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Single valley Dirac fermions in zero-gap HgTe quantum wells

Nature Physics volume 7, pages 418–422 (2011)Cite this article

Abstract

Dirac fermions have been studied intensively in condensed matter physics in recent years. Many theoretical predictions critically depend on the number of valleys where the Dirac fermions are realized. We now report the discovery of a two-dimensional system with a single, spin-degenerate Dirac valley. We study the transport properties of HgTe quantum wells grown at a critical thickness where the band gap vanishes. In a magnetic field, we observe quantum Hall plateaux that exhibit the anomalous sequence characteristic of Dirac systems. The filling factors at which the plateaux occur are direct evidence of the presence of a single Dirac valley in the system. Also the conductivity at the Dirac point and its temperature dependence can be understood from single valley Dirac fermion physics. Our observations pave the way to study quantum interference and ballistic transport phenomena of Dirac fermions, which so far have been hard to access.

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Figure 1: Selected band structure properties of HgTe quantum wells.
Figure 2: Quantum Hall data and the identification of a zero-gap sample.
Figure 3: Experimental Landau level fan charts obtained by plotting ∂ σx y/∂ VG in a colour-coded three-dimensional graph as a function of both VG and .
Figure 4: Conductivity of a zero-gap quantum well in the absence of an external magnetic field.

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Acknowledgements

We acknowledge useful discussions with C. Gould and X. L. Qi and thank F. Gerhard and E. Rupp for assistance in sample growth and in the transport experiments. This work was supported by the German Research Foundation DFG (SPP 1285 ‘Halbleiter Spintronik’, DFG-JST joint research project ‘Topological Electronics’, Emmy Noether program (P.R.) and grants AS327/2-1 (E.G.N.) and HA5893/1-1(E.M.H. and G.T.)), the Alexander von Humboldt Foundation (C.X.L. and S.C.Z.) and the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515 (S.C.Z.).

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Authors and Affiliations

  1. Faculty for Physics and Astronomy and Röntgen Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074, Würzburg, Germany

    B. Büttner, C. X. Liu, G. Tkachov, E. G. Novik, C. Brüne, H. Buhmann, E. M. Hankiewicz, P. Recher, B. Trauzettel & L. W. Molenkamp

  2. Department of Physics, McCullough Building, Stanford University, Stanford, California 94305-4045, USA

    S. C. Zhang

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  1. B. Büttner
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  2. C. X. Liu
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  3. G. Tkachov
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  4. E. G. Novik
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  5. C. Brüne
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  6. H. Buhmann
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  7. E. M. Hankiewicz
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  8. P. Recher
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  9. B. Trauzettel
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  10. S. C. Zhang
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  11. L. W. Molenkamp
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Contributions

B.B., C.B., H.B. and L.W.M. have contributed to the experiments, C.X.L., G.T., E.G.N., E.M.H., P.R., B.T. and S.C.Z. contributed to the theory. All authors have participated in the interpretation of the experiments, the paper was written by B.B., C.X.L., S.C.Z., G.T., E.M.H. and L.W.M., and the Supplementary Information by E.G.N., C.X.L., G.T., E.M.H. and L.W.M.

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Correspondence to L. W. Molenkamp.

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Büttner, B., Liu, C., Tkachov, G. et al. Single valley Dirac fermions in zero-gap HgTe quantum wells. Nature Phys 7, 418–422 (2011). https://doi.org/10.1038/nphys1914

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