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

TL;DR

This paper investigates how the intersection angle and domain wall properties on topological insulators influence the behavior of Dirac fermions, demonstrating controllable beam splitting with potential for electronic applications.

Contribution

It provides an analytic and numerical analysis of Dirac fermion propagation at ferromagnetic domain wall intersections, highlighting the impact of geometric and material parameters on beam splitting.

Findings

Intersection angle determines splitting ratio.

Domain wall width and type affect splitter properties.

Electric gate enables dynamic control of splitting ratio.

Abstract

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