Topological invariants are conventionally known to be responsible forprotection of extended states against disorder. A prominent example is thepresence of topologically protected extended-states in two-dimensional (2D)quantum Hall systems as well as on the surface of three-dimensional (3D)topological insulators. Distinct from such cases, here we introduce a newconcept, that is, the topological protection of bound states againsthybridization. This situation is shown to be realizable in a 2D quantum Hallinsulator put on a 3D trivial insulator. In such a configuration, there existtopologically protected bound states, localized along the normal direction of2D plane, in spite of hybridization with the continuum of extended states. Theone-dimensional edge states are also localized along the same direction as longas their energies are within the band gap. This finding demonstrates the dualrole of topological invariants, as they can also protect bound states againsthybridization in a continuum.
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