  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.
