Finite-size energy gap in weak and strong topological insulators

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.

16 pages, 18 figures

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• Delocalization of surface Dirac electrons in disordered weak topological insulators
• Effective model for massless Dirac electrons on a surface of weak topological insulators
• Chemical Gating of a Weak Topological Insulator: Bi14Rh3I9
• Engineering Dirac electrons emergent on the surface of a topological insulator
• Finite-size scaling analysis of the conductivity of Dirac electrons on a surface of disordered topological insulators
• Anisotropic Quantum Confinement Effect and Electric Control of Surface States in Dirac Semimetal Nanostructures
• Non-unique connection between bulk topological invariants and surface physics