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