Half-Heusler compounds crystallize in a cubic structure with 1:1:1 composition. They attract ample attention because of their flexible electronic structure. By playing with the chemical composition a wide range of materials properties, ground states and functionalities can be realized. New in this respect is the topological insulating ground state, which is insulating in the bulk, but has conducting states at the surface that are protected by topology. This non-trivial topology is related to an inverted band order caused by strong spin-orbit interaction. Yet another attractive aspect is that selected topological half-Heusler compounds, like LaPtBi, YPtBi, LuPtBi and LuPdBi, superconduct. Superconductivity is expected to be unconventional and theory predicts mixed even and odd parity Cooper pair states.
I will present a review of superconductivity in topological half-Heusler compounds, with the focus on a new candidate for topological superconductivity: the semi-metallic noncentrosymmetric half Heusler compound ErPdBi (Y. Pan et al ., Europhysics Letters 104, 27001, 2013). ErPdBi was discovered to superconduct at T c = 1.22 K, but moreover, the Er moments order antiferromagnetically at T N = 1.06 K. Since T c ~ T N , the interaction of superconductivity and magnetism is expected to give rise to a complex ground state. Electronic structure calculations show ErPdBi has a topologically nontrivial band inversion and thus may serve as a new platform to study the interplay of topological states, superconductivity and magnetic order.