Topological Insulators: Electronic Structure, Material Systems and Applications

Abstract

Topological insulators are a new class of materials characterized by fully spin-polarized surface states, a linear dispersion, imperviousness to external non-magnetic perturbations, and a helical character arising out of the perpendicular spin-momentum locking. This article answers in a pedagogical way the distinction between a topological and normal insulator, the role of topology in band theory of solids, and the origin of these surface states. Numerical techniques including diagonalization of the TI Hamiltonians are described to quantitatively evaluate the behaviour of topological insulator states. The Hamiltonians based on continuum and tight binding approaches are contrasted. The application of TIs as components of a fast switching environment or channel material for transistors is examined through I-V curves. The potential pitfall of such devices is presented along with techniques that could potentially circumvent the problem. Additionally, it is demonstrated that a strong internal electric field can also induce topological insulator behaviour with wurtzite nitride quantum wells as representative materials.