may exist.     

The vortex physics which comes from the vortex core

A theoretical view of vortex core states and of their effects on physics of vortices in clean s- and d-wave-type II superconductors is presented based on a semi-classical picture of a vortex core as an Andreev potential well containing many quasiparticle states. We discuss the density of states, the vortex dissipation, Hall effect, and the vortex mass. The dynamic characteristics are determined by relaxation of core excitations driven by a moving vortex. In a d-wave superconductor, gap nodes make the core states more extended and introduce novel features into thermodynamics and kinetics of vortices.     

Effect of surface Andreev bound states on the Bean-Livingston barrier in d-wave superconductors

We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory, we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap.     

Vortex instability and the onset of superfluid turbulence

Quantized circulation, the absence of Galilean invariance due to a clamped normal component, and the vortex mutual friction are the major factors that make superfluid turbulence behave in a way different from that in classical fluids. The model is developed for the onset of superfluid turbulence that describes the initial avalanchelike multiplication of vortices into a turbulent vortex tangle.     

Vortex state in a strongly coupled dilute atomic fermionic superfluid

We show that in a dilute fermionic superfluid, when the fermions interact with an infinite scattering length, a vortex state is characterized by a strong density depletion along the vortex core. This feature can make a direct visualization of vortices in fermionic superfluids possible.     

Giant oscillations of energy levels in mesoscopic superconductors

The interplay of geometrical and Andreev quantization in mesoscopic superconductors leads to giant mesoscopic oscillations of energy levels as functions of the Fermi momentum and/or sample size. Quantization rules are formulated for closed quasiparticle trajectories in the presence of normal scattering at the sample boundaries. Two generic examples of mesoscopic systems are studied: (i) one-dimensional Andreev states in a quantum box and (ii) a single vortex in a mesoscopic cylinder.     

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.     

Dynamical interactions of cosmic strings and flux vortices in superconductors

We perform a numerical simulation of the dynamical interactions of vortex excitations in the abelian Higgs model. These structures can be interpreted as cross sections of cosmic strings or of magnetic flux tubes trapped in a superconductor. Although at a critical value of the coupling constant the interaction energy between static vortices vanishes, colliding vortices interact nontrivially by scattering at 90° in a head-on collision, and are therefore not solitons. We also observe 90° scattering at non-critical values of the coupling constant.     

Plasmonic tomography of optical vortices

We present a method for analyzing the wavefront of optical vortices that does not involve interferometry but rather uses surface plasmon polaritons (SPPs). We employ a subwavelength slit in a gold film to cut slices from an optical vortex beam and measure the diffraction of the generated SPPs by scattering them off a second slit. By moving the slits across the vortex beam, we create a tomogram, from which we can determine the vortex charge of the incident beam at a glance. We present results for vortex beams of integer- and half-integer-vortex charge.     

On neutron diffraction from vortices in uniaxial superconductors

The London approach is used to obtain the neutron scattering form factor ofa vortex in a uniaxial layered superconductor. The form factor depends upon the direction of the scattering vector within the crystal. The structure of the vortex lattice is determined in the same approximation for any orientation of the vortices in the crystal.     

Ultrasound scattering and the study of vortex correlations in disordered flows

In an idealized way, some turbulent flows can be pictured by assemblies of many vortices characterized by a set of particle distribution functions. Ultrasound provides a useful, nonintrusive, tool to study the spatial structure of vorticity in flows. This is analogous to the use of elastic neutron scattering to determine liquid structure. We express the dispersion relation, as well as the scattering cross section, of sound waves propagating in a "liquid" of identical vortices as a function of vortex pair correlation functions. In two dimensions, formal analogies with ionic liquids are pointed out.     

Theory of static and dynamic antiferromagnetic vortices in LSCO superconductors

A key prediction of the SO(5) theory is the antiferromagnetic vortex state. Recent neutron scattering experiment on LSCO superconductors revealed enhanced antiferromagnetic order in the vortex state. Here we review theoretical progress since the original proposal and present a theory of static and dynamic antiferromanetic vortices in LSCO superconductors. It is shown that the antiferromagnetic region induced by the vortices can be greater than the coherence length, due to the light effective mass of the dynamic antiferromagnetic fluctuations at optimal doping, and close proximity to the antiferromagentic state in the underdoped regime. Systematic experiments are proposed to unambiguously determine that the field induced magnetic scattering originates from the vortices and not from the bulk.     

Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor(Li_(0.84)Fe_(0.16))OHFeSe

The Major ana zero mode(MZM), which manifests as an exotic neutral excitation in superconductors, is the building block of topological quantum computing. It has recently been found in the vortices of several iron-based superconductors as a zero-bias conductance peak in tunneling spectroscopy. In particular, a clean and robust MZM has been observed in the cores of free vortices in(Li_(0.84)Fe_(0.16))OHFeSe. Here using scanning tunneling spectroscopy, we demonstrate that Major ana-induced resonant Andreev reflection occurs between the STM tip and this zero-bias bound state,and consequently, the conductance at zero bias is quantized as 2e~2/h. Our results present a hallmark signature of the MZM in the vortex of an intrinsic topological superconductor, together with its intriguing behavior.     

Anomalous Hall effect in the mixed state of high-temperature superconductors

The Hall effect in the mixed state of high-T_c superconductors (HTSC) is of an anomalous nature: near the transition there is a range of temperatures and of magnetic fields where the sign of the Hall effect is opposite to that in the normal state. The universality of the phenomenon in question is indicative of its connection with some general properties of the mixed state of type-II superconductors, namely, with peculiarities of motion of magnetic flux vortex lines (vortices) in these superconductors. This work puts forward a model accounting for a number of vortex motion specific features and providing a possibility to obtain the characteristics of the anomalous Hall effect.

The work is based on the phenomenologically generalized results of Bardeen-Stephen and Nozieres-Vinen, supplemented with an allowance for a new mechanism of vortex “friction” associated with Andreev electron reflection on the interface between the normal core and the superconducting periphery of a vortex. Within the framework of the model suggested, magnetic field (and temperature) dependences of the longitudinal and Hall resistances of a mixed state superconductor have been calculated at temperatures nearing T_c. At certain quite realistic parameters which define the forces acting on the vortices, there is a range of magnetic fields and temperatures where the sign of the Hall effect is opposite to that in the normal state. The lower limit of this range is the irreversibility line and the upper critical field.     

Vortices formation induced by femtosecond laser filamentation in a cloud chamber filled with air and helium

We report on the experimental observation of the airflow motion induced by an 800 nm, 1 k Hz femtosecond filament in a cloud chamber filled with air and helium. It is found that vortex pairs with opposite rotation directions always form both below and above the filaments. We do not observe that the vortices clearly formed above the filament in air just because of the formation of smaller particles with weaker Mie scattering.Simulations of the airflow motion in helium are conducted by using the laser filament as a heat source, and the simulated pattern of vortices and airflow velocity agree well with the experimental results.     

Irregular scattering of acoustic rays by vortices

The scattering of high-frequency sound wave, under geometrical acoustic approximation, by three stationary vortices in two dimensions is investigated. For a sufficiently high Mach number of the vortex flow, the scattering of sound rays becomes irregular, displaying a new example of chaotic scattering for a time-reversal breaking system. The fractal dimension, as well as the unstable and stable manifolds of the scattering dynamics, is presented.     

Scattering of vortex pairs in 2D easy-plane ferromagnets

Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of solitons in two dimensions. We investigate numerically and analytically the dynamics of such vortex pairs. In particular we simulate numerically the head-on collision of two pairs with different velocities for a wide range of the total linear momentum of the system. If the momentum difference of the two pairs is small, the vortices exchange partners, scatter at an angle depending on this difference, and form two new identical pairs. If it is large, the pairs pass through each other without losing their identity. We also study head-tail collisions. Two identical pairs moving in the same direction are bound into a moving quadrupole in which the two vortices as well as the two antivortices rotate around each other. We study the scattering processes also analytically in the frame of a collective variable theory, where the equations of motion for a system of four vortices constitute an integrable system. The features of the different collision scenarios are fully reproduced by the theory. We finally compare some aspects of the present soliton scattering with the corresponding situation in one dimension. Received 18 September 2001     

Shadow on the wall cast by an Abrikosov vortex

At the surface of a d-wave superconductor, a zero-energy peak in the quasiparticle spectrum can be observed. This peak appears due to Andreev bound states and is maximal if the nodal direction of the d-wave pairing potential is perpendicular to the boundary. We examine the effect of a single Abrikosov vortex in front of a reflecting boundary on the zero-energy density of states. We can clearly see a splitting of the low-energy peak and therefore a suppression of the zero-energy density of states in a shadowlike region extending from the vortex to the boundary. This effect is stable for different models of the single Abrikosov vortex, for different mean free paths and also for different distances between the vortex center and the boundary. This observation promises to have also a substantial influence on the differential conductance and the tunneling characteristics for low excitation energies.     

Condensates in double-well potential with synthetic gauge potentials and vortex seeding

We demonstrate an enhancement in the vortex generation when artificial gauge potential is introduced to condensates confined in a double well potential. This is due to the lower energy required to create a vortex in the low condensate density region within the barrier. Furthermore, we study the transport of vortices between the two wells, and show that the traverse time for vortices is longer for the lower height of the well. We also show that the critical value of synthetic magnetic field to inject vortices into the bulk of the condensate is lower in the double-well potential compared to the harmonic confining potential.     

Chaotic Quantum Vortices in He II: Thermodynamic Equilibrium and Turbulence

The use of superfluid helium as a refrigerant in cryogenic systems is governed by the presence of a chaotic tangle of quantum filaments in the superfluid component of helium. Therefore, to describe any hydrodynamic phenomena (in particular, heat transfer) in quantumliquids containing vortex tangles, it is necessary to have information on their structure and statistics. The paper discusses two possible statistical configurations of chaotic vortices: the thermodynamic equilibrium and the highly nonequilibrium turbulent state, as well as the transition between them. Basing on the Langevin approach, we discuss the mechanism of establishment of thermodynamic equilibrium for a chaotic set of quantum vortex filaments. The corresponding Fokker–Planck equation for the probability density functional has a solution in the form of the Gibbs distribution. Basing on the above analysis, we discuss the possible causes and mechanisms of violation of thermodynamic equilibrium and transition to the turbulent regime.