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Pseudo-electromagnetic fields in 3D topological semimetals

Abstract

Dirac and Weyl semimetals react to position-dependent and time-dependent perturbations, such as strain, as if subject to emergent electromagnetic fields, known as pseudo-fields. Pseudo-fields differ from external electromagnetic fields in their symmetries and phenomenology and enable a simple and unified description of a variety of inhomogeneous systems. We review the different physical means of generating pseudo-fields, the observable consequences of pseudo-fields and their similarities to and differences from electromagnetic fields. Among these differences is their effect on quantum anomalies — absences of classical symmetries in the quantum theory — which we revisit from a quantum field theory and a semi-classical viewpoint. We conclude with predicted observable signatures of the pseudo-fields and the status of the nascent experimental research.

Key points

  • Pseudo-electromagnetic fields arise in inhomogeneous Weyl and Dirac semimetals.

  • The action of a pseudo-magnetic field within a Weyl node is indistinguishable from the action of an external magnetic field.

  • Pseudo-magnetic fields generate Landau levels and activate the chiral anomaly for Weyl semimetals.

  • Pseudo-electric fields lead to chiral charge redistribution and ultrasound attenuation.

  • Pseudo-fields have been observed in metamaterials.

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Fig. 1: Physical realizations of emergent pseudo-fields in Weyl semimetals.
Fig. 2: Real and pseudo-magnetic fields.
Fig. 3: Pseudo-electric field and a physical consequence.
Fig. 4: Experimental realizations of pseudo-fields.

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Acknowledgements

The authors thank J. H. Bardarson, J. Behrends, A. Chen, A. Cortijo, Y. Ferreiros, M. Franz, N. Goldman, S. Huber, M. Kolodrubetz, K. Landsteiner, T. Liu, P. Moll, V. Peri, D. Pesin, S. Roy, A. Stern, A. Vishwanath, J. W. F. Venderbos and M. A. H. Vozmediano for discussions and related collaborations. The authors further thank S. Huber and N. Goldman for contributing to Fig. 4, and J. Berhends, V. Peri and K. Landsteiner for their critical reading of the manuscript. R. I. is supported by the ISF (grant no. 1790/18). A.G.G. is supported by the Agence Nationale de la Recherche (ANR) under the grant ANR-18-CE30-0001-01, the Marie Curie programme under EC grant agreement no. 653846 and EC project FET-OPEN SCHINES no. 829044.

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Ilan, R., Grushin, A.G. & Pikulin, D.I. Pseudo-electromagnetic fields in 3D topological semimetals. Nat Rev Phys 2, 29–41 (2020). https://doi.org/10.1038/s42254-019-0121-8

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