Volkov-Pankratov states in topological heterojunctions

We show that a smooth interface between two insulators of opposite topological Z₂ indices possesses multiple surface states, both massless and massive. While the massless surface state is nondegenerate, chiral and insensitive to the interface potential, the massive surface states only appear for a sufficiently smooth heterojunction. The surface states are particle-hole symmetric and a voltage drop reveals their intrinsic relativistic nature, similarly to Landau bands of Dirac electrons in a magnetic field. We discuss the relevance of the massive Dirac surface states in recent angle-resolved photoemission spectroscopy and transport experiments.