Chiral Majorana Edge Modes and Vortex MajoranaZero Modes in Superconducting Antiferromagnetic TopologicalInsulator

The antiferromagnetic topological insulator (AFTI) is topologically protected by the combined time-reversal and translational symmetry $\mathcal{T}_c$. In this paper we investigate the effects of the $s$-wave superconducting pairings on the multilayers of AFTI, which breaks $\mathcal{T}_c$ symmetry and can realize quantum anomalous Hall insulator with unit Chern number. For the weakly coupled pairings, the system corresponds to the topological superconductor (TSC) with the Chern number $C=\pm 2$. We answer the following questions whether the local Chern numbers and chiral Majorana edge modes of such a TSC distribute around the surface layers. By the numerical calculations based on a theoretic model of AFTI, we find that when the local Chern numbers are always dominated by the surface layers, the wavefunctions of chiral Majorana edge modes must not localize on the surface layers and show a smooth crossover from spatially occupying all layers to only distributing near the surface layers, similar to the hinge states in a three dimensional second-order topological phases. The latter phase, denoted by the hinged TSC, can be distinguished from the former phase by the measurements of the local density of state. In addition we also study the superconducting vortex phase transition in this system and find that the exchange field in the AFTI not only enlarges the phase space of topological vortex phase but also enhances its topological stability. These conclusions will stimulate the investigations on superconducting effects of AFTI and drive the studies on chiral Majorana edge modes and vortex Majorana zero modes into a new era.

Vortex phase diagram in 1111-type CaFe0.89Co0.11AsF single crystal

Studying the vortex properties in high-Tc superconductors is crucial for understanding the high temperature superconducting mechanism. However, until now, only few vortex studies have been performed in 1111-type iron-based superconductors due to their smaller-sized single crystals. In this study, we have synthesized the millimeter-sized CaFe0.89Co0.11AsF single crystals by self-flux method. Three dimensional vortex nature was confirmed in the thermally activated flux flow region. Second magnetization peak was observed on the isothermal magnetization curves. Meanwhile, the dominated role of the normal point pinning was also confirmed. Finally, the various phase boundaries of the vortex were determined based on the analysis of the resistivity and magnetization data, and a complete vortex phase diagram of CaFe0.89Co0.11AsF single crystals was established.

High-Accuracy Surface Profile Measurement Based on the Vortex Phase-Shifting Interferometry

According to the principle of phase-shifting interferometry and spiral phase characteristics of the vortex beam, this article proposes a method for detecting the surface profile of a transparent object, in which the +1 order vortex beam is generated by a spatial light modulator and is taken as the reference light. The influence of the nonlinear phase modulation characteristics of the spatial light modulator on the measurement precision is studied. The results show that nonlinear phase modulation has a great impact on the measurement. Then, the vortex lights with initial phases of 0, π/2, π, and 3π/2 are used to measure the H-type thin film sample based on the Twyman-Green interference system after correcting the nonlinear phase modulation characteristics. The experimental results show that the measurement error of the surface profile to an object with the theoretical value of 20 nm is 1.146 nm, and the feasibility of the optical vortex phase-shifting technique used to measure the surface profile of an object is verified.

Hierarchical self-assembly of polydisperse colloidal bananas into a two-dimensional vortex phase

Self-assembly of microscopic building blocks into highly ordered and functional structures is ubiquitous in nature and found at all length scales. Hierarchical structures formed by colloidal building blocks are typically assembled from monodisperse particles interacting via engineered directional interactions. Here, we show that polydisperse colloidal bananas self-assemble into a complex and hierarchical quasi–two-dimensional structure, called the vortex phase, only due to excluded volume interactions and polydispersity in the particle curvature. Using confocal microscopy, we uncover the remarkable formation mechanism of the vortex phase and characterize its exotic structure and dynamics at the single-particle level. These results demonstrate that hierarchical self-assembly of complex materials can be solely driven by entropy and shape polydispersity of the constituting particles.

Caustics of Non-Paraxial Perfect Optical Vortices Generated by Toroidal Vortex Lenses

In this paper, we consider the comparative formation of perfect optical vortices in the non-paraxial mode using various optical elements: non-paraxial and parabolic toroidal vortex lenses, as well as a vortex axicon in combination with a parabolic lens. The theoretical analysis of the action of these optical elements, as well as the calculation of caustic surfaces, is carried out using a hybrid geometrical-optical and wave approach. Numerical analysis performed on the basis of the expansion in conical waves qualitatively confirms the results obtained and makes it possible to reveal more details associated with diffraction effects. Equations of 3D-caustic surfaces are obtained and the conditions of the ring radius dependence on the order of the vortex phase singularity are analyzed. In the non-paraxial mode, when small light rings (several tens of wavelengths) are formed, a linear dependence of the ring radius on the vortex order is shown. The revealed features should be taken into account when using the considered optical elements forming the POV in various applications.

Contrail formation within cirrus: high-resolution simulations using ICON-LEM

Contrail formation within natural cirrus introduces large perturbations in cirrus ice crystal number concentrations leading to modifications in cirrus microphysical and optical properties. The number of contrail ice crystals formed in an aircraft plume depends on the atmospheric state and aircraft and fuel properties. Our aim is to study the impact of pre-existing cirrus on the contrail formation processes. We analyze contrail ice nucleation within cirrus and the survival of contrail ice crystals within the vortex phase and their change due to the presence of cirrus ice crystals within the high-resolution ICON-LEM at a horizontal resolution of 625 m over Germany. We have selected two different synoptic situations sampling a large range of cirrus cloud properties from very thick cirrus connected with a frontal system to very thin cirrus within a high-pressure system. We find that contrail formation within cirrus often leads to increases in cirrus ice crystal numbers by a few orders of magnitude. Pre-existing cirrus has an impact on contrail ice crystal number concentrations only if the cirrus is optically thick. In thick cirrus, contrail ice nucleation rates and ice crystal survival rates within the vortex phase are both increased. The sublimation of the cirrus ice crystals sucked into and subsequently sublimated within the aircraft’s engine leads to an increase in the contrail formation threshold by up to 0.7 K which causes an increase in the number of nucleated contrail ice crystals. This increase can be large at lower flight levels where ambient temperatures are close to the contrail formation threshold temperature and when the ice water content of the pre-existing cirrus cloud is large. During the contrail’s vortex phase the aircraft plume is trapped within the descending vortices in which the decrease in plume relative humidity leads to the sublimation of contrail ice crystals. This contrail ice crystal loss can be modified by the cirrus ice crystals that are mixed into the plume before the start of the vortex phase. In particular, high ice crystal number concentrations and large ice water content of the pre-existing cirrus cloud or low contrail ice crystal numbers are associated with significant increases in the contrail ice crystal survival rates.

Investigation and modification of the inversed vortex phase field method for phase unwrapping

The paper focuses on the problem of the phase unwrapping in spaceborne remote-sensing interferometric synthesized aperture radar (InSAR) systems. Major unwrapping methods and techniques are considered and the modification of the inversed vortex phase field method of phase unwrapping for interferometric data processing of space-borne synthesized aperture radars is proposed. The modification includes the separation and unwrapping of the low-frequency phase only, and obtaining of the residual phase interferogram, which phase range does not exceed 1-2 ambiguity height values. This approach significantly reduces the number of phase residues and increases the processing speed. The other modification implies filter processing of the residual phase without phase unwrapping, which includes iterative separation of the low-frequency using the Gaussian filter and phase subtraction. This approach moves phase fringes to the relief inflection areas, and is similar to the minimum-cost flow unwrapping results. The computational complexity of the algorithm is proportional to the interferogram size and the number of the phase residues of the low-frequency phase interferogram. The accuracy of digital elevation models obtained by the algorithm was estimated using the ALOS PALSAR radar data and the reference altitude data. The results show, that the accuracy is compared with the minimum-cost flow method, but has the less computational complexity.