Topological protection of bound states against the hybridization

Topological invariants are conventionally known to be responsible for protection of extended states against disorder. A prominent example is the presence of topologically protected extended states in two-dimensional quantum Hall systems as well as on the surface of three-dimensional topological insulators. Here we introduce a new concept that is distinct from such cases-the topological protection of bound states against hybridization. This situation is shown to be realizable in a two-dimensional quantum Hall insulator put on a three-dimensional trivial insulator. In such a configuration, there exist topologically protected bound states, localized along the normal direction of two-dimensional plane, in spite of hybridization with the continuum of extended states. The one-dimensional edge states are also localized along the same direction as long as their energies are within the band gap. This finding demonstrates the dual role of topological invariants, as they can also protect bound states against hybridization in a continuum.