  This paper concerns a boundary integral formulation for the two-dimensional
massive Dirac equation. The mass term is assumed to jump across a
one-dimensional interface, which models a transition between two insulating
materials. This jump induces surface waves that propagate outward along the
interface but decay exponentially in the transverse direction. After providing
a derivation of our integral equation, we prove that it has a unique solution
for almost all choices of parameters using holomorphic perturbation theory. We
then extend these results to a Dirac equation with two interfaces. Finally, we
implement a fast numerical method for solving our boundary integral equations
and present several numerical examples of solutions and scattering effects.
