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Transport, magnetic and optical properties of Weyl materials

Nature Reviews Materials volume 5, pages 621–636 (2020)Cite this article

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Abstract

Weyl fermions were originally proposed as massless Dirac fermions in relativistic quantum field theory. In solids, Weyl fermions often appear when either time-reversal symmetry or spatial-inversion symmetry is broken, which lifts the Kramer’s degeneracy of Bloch states at each crystal momentum k. Weyl fermions in solids are characterized by two novel features: spin–momentum locking and a diverging Berry curvature corresponding to a magnetic monopole forming in momentum space. These two effects bring about many novel transport phenomena, magnetic excitations and nonlinear optical effects. In this Review, we discuss some of these phenomena in various systems, in particular, the anomalous Hall effect and magnon excitation in 3D metallic ferromagnets, transition-metal-oxide semiconductors and semimetals; the quantum anomalous Hall effect, axion insulator state and magnetic skyrmions at the 2D magnetic surface of topological insulators; and nonlinear phenomena in noncentrosymmetric Weyl materials.

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Fig. 1: Properties of the ferromagnetic state of SrRuO3.
Fig. 2: Magnetotransport in the half-Heusler alloy GdPtBi.
Fig. 3: Weyl semimetal phases observed in pyrochlore iridates.
Fig. 4: QAH and axion insulator states and their topological responses.
Fig. 5: Edge channels and skyrmions on the surface of topological insulators.
Fig. 6: Nonlinear Hall effect in bilayer WTe2.
Fig. 7: Quantized circular photovoltaic effect in Weyl semimetals.
Fig. 8: Giant SHG response of the Weyl semimetal TaAs.

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Acknowledgements

We thank Hiroaki Ishizuka, Kentaro Ueda, Kenji Yasuda, Masahi Kawasaki, Joel Moore and Joe Orenstein for the useful discussion and support in preparing the manuscript. This work was supported by JST CREST (nos. JPMJCR16F1 and JPMJCR1874) and JSPS KAKENHI Grant number 18H03676.

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Authors and Affiliations

  1. RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama, Japan

    Naoto Nagaosa & Yoshinori Tokura

  2. Department of Applied Physics, The University of Tokyo, Tokyo, Japan

    Naoto Nagaosa, Takahiro Morimoto & Yoshinori Tokura

  3. Tokyo College, The University of Tokyo, Tokyo, Japan

    Yoshinori Tokura

Authors
  1. Naoto Nagaosa
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  2. Takahiro Morimoto
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  3. Yoshinori Tokura
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All authors contributed to the preparation of the manuscript.

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Correspondence to Naoto Nagaosa.

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Nagaosa, N., Morimoto, T. & Tokura, Y. Transport, magnetic and optical properties of Weyl materials. Nat Rev Mater 5, 621–636 (2020). https://doi.org/10.1038/s41578-020-0208-y

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