Topological protection of bound states against the hybridization

TL;DR

This paper introduces a novel form of topological protection that preserves bound states against hybridization with extended states, demonstrated in a 2D quantum Hall insulator on a 3D trivial insulator.

Contribution

It presents the concept of topological protection of bound states against hybridization, expanding the understanding of topological invariants beyond extended states.

Findings

Bound states remain localized despite hybridization with continuum.

Topologically protected edge states are localized within the band gap.

Demonstrates dual role of topological invariants in protecting bound states.

Abstract

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 (2D) quantum Hall systems as well as on the surface of three-dimensional (3D) topological insulators. Distinct from such cases, here we introduce a new concept, that is, the topological protection of bound states against hybridization. This situation is shown to be realizable in a 2D quantum Hall insulator put on a 3D trivial insulator. In such a configuration, there exist topologically protected bound states, localized along the normal direction of 2D 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.