Transversal propagation of helical edge states in quantum spin Hall systems

Abstract

The transversal propagation of the edge states in a two-dimensional quantum spin Hall (QSH) system is classified by the characteristic parameter λ. There are two different types of helical edge states, the normal and special edge states, exhibiting distinct behaviors. The penetration depth of the normal edge state is momentum dependent, and the finite gap for edge bands decays monotonously with sample width, leading to the normal finite size effect. In contrast, the penetration depth maintains a uniform minimal value in the special edge states, and consequently the finite gap decays non-monotonously with sample width, leading to the anomalous finite size effect. To demonstrate their difference explicitly, we compared the real materials in phase diagrams. An intuitive way to search for the special edge states in the two-dimensional QSH system is also proposed.