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.

arXiv comment15 pages, 5 figures

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• Current partition at zero-line intersection of quantum anomalous Hall topologies
• Metallic Network of Topological Domain Walls
• Layer Zero-Line Modes in Antiferromagnetic Topological Insulators
• Transport Induced Dimer State from Topological Corner States
• Physical Origin of Current Partition at a Topological Trifurcation
• Valley selecting current partition at zero-line mode of quantum anomalous Hall topologies
• Controlling the Interferometers of Zero-Line Modes in Graphene by Pseudomagnetic field
• Decoherence of charge density waves in beam splitters for interacting quantum wires
• Twisted bilayer graphene as a terahertz plasmonic crystal