Boundary conditions and bound states in lateral topological insulator-based junctions

Topological insulators have been part of many proposals for applications of topological phases of matter. Many of these involve forming interfaces and junctions with other materials. Recent studies have highlighted that, while both surface and interface states satisfy Dirac-like equations at low energies, the spin-momentum locking may differ between the two. We derive the topological boundary conditions for the wavefunction at a lateral junction between the two, connect it with the detailed structure of both potential and magnetic scattering at the junction, and discuss the existence and the properties of the states localized near such junctions.