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Ternary semiconducting or metallic half-Heusler compounds with an atomic composition 1:1:1 are widely studied for their flexible electronic properties and functionalities. Recently, a new material property of half-Heusler compounds was predicted based on electronic structure calculations: the topological insulator. In topological insulators, the metallic surface states are protected from impurity backscattering due to spin-momentum locking. This opens up new perspectives in engineering multifunctional materials. In this article, we introduce half-Heusler materials from the crystallographic and electronic structure point of view. We present an effective model Hamiltonian from which the topological state can be derived, notably from a non-trivial inverted band structure. We discuss general implications of the inverted band structure with a focus on the detection of the topological surface states in experiments by reviewing several exemplary materials. Special attention is given to superconducting half-Heusler materials, which have attracted ample attention as a platform for non-centrosymmetric and topological superconductivity.
Dirac materials are characterized by exceptional mobility, orders of magnitude higher than any semiconductor, due to the massless pseudorelativistic nature of the Dirac fermions. These systems being semimetallic, the lack of a genuine band-gap poses a serious limitation to their possible applications in electronics. We recently demonstrated that thin TiO2 nanowires can exhibit 1D Dirac states similar to metallic carbon nanotubes, with the crucial difference that these states lie inside the conduction band in proximity of a wide band gap. We analyze the robustness of the Dirac states respect to an Anderson disorder model and substitutional impurity and compare to different one dimensional systems. The results suggest that thin anatase TiO2 nanowires can be a promising candidate material for switching devices.
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