Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

Non-Abrikosov vortices in liquid metallic hydrogen

We consider non-Abrikosov vortex solutions in liquid metallic hydrogen (LMH) in the framework of two-component Ginzburg–Landau model. We have shown that there are three types of non-Abrikosov vortices depending on chosen boundary conditions at the core of vortices, namely, Neumann (N)-type, Dirichlet (D)-type and Gross–Pitaevskii (GP)-type vortices. The Neumann-type vortex has a non-vanishing condensation at the core, that is different from the ordinary vortex, and the magnetic flux could be reversed as well in LMH. Furthermore, we have obtained a new type of a neutral vortex which has no magnetic field. The presence of such a vortex is related to metallic superfluid state suggested by Babaev (2004) [1].     

Crystallized vortex crystals

Numerical simulations of the equations of motion of 300 charged particles confined to a plane with an additional magnetic field orthogonal to the plane reproduce recently observed self-organization of non-neutral plasmas into a small number of interacting vortices. In the presence of damping we observe crystallized vortices, i.e. vortices with regular internal structure. We also observe crystallized vortex crystals, i.e. geometric patterns of crystallized vortices. Fractal vortex arrangements are investigated and found to be stable. Our results are relevant for quantum dots and artificial atoms. Received: 24 February 1998 / Revised: 4 March 1998 / Accepted: 4 May 1998     

Fermion zero modes in symmetric vortices in superfluid He

Fermions localized within vortex cores are considered for the simplest most symmetric vortices in the superfluid phases of ³He. Axisymmetric vortices in the A, A₁ and planar phases contain the fermionic condensate with a completely flat band and zero energy. The o-vortex in the B-phase contains 1D Fermi liquids, formed by fermions occupying the branches which cross the zero level. The number of such Fermi liquids increases with increasing external magnetic field. The fermionic spectrum in this vortex is described by the “orbital” and spin momenta interacting with the effective internal magnetic field produced by the vortex and with the external field. Most of the information is obtained using the vortex symmetry which determines symmetry properties of the fermionic spectrum.     

Vortex deconfinement in the XY model with a magnetic field

We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field, the vortices unbind as the magnetic field is lowered in a two-step process: strings of overturned spins first proliferate and then vortices unbind. The transitions are highly continuous but are not of the Kosterlitz-Thouless type. The unbound vortex fixed point is shown to inherit properties of the underlying lattice, in particular containing a set of nodal lines that reflect the lattice symmetry.     

Vortices in a Josephson junction sandwiched between two superconducting waveguides

For a Josephson junction magnetically coupled to the superconducting waveguides enclosing it, solutions to the equation for the difference of the Cooper pair phases over the Josephson junction are found and the corresponding magnetic field values are calculated. Two gaps imposing an upper limit for the vortex velocity are found for free vortices (moving without dissipation). Existence conditions are found for fast vortices in the two high-velocity allowed regions. The dependence of the transport current on vortex velocity is established in cases where the current flows through the Josephson junction only or through the entire structure. A reverse current phenomenon is discovered in which vortices inside allowed velocity regions move opposite to the usual direction.     

Vortex chains induced by anisotropic spin-orbit coupling and magnetic field in spin-2 Bose-Einstein condensates

We investigate the anisotropic spin-orbit coupled spin-2 Bose-Einstein condensates with Ioffe-Pritchard magnetic field. With nonzero magnetic field, anisotropic spin-orbit coupling will introduce several vortices and further generate a vortex chain. Inside the vortex chain, the vortices connect to each other, forming a line along the axis. The physical nature of the vortex chain can be explained by the particle current and the momentum distribution. The vortex number inside the vortex chain can be influenced via varying the magnetic field. Through adjusting the anisotropy of the spin-orbit coupling, the direction of the vortex chain is changed, and the vortex lattice can be triggered. Moreover, accompanied by the variation of the atomic interactions, the density and the momentum distribution of the vortex chain are affected. The realization and the detection of the vortex chain are compatible with current experimental techniques.     

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.     

Interaction and pinning of plane vortices in a three-dimensional Josephson medium and possible distances between two isolated vortices

Within a continuous vortex model, exact expressions are obtained for the Josephson and magnetic energies of plane (laminar) vortices, as well as for the energy and force of pinning by cells in a three-dimensional Josephson medium. If the porosity of the medium is taken into account, the Josephson and magnetic energies of the vortex differ from those for the continuum case. The contributions to the pinning energy from the Josephson and magnetic energies have opposite signs. An algorithm for numerically solving a system of difference equations is proposed in order to find the shape and the energy of the vortex in its stable and unstable states. The continuous vortex model is shown to fail in predicting correct values of the Josephson and magnetic energy of the vortex, as well as of the pinning energy components. Expressions for the least possible distances between two isolated vortices are obtained for a small pinning parameter. Analytical results are in close agreement with computer simulation. An algorithm for numerically solving a system of difference equations is proposed in order to find the least possible distances between two isolated vortices when the pinning parameter I is not small. The minimal value of I at which the center-to-center distance N of the vortices equals three cells is 1.428; for N=2, I _min=1.947. At I>2.907, the vortices can be centered in adjacent cells.     

Noncollinear orientation of external magnetic field and flux lines penetrating an isotropic hard superconductor

Penetration by Abrikosov flux lines of an isotropic hard superconductor in the critical state induced by changes in the orientation of external magnetic field has been theoretically investigated. The analysis has been based on the microscopic nonlocal model taking into account forces of bulk and surface pinning, alongside magnetic forces of interaction of the row of penetrating vortices with existing flux lines, Meissner currents, and vortex images. New vortices penetrate a superconductor only when the angle through which the field is rotated is larger than a certain critical value. It has been determined that the alignment of entering vortices is essentially different from that of the applied magnetic field. The feasibility of detecting noncollinearity effects is discussed. Zh. éksp. Teor. Fiz. 114, 1804–1816 (November 1998)     

具有面内四极磁场的旋转玻色-爱因斯坦凝聚体的基态结构研究

通过虚时演化方法研究了具有面内四极磁场的旋转玻色-爱因斯坦凝聚体的基态结构.结果发现:面内四极磁场和旋转双重作用可导致中央Mermin-Ho涡旋的产生;随着磁场梯度增强,Mermin-Ho涡旋周围环绕的涡旋趋向对称化排布;在四极磁场下,密度相互作用和自旋交换相互作用作为体系的调控参数,可以控制Mermin-Ho涡旋周围的涡旋数目;该体系自旋结构中存在双曲型meron和half-skyrmion两种拓扑结构.     

Attraction between pancake vortices in the crossing lattices of layered superconductors

The intervortex interaction is investigated in very anisotropic layered superconductors in tilted magnetic field. In such a case, the crossing lattice of Abrikosov vortices (AVs) and Josephson vortices (JVs) appears. The interaction between pancake vortices, forming the AVs and JVs, produces the deformation of the AV line. It is demonstrated that, as a result of this deformation, a long range attraction between AVs is induced. This phenomenon is responsible for the dense vortex chain formation. The vortex structure in the weak perpendicular magnetic field is the vortex chain phase, where only a small part of JVs is occupied by AVs.     

磁通运动的电压噪声频谱分析和动力学相变

用Langevin分子动力学方法模拟磁通运动的纵向电压噪声谱随磁场和电流的变化.计算结果表明，外加磁场增大到磁通运动动力学相变场F_P，电压噪声 谱中低频宽带噪声减小而出现洛伦兹形高频窄带噪声.外加磁场增大到熔化场F_m附近，高频窄带噪声 峰值增高 ，峰值对应频率增大.在外加电流增强到磁通弹性运动区域，高频窄带噪声频谱呈现搓衣板 形式.搓衣板高频窄带噪声产生于磁通平移速度的周期性调制，它表明层状超导体中运动的 磁通格子存在有平移序的BG相. 关键词： 第Ⅱ类超导体 电压噪声 动力学模拟     

Magnetic effects on the coalescence of Kelvin-Helmholtz vortices

We simulate the coalescence process of MHD-scale Kelvin-Helmholtz vortices with the electron inertial effects taken into account. Reconnection of highly stretched magnetic field lines within a rolled-up vortex destroys the vortex itself and the coalescence process, which is well known in ordinary fluid dynamics, is seen to be inhibited. When the magnetic field is initially antiparallel across the shear layer, on the other hand, multiple vortices are seen to coalesce continuously because another type of magnetic reconnection prevents the vortex decay. This type of reconnection at the hyperbolic point also changes the field line connectivity and thus leads to large-scale plasma mixing across the shear layer.     

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 phase diagram of F=1 spinor Bose-Einstein condensates

We have calculated the F=1 ground state of a spinor Bose-Einstein condensate trapped harmonic potential with an applied Ioffe-Pitchard magnetic field. The vortex phase diagram is found in the plane spanned by perpendicular and longitudinal magnetic fields. The ferromagnetic condensate has two vortex phases which differ by winding number in the spinor components. The two vortices for the F(z)=-1 antiferromagnetic condensate are separated in space. Moreover, we considered an average local spin || to testify to what extent it is parallel to magnetic field (the nonadiabatic effects). We have shown that the effects are important at vortex cores.     

Multipolar Structure of Equilibrium Shear Flow Field in Toroidal Plasmas

The multipolar velocity field structures are investigated by 2D momentum conservation equation with 3D equilibrium sheared flows in the full toroidal system. Numerical results show that the non-existence of radial velocity field in equilibrium surfaces is suitable only for the zero-order term of our 2D simulation. The non-zero-order radial velocity field is still preserved, even when converted to conventional magnetic surface coordinates. The distribution of velocity field vectors of the order of 1, 2, and 3 are presented respectively in 2, 4, and 6 polar fields with the local vortex structure. The excitation mechanisms of these velocity vortices are the coupling effects of the magneto-fluid structure patterns and the toroidal effects. These results can help us understand the complexity of core physics, the transverse transport across magnetic field by the radial plasma flow and the formation of velocity vortices.     

磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合

本文采用Hasegawa-Wakatani方程组研究磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合。求得非线性方程组的偶极涡旋解。这些解属于本性电磁涡旋,对应的扰动磁场和纵向电流在涡旋边界上是连续的。 关键词：