We develop a scattering theory for the asymmetric transport observed at interfaces separating
two-dimensional topological insulators. Starting from the spectral decomposition of an
unperturbed interface Hamiltonian, we present a limiting absorption principle and construct
a generalized eigenfunction expansion for perturbed systems. We then relate a physical
observable quantifying the transport asymmetry to the scattering matrix associated to the
generalized eigenfunctions. In particular, we show that the observable is concretely expressed
as a difference of transmission coefficients and is stable against perturbations. We apply
the theory to systems of perturbed Dirac equations with asymptotically linear domain wall.
