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Topology and broken Hermiticity

Abstract

Topology and symmetry have emerged as compelling guiding principles to predict and harness the propagation of waves in natural and artificial materials. Be it for quantum particles (such as electrons) or classical waves (such as light, sound or mechanical motion), these concepts have so far been mostly developed in idealized scenarios, in which the wave amplitude is neither attenuated nor amplified, and time evolution is unitary. In recent years, however, there has been a considerable push to explore the consequences of topology and symmetries in non-conservative, non-equilibrium or non-Hermitian systems. A plethora of driven artificial materials has been reported, blurring the lines between a wide variety of fields in physics and engineering, including condensed matter, photonics, phononics, optomechanics, as well as electromagnetic and mechanical metamaterials. Here we discuss the latest advances, emerging opportunities and open challenges for combining these exciting research endeavours into the new pluridisciplinary field of non-Hermitian topological systems.

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Fig. 1: Classification of topological systems and examples of strategies to engineer symmetries and/or break Hermiticity.
Fig. 2: Emergence of topology and broken symmetry in non-Hermitian materials.

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Acknowledgements

We thank the Dutch Institute for Emergent Phenomena for sponsoring the workshop ‘Topology and broken symmetries: from driven quantum matter to active metamaterials’, which took place in Utrecht, the Netherlands from 1 to 3 July 2019, and the workshop participants for insightful discussions that inspired this Perspective. We acknowledge funding by ERC-StG-Coulais-852587-Extr3Me (C.C.) and by the Swiss National Science Foundation under SNSF grant number 172487 and the SNSF Eccellenza award number 181232 (R.F.).

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Correspondence to Corentin Coulais, Romain Fleury or Jasper van Wezel.

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Coulais, C., Fleury, R. & van Wezel, J. Topology and broken Hermiticity. Nat. Phys. 17, 9–13 (2021). https://doi.org/10.1038/s41567-020-01093-z

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