Correlated Electron Research Group (CERG), Advanced Science Institute, RIKEN, Wako, Saitama 351-0198, Japan.
Nat Commun. 2013;4:1524. doi: 10.1038/ncomms2524.
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.
拓扑不变量通常被认为是保护扩展态免受无序影响的原因。一个突出的例子是二维量子霍尔系统以及三维拓扑绝缘体表面存在拓扑保护的扩展态。在这里，我们引入了一个与上述情况不同的新概念——束缚态对杂化的拓扑保护。这种情况在置于三维平凡绝缘体上的二维量子霍尔绝缘体中是可以实现的。在这种配置中，尽管与扩展态的连续谱发生杂化，但仍存在拓扑保护的束缚态，这些束缚态沿二维平面的法向局域化。只要其能量在能带隙内，一维边缘态也沿相同方向局域化。这一发现证明了拓扑不变量的双重作用，因为它们也可以保护连续谱中的束缚态免受杂化的影响。
