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arXiv · 1612.05126

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

J. R. Anglin·A. Schulz
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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.

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J. R. Anglin, A. Schulz. 2016-12-15. Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection. https://doi.org/10.1103/physrevb.95.045430

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