Vortices, tunneling, and deconfinement in bilayer quantum Hall excitonic superfluid

The physics of vortices, instantons, and deconfinement is studied for layered superfluids in connection to bilayer quantum Hall systems at filling fraction nu = 1. We develop an effective gauge theory taking into account both vortices and instantons induced by interlayer tunneling. The renormalization group flow of the gauge charge and the instanton fugacity shows that the coupling of the gauge field to vortex matter produces a continuous transition between the confining phase of free instantons and condensed vortices and a deconfined gapless superfluid where magnetic charges are bound into dipoles. The interlayer tunneling conductance and the layer-imbalance induced inhomogeneous exciton condensate are discussed in connection to experiments.     

Dynamics of topological multipoles: II. Creation, annihilation, and evolution of nonparaxial optical vortices

The behavior of nonparaxial combined beams transferring two or four optical vortices with opposite topological charges (topological dipole or quadrupole) is studied. The paraxial and nonparaxial approaches are compared. It is shown that the behavior of a topologically neutral wave system is well characterized by the position of a representative point on the parametric plane. It is found that there exists a large region on this plane for which spatial trajectories of the optical vortices, both for dipoles and quadrupoles, do not intersect the focal plane, i.e., the vortices cannot exist within the forbidden zone. At the edges of the forbidden zone, the vortices are either created or annihilated. In contrast, there exists a region on the parametric plane for which the optical vortices can exist only near the waist plane.     

Velocity field vortices and Mermin-Ho vortices in two-component spinor BEC

In light of the φ-mapping topological current theory, two important vortex structures in two-component spinor BEC—the velocity field vortices and the Mermin-Ho vortices are discussed. It is revealed that these two different kinds of vortices are created respectively from the zero points of two different order parameter configurations in the condensates, and both their topological charges, locations and motions can be determined by the φ-mapping theory.     

Disorder induced transitions in layered coulomb gases and superconductors

A 3D layered system of charges with logarithmic interaction parallel to the layers and random dipoles is studied via a novel variational method and an energy rationale which reproduces the known phase diagram for a single layer. Increasing interlayer coupling leads to successive transitions in which charge rods correlated in N>1 neighboring layers are nucleated by weaker disorder. For layered superconductors in the limit of only magnetic interlayer coupling, the method predicts and locates a disorder induced defect-unbinding transition in the flux lattice. While N = 1 charges dominate there, N>1 disorder induced defect rods are predicted for multilayer superconductors.     

Interference of intersecting singular beams

A vorticity of the light field created by interference of two intersecting Laguerre–Gaussian singular beams is analysed. It is demonstrated that the number and location of the vortices present in the field depend on the propagation length as well as on the topological charges of the individual beams, their intersection angle and amplitude ratio.     

Unusual Nernst effect suggesting time-reversal violation in the striped cuprate superconductor La(2-x)Ba(x)CuO4

The striped cuprate La(2-x)Ba(x)CuO(4) (x=1/8) undergoes several transitions below the charge-ordering temperature T(co)=54 K. From Nernst experiments, we find that, below T(co), there exists a large, anomalous Nernst signal e(N,even)(H,T) that is symmetric in field H, and remains finite as H→0. The time-reversal violating signal suggests that, below T(co), vortices of one sign are spontaneously created to relieve interlayer phase frustration.     

Half-plane diffraction of Gaussian beams carrying two vortices of equal charges

This paper derives explicit expressions for the propagation of Gaussian beams carrying two vortices of equal charges m=±1 diffracted at a half-plane screen, which enables the study of the dynamic evolution of vortices in the diffraction field. It shows that there may be no vortices, a pair or several pairs of vortices of opposite charges m=+1, -1 in the diffraction field. Pair creation, annihilation and motion of vortices may appear upon propagation. The off-axis distance additionally affects the evolutionary behaviour. In the process the total topological charge is equal to zero, which is unequal to that of the vortex beam at the source plane. A comparison with the free-space propagation of two vortices of equal charges and a further extension are made.     

脉冲激励下超音速混合层涡结构的演化机理

采用大涡模拟方法对脉冲激励作用下的超音速混合层流场进行数值模拟,所得结果清晰展示了流场中涡结构的独特生长机理.基于涡核位置提取方法,对超音速混合层流场中涡结构的空间尺寸和瞬时对流速度等动态特性进行了定量计算.通过分析流场中涡结构的动态特性在不同频率脉冲激励下的变化,揭示出受脉冲激励超音速混合层流场中涡结构的演化机理:涡结构的生长不再是依靠相邻涡-涡结构之间的配对与融合,而是通过涡核外围的一串小涡旋结构被依次吸进涡核来实现,且受激励流场中各个涡结构的空间尺寸变化较小;流场中的涡结构数量与脉冲频率成正比例关系,而涡结构的空间尺寸与脉冲频率成反比例关系;涡结构的平均对流速度随脉冲频率的增大而减小.针对受脉冲激励超音速混合层,给出了能够表征涡结构特性与脉冲激励参数之间关系的方程式,即受激励流场中涡结构的平均对流速度与脉冲周期的乘积近似等于流场中涡结构的空间尺寸(涡结构平均直径).     

Vortices in weakly coupled layered superconductors

The vortex system in high-temperature layered superconductors exhibits a rich phase diagram with many proposals of phase transitions modifying the correlations both within and between the layers. We focus on the limit where the magnetic coupling between “pancake” vortices dominates over the interlayer Josephson coupling. The weak, but long-ranged nature of this magnetic interaction allows for an accurate “mean-field” treatment where the pancakes in each layer move independently in a self-consistent substrate potential. We calculate the form of the two relevant phase transitions in this system. First, we determine when the substrate potential is too weak to stabilize the two-dimensional (2D) fluctuations and the lattice evaporates to a pancake gas. Second, within the lattice we find a Kosterlitz–Thouless unbinding transition of vacancies and interstitials. For a small but finite Josephson term, this is identified with the phase-decoupling transition.     

Renormalization group studies of phase diagrams of Ising and XY-model films of variable thickness

We compare the critical behavior of $\text{spin}\text{-}\text{1}\text{2}$ Ising model (ordinary phase transition in two dimensions) and classical XY-model (topological phase transition in two dimensions) films, with two flat surfaces and nearest neighbor couplings K_S between surface spins and K_B between all others, as a function of film thickness. We carry out a real space Migdal-style renormalization in two stages. In the bulk stage the film is first renormalized towards a double layer, with the renormalized parameters as inter- and intra-layer couplings. Then the double layer is renormalized with those couplings as initial parameters. From the RG-equations for the bulk stage we find a tricritical point, not only for the Ising model (in which case it is well known) but also for the XY-model. It signals the existence of distinct surface and bulk transitions for sufficiently large values of $\text{K}{}_{\mathrm{<mtext>S</mtext>}}\text{K}{}_{\mathrm{<mtext>B</mtext>}}$. For the Ising model the complete program can be carried out and the phase diagram for films of arbitrary thickness is constructed. For the double layer XY-model a sufficiently complex Migdal-style renormalization appears to be unfeasible, presumably due to the possible presence of strings between the layers. Therefore, in an alternative approach, two representations for the partition function of the double layer XY-model are given. The system can be described in terms of its topological excitations, i.e., vortices on each layer and strings, either closed or terminating in vortices, between them. The system is also written as three coupled Coulomb gases. Based on this representation a renormalization group is found, and used, together with a Griffiths inequality for the correlation functions, to obtain information on the phase diagram. If there is a single phase transition, there is one phase where the correlations exhibit power law behavior and another where they fall off exponentially. The transition temperature increases monotonously with interlayer coupling to twice its value in two dimensions, but the nature of the phase transition for any finite inter-layer coupling appears to be different from that at zero coupling. We suggest that this is associated with the behavior of the internal strings. These results should be relevant for the renormalization of the film with isotropic bulk couplings as well as for layered systems of finite thickness, with different inter- and intra-layer couplings.     

带有相反拓扑指数的光学涡流间相互作用研究

对线性介质中光学涡流间相互作用做了数值分析，发现当拓扑指数相反时，含有涡流对的光场产生了类似于对称破缺的不稳定性，螺旋位错在传播过程中演变为一种新的位错——边位错，作用过程中拓扑指数守恒. 关键词： 光学涡流 拓扑指数 位错     

Vortex structure in superconductors with a many-component order parameter

Abstract

The phenomenological theory of superconductors with a many-component order parameter (OP) is developed. On the basis of a generalized Ginzburg-Landau functional, equations for a two-component-OP superconductor are derived. It is shown that such a superconductor is specified by three length dimensionality parameters—penetration depth λ, correlation length ζ, and width d of the boundary between two superconducting-phase domains. With λ ? d ? ζ, the equations for the OP of a superconductor in a magnetic field can be explored analytically. The transition from the superconducting to the mixed phase may occur not only by the formation of ordinary Abrikosov vortices, but also owing to vortices that have two cores, each transferring a half-integral flux quantum. The total flux transferred by a vortex certainly constitutes an integral quantum. The cores of such a dimer are interconnected by two domain walls, which exercise confinement within the dimer. The distance between the cores in the dimer is of the order of d. Within a domain wall that separates two superconducting-phase domains, a dimer may fall apart into two vortices with a half-integral flux quantum.

For many-component-OP superconductors in a magnetic field, vortex structures of a more complicated nature than a dimer may occur. An individual core may transfer a fractional flux quantum, but the structure as a whole transfers an integral flux quantum. Confinement of individual cores occurs owing to a complicated system of domain walls determined by the topological charges of these vortices.

Under certain conditions, on attaining field H _c1, vortices may arise first in the domain walls, carrying a fractional flux quantum, and then within the superconducting domains.     

Ferromagnet–superconductor hybrids

The new class of phenomena described in this review is based on the interaction between spatially separated, but closely located ferromagnets and superconductors, the so-called ferromagnet–superconductor hybrids (FSH). Typical FSH are: coupled uniform and textured ferromagnetic and superconducting films, magnetic dots over a superconducting film, magnetic nanowires in a superconducting matrix, etc. The interaction is provided by the magnetic field generated by magnetic textures and supercurrents. The magnetic flux from magnetic structures or topological defects can pin vortices or create them, changing the transport properties and transition temperature of the superconductor. On the other hand, the magnetic field from supercurrents (vortices) strongly interacts with the magnetic subsystem, leading to formation of coupled magnetic–superconducting topological defects.

The proximity of ferromagnetic layer dramatically changes the properties of the superconducting film. The exchange field in ferromagnets not only suppresses the Cooper-pair wavefunction, but also leads to its oscillations, which in turn leads to oscillations of observable values: the transition temperature and Josephson current. In particular, in the ground state of the Josephson junction the relative phase of two superconductors separated by a layer of ferromagnetic metal is equal to?π?instead of the usual zero (the so-called π-junction). Such a junction carries a spontaneous supercurrent and possesses other unusual properties. Theory predicts that rotation of magnetization transforms s-pairing into p-pairing. The latter is not suppressed by the exchange field and serves as a carrier of long-range interaction between superconductors.     

Rossby solitary vortices,on giant planets and in the laboratory

This is a review of laboratory experiments with a layer of shallow water having a free surface and rotating together with a vessel of parabolic form. Such a (rather original) setup has allowed one to create Rossby solitary vortex for the first time. The latter is an anticyclonic Rossby vortex not subjected to dispersive spread owing to its compensation by the nonlinearity of KdV type. By its structural, collisional, and other properties, including clear-cut cyclonic-anticyclonic asymmetry, it may be considered as a physical prototype of the large-scale long-lived anticyclonic Rossby vortices like the Great Red Spot of Jupiter or the Great Dark Spot of Neptune (this remarkable vortex was discovered by the spacecraft Voyager-2 during its farewell to the Solar System) and other vortices dominating in the atmospheres of giant planets and created by the unstable zonal flows. It has been shown that the vortex under study is a long-lived entity provided it satisfies "antitwisting condition," i.e., it has rather large amplitude (at which it rotates more quickly than it propagates and thereby carries the trapped fluid). In this case, it is not subjected to the "twisting" deformation and may be ascribed by the generalized Charney-Obukhov equation for Rossby vortices on shallow water with a free surface. The results of creating the vortex under consideration by the different methods have been compared with the results obtained by other authors in the experiments on shear-flow generation of Rossby vortices.     

无序超导体磁通运动的两次退钉扎效应和重新进入超导相

考虑平面内和不同平面磁通之间的相互作用力，计算了无序各向异性超导体中磁通运动的平均速度、微分电阻随驱动力F_l的变化规律，用层间关联函数C_z的值来判断2D塑性流动和3D关联流动的运动图像.观察到随着外驱动力的增大微分电阻出现两个尖峰，它对应着磁通运动存在两次退钉扎现象.在一定层间耦合条件下，在微分电阻双峰之间，可观察到重新进入微分电阻为零的钉扎相.这与最近实验上新发现的无序弱钉扎超导体有重新进入超导相的巨大峰值效应相吻合.同时，也可发现随着驱动电流的增大，磁通运动出现由2D塑性流动到3D弹性流动的相变，这一维度的变化对应着微分电阻dV/dI曲线中的二次峰位置. 并证明当层间耦合(即代表磁场的大小)在一定范围时，3D-2D相变对应的临界电流随磁场的增大而增大, 反映了第二磁化峰附近的磁通格子软硬度改变的微观图像. 关键词： 第Ⅱ类超导体 磁通线格子 钉扎 峰值效应     

Gauge theories of Josephson junction arrays

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with a periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system with an antisymmetric Kalb-Ramond gauge field.     

Vortex sublattice melting in a two-component superconductor

We consider the vortices in a superconductor with two individually conserved condensates in a finite magnetic field. The ground state is a lattice of cocentered vortices in both order parameters. We find two phase transitions: (i) a "vortex sublattice melting" transition where vortices in the field with lowest phase stiffness ("light vortices") lose cocentricity with the vortices with large phase stiffness ("heavy vortices"), entering a liquid state (the structure factor of the light vortices vanishes continuously; this transition is in the 3Dxy universality class); (ii) a first-order melting transition of the lattice of heavy vortices, in a liquid of light vortices.     

Distribution characteristics of intensity and phase vortices of speckle fields produced by N-pinhole random screens

We analyze the distribution properties of phase and phase vortices in a speckle field generated by N-pinhole random screens, and find that the phase vortex distributions show similarity and clustering in local regions. The phase patterns have a lot of sets composed of two phase vortices with opposite signs or four phase vortices which are positive and negative vortices alternately. Cases are also found where two adjacent phase vortices have the same topological charges. The density of phase vortices becomes larger with the increase of the radius of circumference and the number of pinholes on screen.Then, the relative positions of phase vortices can be adjusted by changing the radius of circumference and the number of pinholes.     

Tight focusing properties of linearly polarized Gaussian beam with a pair of vortices

The properties of a pair of vortices embedded in a Gaussian beam focused by a high numerical-aperture are studied on the basis of vector Debye integral. The vortices move and rotate in the vicinity of the focal plane for a pair of vortices with equal topological charges. For incident beam with a pair of vortices with opposite topological charges, the vortices move toward each other, annihilate and revive in the vicinity of focal plane.     

外场作用下铁电/铁磁双层膜的极化磁化性质

建立了铁电/铁磁双层膜模型,铁电层的电矩用连续标量描述,而铁磁层的自旋应用经典矢量描述.利用蒙特卡罗方法模拟了体系的热力学性质和极化、磁化行为.给出了零场下体系的内能、比热、极化和磁化随温度变化的关系,并分别研究了体系在外磁场和外电场下的极化和磁化行为.模拟结果表明,双层膜体系的内能、比热、极化和磁化性质因层间耦合系数的不同而明显不同,当界面耦合较弱时,双层膜表现出各自的热力学性质,当层间耦合增强到一定程度时,双层膜耦合为一个整体,表现出统一的热力学性质.该双层膜在外场中形成电滞回线和磁滞回线,并表现出偏置特性,界面耦合强度和温度影响滞后回线和偏置现象.