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Field-induced polarization of Dirac valleys in bismuth

Nature Physics volume 8, pages 89–94 (2012)Cite this article

Abstract

The electronic structure of certain crystal lattices can contain multiple degenerate ’valleys’ for their charge carriers to occupy. This valley degree of freedom could be useful in the development of electronic devices. The principal challenge in the development of ’valleytronics’ is to lift the valley degeneracy of charge carriers in a controlled way. Here we show that in semi-metallic bismuth the flow of Dirac fermions along the trigonal axis is extremely sensitive to the orientation of in-plane magnetic field. Thus, a rotatable magnetic field can be used as a valley valve to tune the contribution of each valley to the total conductivity. At high temperature and low magnetic field, bismuth’s three valleys are interchangeable and the three-fold symmetry of its lattice is maintained. As the temperature is decreased or the magnetic field increased, this symmetry is spontaneously lost. This loss may be an experimental manifestation of the recently proposed valley-nematic Fermi liquid state.

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Figure 1: The experimental configuration, the structure of the Fermi surface and angle-dependent magnetoresistance.
Figure 2: The contribution of different components of the Fermi surface to the total conductivity in polar coordinates.
Figure 3: Field-induced valley polarization across a wide temperature range.
Figure 4: Spontaneous loss of three-fold symmetry by lowering the temperature or increasing the magnetic field.
Figure 5: Magnetoresistance data with rotation in two perpendicular planes.
Figure 6: The emerging magnetoresistance anisotropy at different magnetic fields.

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Acknowledgements

We thank Y. Fuseya, A. J. Millis and N. P. Ong for discussions. This work is supported by ANR as part of DELICE and QUANTHERM projects and by a grant attributed by the Ile de France regional council. W.K. is supported by the government of Korea through NRF of Korea Grants (2011-0000982, 0018744, 0019893). We also acknowledge STAR, a France-Korea collaboration program.

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Authors and Affiliations

  1. LPEM (UPMC-CNRS), Ecole Supérieure de Physique et de Chimie Industrielles, 75005 Paris, France

    Zengwei Zhu, Aurélie Collaudin, Benoît Fauqué & Kamran Behnia

  2. Department of Physics, Ewha Womans University, Seoul 120-750, Korea

    Woun Kang

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  1. Zengwei Zhu
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Contributions

Z.Z. and A.C. (assisted by B.F.) carried out the measurements and (assisted by K.B. and B.F.) analysed the data. W.K. made the set-up and obtained the data leading to Fig. 5. K.B. led the project and wrote the paper.

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Correspondence to Kamran Behnia.

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Zhu, Z., Collaudin, A., Fauqué, B. et al. Field-induced polarization of Dirac valleys in bismuth. Nature Phys 8, 89–94 (2012). https://doi.org/10.1038/nphys2111

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