Half-Heusler topological insulators
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Introduction The discovery of a new class of materials, topological insulators (TIs), has ignited intense research activity in the condensed matter physics and materials science communities. TIs have the extraordinary property that the interior of the material is insulating, while the boundaries host exotic metallic surface states as a result of a non-trivial topology in the band structure.1,2 The existence of TIs was predicted from the electronic band structure of classes of crystalline insulators for generic symmetries, such as time-reversal and charge conjugation symmetries (see Reference 3 for a review and the Introductory article in this issue). Solving the Hamiltonian near the surface of the insulator produces the unique feature of TIs: gapless boundary states with extended wave functions that are protected against deformation or perturbations as long as the topology of the bulk band structure that is characterized by a topological index, called Z2,1,2 is preserved. The topological protection of the metallic surface states is a novel phenomenon in the domain of quantum electronic materials and has generated much excitement in view of its exploitation in fields ranging from spintronics and magnetoelectrics to quantum computation. Topological insulating band order was first predicted and realized in two-dimensional (2D) quantum wells derived from the semimetal HgTe,4,5 but with the predictions and realization of three-dimensional (3D) topological insulators,6–8 the resources for engineering new TIs with concurrent functionalities become almost unlimited. While a 2D TI
is usually a thin film with metallic topological edge states, a 3D TI is an insulating bulk material that exhibits metallic topological surface states on all outer surfaces. The (Bi,Sb)2(Te,Se)3 type of 3D TIs9–12 are currently the most extensively studied TI materials. A crucial ingredient in these is the presence of a “heavy” element (e.g., an element in period 4 or above) that exhibits strong spin–orbit coupling (SOC). The strong SOC gives rise to an additional level crossing (band inversion) that drives the system into a topological phase. In this review, we focus on half-Heusler TIs. HalfHeusler compounds form a vast group of cubic ternary crystalline materials with composition XYZ that are derived from cubic X2YZ compounds named after their discoverer, Fritz Heusler.13 (Half-)Heusler compounds have attracted ample attention not only as multifunctional materials in the fields of spintronics and thermoelectricity, but also as tunable laboratory tools to study a wide range of intriguing physical phenomena, such as half-metallic magnetism, giant magnetoresistance, and Kondo or heavy-fermion physics (for a review see Reference 14). We now may add TI phenomena to this list. Recently, ab initio electronic structure calculations on a series of “heavy-element” half-Heuslers15,16 show that these materials are zero-gap semi-metals, but with a band inversion like that observed in HgTe. The real TI state may subsequently be realized, for instance, by applyi
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