Direct observation of geometrical phase transitions in mesoscopic superconductors by scanning tunneling microscopy

Using scanning tunneling microscopy, we mapped the distribution of the local density of states in a single crystal superconductor heterostructure with an array of submicron normal metal islands. We observe the coexistence of strongly interacting multiquanta vortex lattice with interstitial Abrikosov vortices. The newly formed composite magnetic flux structure undergoes a series of phase transitions between different topological configuration states. The vortex configuration states are strongly dependent on the number of flux quanta and the nanoscale confinement architecture of the mesoscopic superconductor. Here, we present images of vortex phase transitions due to confinement effects when the number of magnetic flux quanta in the system changes. The vortex dynamics in these systems could serve as a model for behavior of confined many-body systems when the number of particles changes.     

推广的Gross-Pitaevskii理论中的涡旋问题(英文)

利用推广 Gross- Pitaevskii方程 ,分别研究了 (2 +1 )维时空和 3维空间的 Bose- Einstein凝聚体中涡旋的拓扑结构 .这一推广的方程能够被用于非均匀并且高度非线形的 Bose- Einstein凝聚系统 .利用Φ映射拓扑流理论 ,给出了基于序参数的涡旋速度场,以及该速度场的拓扑结构 .最后 ,仔细地探讨了这两种 Bose- Einstein系统中涡旋的各种分支条件.We studied the topological structure of vortex in the Bose-Einstein condensation with a generalized Gross-Pitaevskii equation in (2+1)-dimensional space-time and 3-dimensional space, respectively. Such equation can be used in discussing Bose-Einstein condensates in heterogeneous and highly nonlinear systems. An explicit expression for the vortex velocity field as a function of the order parameter field is derived in terms of the Φ -mapping theory, and the topological structure of ...     

Chiral vortical effect generated by chiral anomaly in vortex-skyrmions

We discuss the type of the general macroscopic parity-violating effects, when there is the current along the vortex, which is concentrated in the vortex core. We consider vortices in chiral superfluids with Weyl points. In the vortex core, the positions of the Weyl points form the skyrmion structure. We show that the mass current concentrated in such a core is provided by the spectral flow through the Weyl points according to the Adler–Bell–Jackiw equation for chiral anomaly.     

磁通密度对第Ⅱ类超导体磁通动力学的影响

计算了二维无序钉扎系统中磁通运动的平均速度、微分电阻、纵向电压噪声和静态结构因子.通过在不同磁通密度下的磁通运动形式,给出了磁通运动的动力学相图.研究表明,磁通晶格存在钉扎相、塑性流相、近晶流相,和运动玻璃相.在运动玻璃相中,随着驱动力的进一步增加,横向玻璃态和运动Bragg玻璃态相继出现.磁通密度增大有利于有序相的出现.当磁通密度增大到一定程度时,近晶流动相会消失.磁通运动随着外加驱动电流增大发生从塑性流动相到运动玻璃相的转变 关键词： Ⅱ类超导体 磁通动力学 运动玻璃     

Vortex washboard voltage noise in type-II superconductors

In order to characterize flux flow through disordered type-II superconductors, we investigate the effects of columnar and point defects on the vortex velocity/voltage power spectrum in the driven non-equilibrium steady state. We employ three-dimensional Metropolis Monte Carlo simulations to measure relevant physical observables including the force-velocity/current-voltage (I-V) characteristics, vortex spatial arrangement and structure factor, and mean flux line radius of gyration.Our simulation results compare well to earlier findings and physical intuition.We focus specifically on the voltage noise power spectra in conjunction with the vortex structure factor in the presence of weak columnar and point pinning centers. We investigate the vortex washboard noise peak and associated higher harmonics,and show that the intensity ratios of the washboard harmonics are determined bythe strength of the material defects rather than the type of pins present.Through varying columnar defect lengths and pinning strengths as well as magnetic flux density we further explore the effect of the material defects on vortex transport.It is demonstrated that the radius of gyration displays quantitatively uniquefeatures that depend characteristically on the type of material defects presentin the sample.     

Eigenstates of the linearlized Ginzburg–Landau equation for mesoscopic multiply-connected superconductor

Multiply-connected mesoscopic superconductors have rich structures of vortex systems that result from interference of order parameter. We studied magnetic field dependence of transition temperatures and vortex arrangements of finite sized honeycomb superconducting networks with 6-fold rotational symmetries. Near and above the lower critical field, vortices locate at center of the network. As increasing the field, vortices form a hexagon or hexagonal multi-shell structure. In higher field, order parameter damps exponentially from the central point of the network to the edge of the network.     

Switching of vortex polarization in 2D easy-plane magnets by magnetic fields

We investigate the dynamics of out-of-plane (OP) vortices, in a 2-dimensional (2D) classical Heisenberg magnet with a weak anisotropy in the coupling of z-components of spins (easy plane anisotropy), on square lattices, under the influence of a rotating in-plane (IP) magnetic field. Switching of the z-component of magnetization of the vortex is studied in computer simulations as a function of the magnetic field's amplitude and frequency. The effects of the size and the anisotropy of the system on the switching process are shown. An approximate dynamical equivalence of the system, in the bulk limit, to another system with both IP and OP static fields in the rotating reference frame is demonstrated, and qualitatively the same switching and critical behavior is obtained in computer simulations for both systems. We briefly discuss the interplay between finite size effects (image vortices) and the applied field in the dynamics of OP vortices. In the framework of a discrete reduced model of the vortex core we propose a mechanism for switching the vortex polarization, which can account qualitatively for all our results. A coupling between the IP movement (trajectories) of the vortex center and the OP core structure oscillations, due to the discreteness of the underlying lattice, is shown. A connection between this coupling and our reduced model is made clear, through an analogy with a generalized Thiele equation. Received 6 June 2002 / Received in final form 4 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: juan.zagorodny@uni-bayreuth.de     

Vortex lines in a ferromagnetic spin-triplet superconductor

Based on Duan's topological current theory, we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines. Such defects are different from the Abrikosov vortices in one-component condensate systems. We investigate the inner topological structure of the vortex lines. The topological charge density, velocity, and topological current of the vortex lines can all be expressed in terms of δ function, which indicates that the vortices can only arise from the zero points of an order parameter field. The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping. The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function. Finally, based on the implicit function theorem and the Taylor expansion, we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.     

Vortex-to-polarization phase transformation path in ferroelectric Pb(ZrTi)O3 nanoparticles

Phase transformation in finite-size ferroelectrics is of fundamental relevance for understanding collective behaviors and balance of competing interactions in low-dimensional systems. We report a first-principles effective Hamiltonian study of vortex-to-polarization transformation in Pb(Zr0.5Ti0.5)O3 nanoparticles, caused by homogeneous electric fields normal to the vortex plane. The transformation is shown to (1) follow an unusual macroscopic path that is symmetry nonconforming and characterized by the occurrence of a previously unknown structure as the bridging phase, and (2) lead to the discovery of a striking collective phenomenon, revealing how ferroelectric vortex is annihilated microscopically. Interactions underlying these behaviors are discussed.     

Interactions between vortex and magnetic rings at high kinetic and magnetic Reynolds numbers

Interactions between magnetic and vortex rings are studied over a wide interval of interaction parameter values ranging from negligible magnetic effects on vorticity structure, to very strong effects. The employed interaction parameter measures the strength of the Lorentz force in units of the inertial force. At small interaction parameters, the vortex ring shapes part of the magnetic ring into a dissipative, curved, magnetic sheet structure. At high interaction parameters, the Lorentz force acts as an agent of proliferation of vortex rings, since it generates two vortex rings adjacent to the original magnetic structure, one of which is pulled (together with the advected magnetic field) into the wake of the original vortex ring, while the other escapes, ready to interact with another magnetic ring. Once within the initial vortex ring wake, both magnetic and vorticity structures are stretched into spirals, whilst the Lorentz force continuously generates new, intense vorticity at high magnetic field sites.     

Vortex dynamics and correlated disorder in high-Tc superconductors

We develop a theory for the vortex motion in the presence of correlated disorder in the form of twin boundaries and columnar defects. Mapping vortex trajectories onto boson world lines enables us to establish the duality of the vortex transport in systems with correlated disorder and the hopping conductivity of charged particles in 2D systems. A glassy-like dynamics of the vortex lines with zero linear resistivity and strongly nonlinear current-voltage behavior as V ∝ exp(-const/J^μ) in a Bose glass state is predicted.     

Unconventional dynamics of vortex shells in mesoscopic superconducting corbino disks

The dynamics of vortex matter in mesoscopic superconducting Corbino disk is strongly influenced by the discrete vortex structure arranged in shells. While in previous works the vortex dynamics has been studied in large (macroscopic) and in very small mesoscopic disks (containing only few shells), in the intermediate-size regime it is much more complex and unusual, due to: (i) the competition between the vortex–vortex interaction and confinement and (ii) (in)commensurability among the vortex shells. We found that the interplay between these effects can result in a very unusual vortex dynamical behavior: (i) unconventional angular melting (i.e., propagating from the boundary, where the shear stress is minimum, towards the center) and (ii) unconventional dynamics of shells (i.e., the inversion of shell velocities with respect to the gradient driving force). This unusual behavior is found for different number of shells.     

Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems

We analyze the evolution of the vortex and the asymmetrical parts of orbital angular momentum during its propagation through separable first-order optical systems. We find that the evolution of the vortex part depends on only parameters a(x), a(y), b(x), and b(y) of the ray transformation matrix and that isotropic systems with the same ratio b/a produce the same change of the vortex part of the orbital angular momentum. Finally, it is shown that, when light propagates through an optical fiber with a quadratic refractive-index profile, the vortex part of the orbital angular momentum cannot change its sign more than four times per period.     

Superheating and supercooling of vortex matter in a Nb single crystal: direct evidence for a phase transition at the peak effect from neutron diffraction

We report the first observation of a striking history dependence of the structure function of vortex matter in the peak effect regime in a Nb single crystal by using small angle neutron scattering combined with in situ magnetic susceptibility measurements. Metastable phases of vortex matter, supercooled vortex liquid and superheated vortex solid, have been identified. We interpret our results as direct structural evidence for a first-order vortex solid-liquid transition at the peak effect.     

Images of a spin-torque-driven magnetic nano-oscillator

We present the first space- and time-resolved images of the spin-torque-induced steady-state oscillation of a magnetic vortex in a spin-valve nanostructure. We find that the vortex structure in a nanopillar is considerably more complicated than the 2D idealized structure often-assumed, which has important implications for the driving efficiency. The sense of the vortex gyration is uniquely determined by the vortex core polarity, confirming that the spin-torque acts as a source of negative damping even in such a strongly nonuniform magnetic system. The orbit radius is ～10 nm, in agreement with micromagnetic simulations.     

Pinning of vortices in a Bose-Einstein condensate by an optical lattice

We consider the ground state of vortices in a Bose-Einstein condensate. We show that turning on a weak optical periodic potential leads to a transition from the triangular Abrikosov vortex lattice to phases where the vortices are pinned by the optical potential. We discuss the phase diagram of the system for a two-dimensional optical periodic potential with one vortex per optical lattice cell. We also discuss the influence of a one-dimensional optical periodic potential on the vortex ground state. The latter situation has no analog in other condensed-matter systems.     

Spatial structure of a vortex in low density neutron matter

We study in a fully self-consistent approach the structure of a vortex in low density superfluid neutron matter. We determine that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid.     

Magnetization in uniaxial spherical nanoparticles: Consequence on the interparticle interaction

We investigate the interaction between spherical magnetic nanoparticles which present either a single domain or a vortex structure. First the magnetic structure of a uniaxial soft sphere is revisited, and then the interaction energy is calculated from a micromagnetic simulation. In the vortex regime the orientation of the vortex relative to the easy axis depends on both the particle size and the anisotropy constant. We show that the leading term of the interaction is the dipolar interaction energy between the magnetic moments. For particles presenting a vortex structure, we show that the polarization due to the dipolar field must be included. The parameters entering in the dipolar interaction are deduced from the magnetic behavior of the isolated particle.     

Quantitative theory of thermal fluctuations and disorder in the vortex matter

A metastable supercooled homogeneous vortex liquid state exists down to zero fluctuation temperature in systems of mutually repelling objects. The zero temperature liquid state therefore serves as a (pseudo) ‘fixed point’ controlling the properties of vortex liquid below and even around the melting point. Based on this picture, a quantitative theory of vortex melting and glass transition in Type II superconductors in the framework of Ginzburg-Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps are calculated. The point-like disorder shifts the line downwards and joins the order-disorder transition line. On the other hand, the disorder induces irreversible effects via replica symmetry breaking. The irreversibility line can be calculated within the Gaussian variational method. Therefore, the generic phase diagram contains four phases divided by the irreversibility line and melting line: liquid, solid, vortex glass and Bragg glass. We compare various experimental results with the theoretical formula.