Effects of topological defects and local curvature on the electronic properties of planar graphene

A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon–heptagon pairs and Stone–Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.     

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.     

Topological defects in incommensurate magnetic and crystal structures and quasi-periodic solutions of the elliptic sine-Gordon equation

Vortex-type singular solutions with a topological charge of the elliptic sine-Gordon equation have been studied. One- and two-dimensional vortex lattices on a homogeneous and periodic background are constructed in the explicit form using the Bäcklund transformation. The interaction of vortices is investigated and finite energy configurations are found. On the basis of the obtained results new topological defects in incommensurate magnetic and crystal structures are predicted and described. The interaction of vortex magnetic structures with nonlinear spin waves is considered.     

Dynamical theory of topological defects

A method is presented to obtain stochastic equations of motion for topological defects from the underlying TDGL-like stochastic dissipative field equations. The method makes use of virtual displacements of the Goldstone coordinates of topological defects. Effects of kinematical constraints among Goldstone coordinates are studied. The method is applied to modulated systems and we obtain stochastic equations of motion for interfaces (domain walls) and vortex lines (dislocation or defect lines). The driving force for a vortex line is found to include besides the usual surface tension force a new force due to misfit, which is an analogue of the Magnus force on a quantized vortex line and the Peach-Kochler force on a dislocation. A general expression for interactions between parts of interfaces is obtained in terms of asymptotic forms of field variables far from interfaces.     

A cosmological model for corrugated graphene sheets

Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or other potential defects. In this work we review previous models for topological defects in graphene. A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon–heptagon pairs and Stone-Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.     

Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media

Both azimuthally and radially polarized vortex solitons are investigated to be able to exist in highly nonlocal nonlinear media. We get exactly analytical solutions of azimuthally polarized vortex solitons with only polarization singularities and radially polarized vortex solitons with both phase singularities and polarization singularities. Both azimuthally and radially polarized vortex solitons can exist in nonlocal self-focusing nonlinear media with proper modulation of the beam power and the degree of nonlocality. Contrary to those of radially polarized counterparts in local Kerr media, the topological charge can be any integer. When the topological charge m ≠ 0, both phase singularities and polarization singularities work. When m = 0, the polarization singularities work. Azimuthally polarized vortex solitons with polarization singularities corresponds to the linearly polarized vortex solitons with single charge. Our results show that polarization singularities work the same way as phase singularities in some sense.     

Vortex condensation in the dual Chern–Simons–Higgs model

The contribution of nontrivial vacuum (topological) excitations, more specifically vortex configurations of the self-dual Chern–Simons–Higgs model, to the functional partition function is considered. By using a duality transformation, we arrive at a representation of the partition function in terms of which explicit vortex degrees of freedom are coupled to a dual gauge field. By matching the obtained action to a field theory for the vortices, the physical properties of the model in the presence of vortex excitations are then studied. In terms of this field theory for vortices in the self-dual Chern–Simons–Higgs model, we determine the location of the critical value for the Chern–Simons parameter below which vortex condensation can happen in the system. The effects of self-energy quantum corrections to the vortex field are also considered.     

Onset of motion and dynamic reordering of a vortex lattice

Time resolved transport measurements on a driven vortex lattice in an undoped 2H-NbSe2 crystal show that the response to a current pulse is governed by healing of defects as the lattice evolves from a stationary to a moving steady state and that the response time reflects the degree of order in the initial vortex state. We find that stationary field cooled vortex lattices become more ordered with decreasing temperature and identify a temperature below which a qualitative change in the response signals the disappearance of topological defects.     

Stochastic electromagnetic vortex beam and its propagation

The recent theory formulated in terms of the 2×2 cross-spectral density matrix and the propagation law of cross-spectral density are employed to investigate the stochastic electromagnetic vortex beam and its propagation characterization. Based on these, we derived the general formulae for the intensity distribution, degree of coherence and degree of polarization for stochastic electromagnetic vortex beam while propagating in free space. It is shown that the intensity distribution and the degree of polarization of the stochastic electromagnetic vortex beam propagating in free space depend on the correlation length and the topological charge of the vortex beam.     

Topological charge inversion in polynomial astigmatic Gaussian beams

The evolution of the global topological charge in a general polynomial astigmatic Gaussian beam is investigated. The leading order terms of the polynomial prefactor determines the global topological charge and can be expressed as a product of first order polynomials, each representing an optical vortex function. We show that the global topological charge is bounded by the order of the polynomial and change during propagation in steps of 2 every time one of the optical vortices undergo topological charge inversion. We investigate the locations of the flip planes where charge inversions occur and provide expressions for a number of special cases. Numerical results are provided for an example of such a polynomial astigmatic Gaussian beam.     

Scanning tunneling microscopy study of pinning-induced vortex lattice distortion in ion-irradiated NbSe2

We observe vortex pinning in 2.2 GeV Au-ion irradiated NbSe₂ by scanning tunneling microscopy (STM) at 3K. The ion irradiation generates columnar defects which act as pinning sites. At various external magnetic fields the vortex arrangement is clearly resolved but shows strong distortion. The location of individual defects is extracted from STM data and compared to the vortex arrangement.     

Topological Aspects of Triplet Superconductors

In this paper, using the Φ-mapping theory, it is shown that two kinds of topological defects, i.e., the vortex lines and the monopoles exist in the helical configuration of magnetic field in triplet superconductors. And the inner topological structure of these defects is studied. Because the knot solitons in the triplet superconductors are characterized by the Hopf invariant, we also establish a relationship between the Hopf invariant and the linking number of knots family, and reveal the inner topological structure of the Hopf invariant.     

Focusing of Partially Coherent Vortex Beams by an Aperture Lens

The focusing properties of partially coherent vortex wave fields are studied. Expressions are derived for the intensity distribution and the degree of coherence near the geometrical focus. It is found that the size of coherence vortex dark core in the focal region depends on the topological charges and normalized coherence lengths. It is found that the desired vortex dark core near the geometrical focus can be generated by choosing appropriate values of parameters. The degree of coherence possesses a pair of phase singularities regions in the geometrical focus neighbourhood.     

线偏振相位涡旋光束的像散特性

提出采用像散系数表征涡旋光束的像散特性。利用螺旋相位板产生了线偏振相位涡旋光束,并对其光束质量及像散特性进行了实际测量。数值模拟了不同拓扑荷数的涡旋光束的传输特性及光束质量,分析了像散系数随拓扑荷数变化的规律,结果表明:当拓扑荷数为整数时,光束无像散,像散系数为零;当拓扑荷数为半奇数时,光束的像散特性明显,像散系数达到极大值;随着拓扑荷数整数部分的增加,像散系数的极大值减小。     

Transition micromagnetic structures in the Bloch and Néel asymmetric domain walls containing singular points

A three-dimensional computer simulation of transition structures separated from each other by regions of vortex asymmetric domain walls of the Bloch and Néel types in magnetically uniaxial permalloy films with in-plane anisotropy has been performed. The structures without localized magnetostatic poles on the surface of the film with one or two singular points have been investigated. It has been shown that the singular points and the vortex formations being elements of the domain walls can be considered as topological structures. A method has been proposed for visualizing the topology of magnetic configurations, which is based on the numerical determination of spatial distributions of topological charges of two types.     

Polycrystalline graphene: Atomic structure,energetics and transport properties

Recent experimental investigations show that large-area samples of graphene tend to be polycrystalline. Physical properties of such samples are strongly affected by the presence of intrinsic topological defects of polycrystalline materials—dislocations and grain boundaries. This article reviews recent progress in understanding dislocations and grain boundaries in graphene. First, a systematic approach towards constructing topological defects in graphene is introduced. Then, the review discusses the formation energies of these defects, stressing the dramatic stabilization of dislocations and small-angle grain boundaries in graphene due to the two-dimensional nature of this material. Finally, the electronic transport properties of polycrystalline graphene are considered, showing that topological defects may present novel opportunities towards engineering electronic devices based on graphene.     

Generation of Optical Vortex Using a Spiral Phase Plate Fabricated in Quartz by Direct Laser Writing and Inductively Coupled Plasma Etching

A simple, economical and reliable technique is proposed for fabricating a spiral phase plate （SPP） in a quartz substrate to generate optical vortex with a unit topological charge at the wavelengths of 632.8nm. The spiral phase plate is first formed in the photoresist by direct laser writing lithography and then transferred into the quartz substrate by inductively coupled plasma etching. The performance of the fabricated SPP is verified by using beam intensity distribution, which is in agreement with the theoretical calculation result. The interference measurement suggests that we have succeeded to generate optical vortex with a unit topological charge with the fabricated SPP.     

Antiferromagnetic-vortex dynamics driven by spin-polarized current in small thin disks

We investigate vortex configuration confined in antiferromagnetic thin disks. By virtue of sublattice mismatch at the disk borders, we propose a model that takes such a magnetostatic-like cost into account. The model predicts that onion-like configuration interpolates between curly and divergent vortex. Concerning its dynamics, it is shown that the vortex acquires oscillatory dynamics with well-defined amplitude and frequency that may be controlled on demand by an alternating spin-polarized current. These findings may be useful for the emerging field of antiferromagnetic topological spintronics, once vortex dynamics may be controlled by purely electronic means.     

Estimating topological charge of propagating vortex from single-shot non-imaged speckle

Encoding information using the topological charge of vortex beams has been proposed for optical communications. The conservation of the topological charge on propagation and the detection of the topological charge by a receiver are significant in these applications and have been well established in free-space. However, when vortex beams enter a diffuser,the wavefront is distorted, leading to a challenge in the conservation and detection of the topological charge. Here, we present a technique to measure the value of the topological charge of a vortex beam obscured in the randomly scattered light. The results of the numerical simulations and experiments are presented and are in good agreement. In particular, only a single-shot measurement is required to detect the topological charge of vortex beams, indicating that the method is applicable to a dynamic diffuser.