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arXiv · 1208.0654

Finite-size energy gap in weak and strong topological insulators

Ken-Ichiro Imura·Mayuko Okamoto·Yukinori Yoshimura·Yositake Takane·Tomi Ohtsuki
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Abstract

The non-trivialness 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 non-trivialness 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, exhibits various scaling behaviors of the gap. The spin-to-surface locking provides one of such gap-opening mechanisms, resulting in a power-law scaling of the energy gap. Weak and strong TI's 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.

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Ken-Ichiro Imura, Mayuko Okamoto, Yukinori Yoshimura, Yositake Takane, Tomi Ohtsuki. 2012-09-26. Finite-size energy gap in weak and strong topological insulators. https://doi.org/10.1103/physrevb.86.245436

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