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The current flow along the boundary of graphene stripes in a perpendicular magnetic field is studied theoretically by the nonequilibrium Green's function method. In the case of specular reflections at the boundary, the Hall resistance shows equidistant peaks, which are due to classical cyclotron motion. When the strength of the magnetic field is increased, anomalous resistance oscillations are observed, similar to those found in a nonrelativistic 2D electron gas [New. J. Phys. 15:113047 (2013)]. Using a simplified model, which allows to solve the Dirac equation analytically, the oscillations are explained by the interference between the occupied edge states causing beatings in the Hall resistance. A rule of thumb is given for the experimental observability. Furthermore, the local current flow in graphene is affected significantly by the boundary geometry. A finite edge current flows on armchair edges, while the current on zigzag edges vanishes completely. The quantum Hall staircase can be observed in the case of diffusive boundary scattering. The number of spatially separated edge channels in the local current equals the number of occupied Landau levels. The edge channels in the local density of states are smeared out but can be made visible if only a subset of the carbon atoms is taken into account. [ABSTRACT FROM AUTHOR]

Recent theoretical and experimental attempts have been successful in finding magnetic Weyl semimetal phases, which show nodal‐point structure in the electronic bands as well as magnetic orders. Beyond uniform ferromagnetic or antiferromagnetic orders, nonuniform magnetic textures, such as domain walls and skyrmions, enrich the properties of the Weyl electrons even more in such materials. Here, a topical review on interplay between Weyl electrons and magnetic textures in those magnetic Weyl semimetals is given. The basics of magnetic textures in nontopological magnetic metals are reviewed first, and then the effect of magnetic textures in Weyl semimetals is discussed, regarding the recent theoretical and experimental progress therein. The idea of the fictitious "axial gauge fields" is pointed out, which effectively describes the effect of magnetic textures on the Weyl electrons and can well account for the properties of the electrons localized around magnetic domain walls. [ABSTRACT FROM AUTHOR]

Excitation of a topological insulator by a high‐frequency electric field of a laser radiation leads to a dc electric current in the helical edge channel whose direction and magnitude are sensitive to the radiation polarization and depend on the physical properties of the edge. An overview of theoretical and experimental studies of such edge photoelectric effects in 2D topological insulators based on semiconductor quantum wells is presented. First, a phenomenological description is given of edge photocurrents, which may originate from the photogalvanic effects or the photon drag effects, for edges of all possible symmetry. Then, microscopic mechanisms of photocurrent generation for different types of optical transitions involving helical edge states are discussed. They include direct and indirect optical transitions within the edge channel and edge‐to‐bulk optical transitions. [ABSTRACT FROM AUTHOR]