Topological protection of localization against the hybridization

Localization of electronic wave functions is governed by their topological nature as well as the symmetry and dimensionality of the system. Two prominent examples are the presence of the extended states in two-dimensional quantum Hall systems and the absence of localization for the surface states of three dimensional topological insulators. In these cases, the extended states are protected by topological invariants. Here, we show that the two-dimensional quantum Hall system put on the three dimensional trivial insulator manifests a new class of localization phenomena of topological origin, where the two dimensional states remain localized along the surface normal direction in spite of the hybridization with the continuum extended states. The one-dimensional edge channel is also localized along the same direction as long as its energy is within the band gap. This finding demonstrates that the localized states are protected by the topological invariants against the hybridization with the continuum.