Finite-size energy gap in weak and strong topological insulators

TL;DR

This paper investigates how finite-size effects influence the energy gap in weak and strong topological insulators, revealing different scaling behaviors and geometric sensitivities that impact their surface state properties.

Contribution

It introduces a detailed analysis of finite-size energy gaps in topological insulators, highlighting differences between weak and strong TIs and the role of geometry and topological indices.

Findings

Strong TIs exhibit more sensitivity to sample geometry than weak TIs.

Finite-size energy gaps can scale as a power law due to spin-to-surface locking.

Rectangular prism nanowires of strong TIs are more gapped than weak TIs of the same shape.

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.