Self-induced Berry flux and spontaneous non-equilibrium magnetism


When a physical system is governed by statistical or dynamical equations possessing certain symmetries, its stationary states can be classified into phases according to which of those symmetries are preserved, and which are broken1,2. Near equilibrium, the properties of the system’s collective excitations reflect the symmetries of the underlying phase and thereby provide means for detecting these phases3,4. Here, we show that, in driven systems, the collective modes may take on a separate life, exhibiting their own spontaneous symmetry-breaking phenomena independent of the underlying equilibrium phase. We illustrate this principle by demonstrating a mechanism through which a non-magnetic interacting metal subjected to a linearly polarized driving field can spontaneously magnetize. The strong internal a.c. fields of the metal driven close to its plasmonic resonance5,6 enable Berryogenesis: the spontaneous generation of a self-induced Bloch band Berry flux. The self-induced Berry flux supports and is sustained by a chiral circulating plasmonic motion that breaks the mirror symmetry of the system. This non-equilibrium phase transition may be of either continuous or discontinuous type. Berryogenesis can occur in a wide variety of multiband metals with high-quality plasmons, as available in present-day graphene devices7,8,9.

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Fig. 1: Spontaneous generation of Berry flux via plasmonic internal fields.
Fig. 2: Berry flux generation and nonlinear plasmon dynamics.
Fig. 3: Spontaneous magnetization in the presence of a linearly polarized drive.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


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We thank D. Huse, M. Kats, M. Katsnelson, L. Levitov, R. Nandkishore, L. Radzihovsky and G. Refael for helpful discussions. M.S.R. gratefully acknowledges the support of the European Research Council under the European Union Horizon 2020 Research and Innovation Programme (grant agreement no. 678862), and the Villum Foundation. J.C.W.S. gratefully acknowledges the support of the Singapore National Research Foundation (NRF) under NRF fellowship award NRF-NRFF2016-05, and a start-up grant from the Nanyang Technological University.

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M.S.R. and J.C.W.S. designed the research, performed the research and wrote the paper together.

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Correspondence to Mark S. Rudner or Justin C. W. Song.

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Additional theoretical details and refs. 1–15.

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Rudner, M.S., Song, J.C.W. Self-induced Berry flux and spontaneous non-equilibrium magnetism. Nat. Phys. 15, 1017–1021 (2019).

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