Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection

Abstract

Numerical simulations in a tight-binding model have shown that an intersection of topologically protected one-dimensional chiral channels can function as a beam splitter for non-interacting fermions on a two-dimensional lattice \cite{Qiao2011,Qiao2014}. Here we confirm this result analytically in the corresponding continuum $\mathbf{k}\cdot \mathbf{p}$ model, by solving the associated two-dimensional Dirac equation, in the presence of a `checkerboard' potential that provides a right-angled intersection between two zero-line modes. The method by which we obtain our analytical solutions is systematic and potentially generalizable to similar problems involving intersections of one-dimensional systems.

15 pages, 5 figures

References in corpus (4)

• Topological confinement in bilayer graphene
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
• Electronic Highways in Bilayer Graphene
• Valley-Hall Kink and Edge States in Multilayer Graphene

Cited by in corpus (4)

• Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve and universal reversible logic gate
• Current partition at zero-line intersection of quantum anomalous Hall topologies
• Transport Induced Dimer State from Topological Corner States
• Twisted bilayer graphene as a terahertz plasmonic crystal