Engineering Dirac electrons emergent on the surface of a topological insulator

TL;DR

This paper reviews the unique electronic properties of topological insulator surface states, especially in nanostructures, and discusses their robustness and relation to Dirac and Weyl semimetals.

Contribution

It provides a comprehensive review of finite-size effects, electronic properties, and robustness of surface states in topological insulator nanostructures, contrasting weak and strong TIs.

Findings

Surface states exhibit finite-size effects in nanostructures.

Robustness of surface and bulk states against disorder is analyzed.

Connections between topological insulators and Dirac/Weyl semimetals are discussed.

Abstract

The concept of topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin-orbit coupled materials, some classes of nodal superconductors and superfluid $^3$He, etc. From a technological point of view, topological insulator is expected to serve as a platform for realizing dissipationless transport in a non-superconducting context. The topological insulator exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context contrast the cases of weak and strong TIs. We study robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new perspective of research in the field.