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The intersection of two ferromagnetic domain walls placed on the surface oftopological insulators provides a one-way beam splitter for domain-wall Diracfermions. Based on an analytic expression for a static two-soliton magnetictexture we perform a systematic numerical study of the propagation of Diracwave packets along such intersections. A single-cone staggered-grid finitedifference lattice scheme is employed in the numerical analysis. It is shownthat the angle of intersection plays a decisive role in determining thesplitting ratio of the fermion beam. For a non-rectangular intersection, thewidth and, to a lesser extent, the type of domain walls, e.g. Bloch orN{\'e}el, determine the properties of the splitter. As the ratio betweendomain-wall width and transverse localization length of the Dirac fermion isincreased its propagation behavior changes from quantum-mechanical (wave-like)to classical ballistic (particle-like). An electric gate placed near theintersection offers a dynamic external control knob for adjusting the splittingratio.

Dynamics of domain-wall Dirac fermions on a topological insulator: a chiral fermion beam splitter