Abstract
Solid-state physics and quantum electrodynamics, with its ultrarelativistic (massless) particles, meet in the electronic properties of one-dimensional carbon nanotubes, two-dimensional graphene or topological-insulator surfaces. However, clear experimental evidence for electronic states with a conical dispersion relation in all three dimensions, conceivable for certain bulk materials, is still missing. Here, we study a zinc-blende crystal, HgCdTe, at the point of the semiconductor-to-semimetal topological transition. For this compound, we observe three-dimensional massless electrons, as certified from the dynamical conductivity increasing linearly with the photon frequency, with a velocity of about 106 m s−1. Applying a magnetic field B results in a 
-dependence of dipole-active inter-Landau-level resonances and spin splitting of Landau levels also following a 
-dependence—well-established signatures of ultrarelativistic particles but until now not observed experimentally in any solid-state electronic system.
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Acknowledgements
The authors acknowledge helpful discussions with T. Brauner, R. Grill, M. Grynberg, A. A. Nersesyan, V. Novák, M. L. Sadowski and W. Zawadzki. The work has been supported by the ERC project MOMB, by EuroMagNET II under the EU Contract No. 228043, by the GDR-I project ‘Semiconductor sources and detectors of THz frequencies’ and by the Scientific Council of Montpellier II University. We also acknowledge the support received from the Ambassade de France en Russie for the French–Russian collaboration and exchange of PhD students.
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The experiment was proposed by M.O. and M.P.; the underlying theory was formulated by D.M.B. The sample growth was performed by N.N.M. and S.A.D. The sample was characterized by M.S.Z., F.T., W.K. and V.I.G. Magneto-optical experiments were performed by M.O., G.M., M.S.Z., P.N., C.F. and A-L.B. All coauthors discussed the data. M.O., M.P. and D.M.B. wrote the manuscript.
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Orlita, M., Basko, D., Zholudev, M. et al. Observation of three-dimensional massless Kane fermions in a zinc-blende crystal. Nature Phys 10, 233–238 (2014). https://doi.org/10.1038/nphys2857
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DOI: https://doi.org/10.1038/nphys2857
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