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A gap-protected zero-Hall effect state in the quantum limit of the non-symmorphic metal KHgSb

Nature Materials volume 18, pages 443–447 (2019)Cite this article

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Abstract

A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z2 topological insulators by time-reversal symmetry1,2,3. Recently, interest has turned to unusual surface states in the large class of non-symmorphic materials4,5,6,7,8,9,10,11,12. In particular, KHgSb is predicted to exhibit double quantum spin Hall states10. Here we report measurements of the Hall conductivity in KHgSb in a strong magnetic field B. In the quantum limit, the Hall conductivity is observed to fall exponentially to zero, but the diagonal conductivity is finite. A large gap protects this unusual zero-Hall state. We theoretically propose that, in this quantum limit, the chemical potential drops into the bulk gap, intersecting equal numbers of right- and left-moving quantum spin Hall surface modes to produce the zero-Hall state. The zero-Hall state illustrates how topological protection in a non-symmorphic material with glide symmetry may lead to highly unusual transport phenomena.

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Fig. 1: The quantum limit in KHgSb.
Fig. 2: Emergence of a zero-Hall state and gap in sample A4.
Fig. 3: The zero-Hall state in Bi-doped KHgSb (batch B).
Fig. 4: Ab initio band structure of KHgSb near Γ in B = 0 and in strong B.

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Data availability

All of the data displayed in the main text and Supplementary Information are available from S.H.L. (sihangl@princeton.edu) or N.P.O. (npo@princeton.edu) upon request.

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Acknowledgements

The research was supported by the Department of Energy (DE-SC0017863) and the Gordon and Betty Moore Foundation’s EPiQS initiative through grants GBMF4539 (to N.P.O.) and GBMF-4412 (to R.J.C.). The crystal growth and characterization were supported by the ARO MURI on topological insulators (contract W911NF-12-1-0461), and by the US National Science Foundation (grant DMR 1420541). The high-field experiments were performed at both the National High Magnetic Field Lab. NHMFL (Tallahassee) and at the Pulsed Field Facility (Los Alamos National Laboratory). NHMFL is supported by the National Science Foundation Cooperative Agreement no. DMR-1157490, the State of Florida and the US Department of Energy. The theory work was supported by grants to B.A.B. from the Department of Energy DE- SC0016239, Simons Investigator Award and NSF EAGER Award NOA - AWD1004957. B.S. is supported by the NSF STC ‘Center for Integrated Quantum Materials’ under Cooperative Agreement no. DMR-1231319.

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Author notes

  1. Jian Li

    Present address: School of Science, Westlake University, Hangzhou, China

Authors and Affiliations

  1. Department of Physics, Princeton University, Princeton, NJ, USA

    Sihang Liang, Tong Gao, Max Hirschberger, Jian Li, Zhijun Wang, B. A. Bernevig & N. P. Ong

  2. Department of Chemistry, Princeton University, Princeton, NJ, USA

    Satya Kushwaha, Karoline Stolze & R. J. Cava

  3. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Brian Skinner

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Contributions

The experiment was planned by S.L., S.K., R.J.C., Z.W., B.A.B. and N.P.O. S.L. led the measurement effort with assistance from T.G. and M.H. The crystals were grown and characterized by S.K., K.S. and R.J.C. Theoretical support was provided by J.L., Z.W., B.A.B. and B.S. The manuscript was written by N.P.O. with contributions from all authors.

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Correspondence to N. P. Ong.

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Supplementary Information

Supplementary Notes 1–10, Supplementary Table 1, Supplementary References 1–19, Supplementary Figures 1–15

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Liang, S., Kushwaha, S., Gao, T. et al. A gap-protected zero-Hall effect state in the quantum limit of the non-symmorphic metal KHgSb. Nat. Mater. 18, 443–447 (2019). https://doi.org/10.1038/s41563-019-0303-x

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