# Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena

## Abstract

Recent discovery of spin-polarized single-Dirac-cone1,2,3,4,5,6 insulators7,8,9,10,11,12, whose variants can host magnetism13 and superconductivity14, has generated widespread research activity in condensed-matter and materials-physics communities. Some of the most interesting topological phenomena, however, require topological insulators to be placed in multiply connected, highly constrained geometries with magnets and superconductors15,16,17,18,19,20,21, all of which thus require a large number of functional variants with materials design flexibility as well as electronic, magnetic and superconducting tunability. Given the optimum materials, topological properties open up new vistas in spintronics, quantum computing and fundamental physics. We have extended the search for topological insulators from the binary Bi-based series2,3,4,5,6 to the ternary thermoelectric Heusler compounds22,23,24,25. Here we show that, although a large majority of the well-known Heuslers such as TiNiSn and LuNiBi are rather topologically trivial, the distorted LnPtSb-type (such as LnPtBi or LnPdBi, Ln=fn lanthanides) compounds belonging to the half-Heusler subclass harbour Z2=−1 topological insulator parent states, where Z2 is the band purity product index. Our results suggest that half-Heuslers provide a new platform for deriving a host of topologically exotic compounds and their nanoscale or thin-film device versions through the inherent flexibility of their lattice parameter, spin–orbit strength and magnetic moment tunability paving the way for the realization of multifunctional topological devices.

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## Acknowledgements

M.Z.H. acknowledges discussions with B. A. Bernevig and C. L. Kane and support from the US DOE and an A. P. Sloan Research Fellowship. H.L. acknowledges visiting scholar support from Princeton University. A.B. acknowledges support from the DOE. R.J.C. acknowledges discussions and long-standing collaborations with C. Felser and T. Kilmczuk on thermoelectric and superconducting Heusler phases and with Y. S. Hor on ternary topological materials, and support from NSF-MRSEC.

## Author information

Authors

### Contributions

M.Z.H. and R.J.C. conceived the search for multifunctional ternary topological insulators. S.J. and R.J.C. grew the ternary materials; S.J. and S.X. characterized the samples for lattice constants and checked for time-reversal invariance. H.L. carried out the calculations with assistance from M.Z.H.; L.A.W. and Y.X. contributed ideas and to writing the paper; R.J.C., A.B. and M.Z.H. supervised the overall project.

### Corresponding author

Correspondence to M. Zahid Hasan.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

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Lin, H., Wray, L., Xia, Y. et al. Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena. Nature Mater 9, 546–549 (2010). https://doi.org/10.1038/nmat2771

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