Finite-size energy gap in weak and strong topological insulators

Abstract

The nontrivialness of a topological insulator (TI) is characterized either by a bulk topological invariant or by the existence of a protected metallic surface state. Yet, in realistic samples of finite size, this nontrivialness does not necessarily guarantee the gaplessness of the surface state. Depending on the geometry and on the topological indices, a finite-size energy gap of different nature can appear, and, correspondingly, exhibit various scaling behaviors of the gap. The spin-to-surface locking provides one such gap-opening mechanism, resulting in a power-law scaling of the energy gap. Weak and strong TIs show different degrees of sensitivity to the geometry of the sample. As a noteworthy example, a strong TI nanowire of a rectangular-prism shape is shown to be more gapped than that of a weak TI of precisely the same geometry. © 2012 American Physical Society.