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Tunable multifunctional topological insulators in ternary Heusler compounds


Recently the quantum spin Hall effect was theoretically predicted and experimentally realized in quantum wells based on the binary semiconductor HgTe (refs 13). The quantum spin Hall state and topological insulators are new states of quantum matter interesting for both fundamental condensed-matter physics and material science1,2,3,4,5,6,7,8,9,10,11. Many Heusler compounds with C1b structure are ternary semiconductors that are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the bandgap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by the lattice parameter) and magnitude of spin–orbit coupling (by the atomic charge). Based on first-principle calculations we demonstrate that around 50 Heusler compounds show band inversion similar to that of HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantum-well structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare-earth element Ln, which can realize additional properties ranging from superconductivity (for example LaPtBi; ref. 12) to magnetism (for example GdPtBi; ref. 13) and heavy fermion behaviour (for example YbPtBi; ref. 14). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors.

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Figure 1: Comparison of the zinc-blende and the C1b crystal structure.
Figure 2: Bandstructures of CdTe and HgTe compared with ScPtSb and ScPtBi Heuslers.
Figure 3: EΓ6EΓ8 difference calculated for various Heuslers at their experimental lattice constants.
Figure 4: EΓ6EΓ8 difference for YPdBi.
Figure 5: Bandstructure of YPdBi under tetragonal strain (c/a=0.97).


  1. Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    CAS  Article  Google Scholar 

  2. König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    Article  Google Scholar 

  3. Dai, X. et al. Helical edge and surface states in HgTe quantum wells and bulk insulators. Phys. Rev. B 77, 125319 (2008).

    Article  Google Scholar 

  4. Qi, X-L. & Zhang, S-C. The quantum spin Hall effect and topological insulators. Phys. Today 63, 33–38 (2010).

    CAS  Article  Google Scholar 

  5. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    CAS  Article  Google Scholar 

  6. Bernevig, B. A. & Zhang, S. C. Quantum spin Hall effect. Phys. Rev. Lett. 96, 106802 (2006).

    Article  Google Scholar 

  7. Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).

    Article  Google Scholar 

  8. Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008).

    CAS  Article  Google Scholar 

  9. Zhang, H. et al. Topological insulators in Bi2Se3,Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438–442 (2009).

    CAS  Article  Google Scholar 

  10. Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009).

    CAS  Article  Google Scholar 

  11. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3 . Science 325, 178–181 (2009).

    CAS  Article  Google Scholar 

  12. Goll, G. et al. Thermodynamic and transport properties of the noncentrosymmetric superconductor LaBiPt. Physica B 403, 1065–1067 (2008).

    CAS  Article  Google Scholar 

  13. Canfield, P. C. et al. Magnetism and heavy fermion-like behavior in the RBiPt series. J. Appl. Phys. 70, 5800–5802 (1991).

    CAS  Article  Google Scholar 

  14. Fisk, Z. et al. Massive electron state in YbBiPt. Phys. Rev. Lett. 67, 3310–3313 (1991).

    CAS  Article  Google Scholar 

  15. Villars, P. & Calvert, L. D. Pearson’s Handbook of Crystallographic Data for Intermetallic Phases (Amer Soc Metals, 1991).

    Google Scholar 

  16. Qi, X-L., Li, R., Zang, J. & Zhang, S-C. Inducing a magnetic monopole with topological surface states. Science 323, 1184–1187 (2009).

    CAS  Article  Google Scholar 

  17. Li, R., Wang, J., Qi, X-L. & Zhang, S-C. Dynamical axion field in topological magnetic insulators. Nature Phys. 6, 284–288 (2010).

    CAS  Article  Google Scholar 

  18. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    Article  Google Scholar 

  19. Felser, C., Fecher, G. H. & Balke, B. Spintronics: A challenge for materials science and solid-state chemistry. Angew. Chem. Int. Ed. 46, 668–699 (2007).

    CAS  Article  Google Scholar 

  20. Galanakis, I., Dederichs, P. H. & Papanikolaou, N. Slater–Pauling behavior and origin of the half-metallicity of the full-Heusler alloys. Phys. Rev. B 66, 174429 (2002).

    Article  Google Scholar 

  21. Jung, D., Koo, H. J. & Whangbo, M. H. Study of the 18-electron band gap and ferromagnetism in semi-Heusler compounds by non-spin-polarized electronic band structure calculations. J. Mol. Struct. Theochem. 527, 113–119 (2000).

    CAS  Article  Google Scholar 

  22. Galanakis, I., Dederichs, P. H. & Papanikolaou, N. Origin and properties of the gap in the half-ferromagnetic Heusler alloys. Phys. Rev. B 66, 134428 (2002).

    Article  Google Scholar 

  23. Kandpal, H. C., Felser, C. & Seshadri, R. Covalent bonding and the nature of band gaps in some half-Heusler compounds. J. Phys. D 39, 776–785 (2006).

    CAS  Article  Google Scholar 

  24. Sakurada, S. & Shutoh, N. Effect of Ti substitution on the thermoelectric properties of (Zr, Hf)NiSn half-Heusler compounds. Appl. Phys. Lett. 86, 082105 (2005).

    Article  Google Scholar 

  25. von Middendorff, A., Kohler, H. & Landwehr, G. Thermoelectric power of n-type Bi2Se3 in strong transverse magnetic-fields. Phys. Status Solidi B 57, 203–210 (1973).

    CAS  Article  Google Scholar 

  26. Hor, Y. S. et al. p-type Bi2Se8 for topological insulator and low-temperature thermoelectric application. Phys. Rev. B 79, 195208 (2009).

    Article  Google Scholar 

  27. Vosko, S. H., Wilk, L. & Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis. Can. J. Phys. 58, 1200–1211 (1980).

    CAS  Article  Google Scholar 

  28. Dzero, M., Sun, K., Galitski, V. & Coleman, P. Topological Kondo insulators. Phys. Rev. Lett. 104, 106408 (2010).

    Article  Google Scholar 

  29. Qi, X. L., Hughes, T. & Zhang, S. C. Topological invariants for the Fermi surface of a time-reversal-invariant superconductor. Phys. Rev. B 81, 134508 (2010).

    Article  Google Scholar 

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We acknowledge C. X. Liu for discussion. This work is supported by ARO, grant number W911NF-09-1-0508. Financial support by the Deutsche Forschungsgemeinschaft (DFG, research unit FOR 559, project P 07) is gratefully acknowledged.

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All authors contributed equally to the work presented in this Letter.

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Correspondence to Claudia Felser or Shou Cheng Zhang.

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Chadov, S., Qi, X., Kübler, J. et al. Tunable multifunctional topological insulators in ternary Heusler compounds. Nature Mater 9, 541–545 (2010).

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