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Topology and geometry under the nonlinear electromagnetic spotlight

Nature Materials volume 20, pages 1601–1614 (2021)Cite this article

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Abstract

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this Review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing theoretical ideas, experiments and the materials that drive them. We conclude by discussing how these techniques can be combined with device architectures to uncover, probe and ultimately control quantum phases with emergent topological and correlated properties.

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Fig. 1: Overview of nonlinear approaches and their applications in studying new materials and quantum phases.
Fig. 2: Summary of second-order nonlinear processes.
Fig. 3: Nonlinear responses in topological insulators and inversion-breaking Weyl semimetals.

figure adapted with permission from ref. 70, APS (a); ref. 30, Springer Nature Ltd (b); ref. 78, Springer Nature Ltd (c); ref. 76, Springer Nature Ltd (d, top); ref. 32, APS (d, bottom).

Fig. 4: Nonlinear responses enabled by Berry curvature dipole and valley-contrasting Berry curvature.

figure adapted from ref. 66, Springer Nature Ltd (c); ref. 62, Springer Nature Ltd (d); ref. 64, AAAS (e); ref. 58, Springer Nature Ltd (f).

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Acknowledgements

We thank F. de Juan (Donostia International Physics Center), J. Song (Nanyang Technological University), S. Xu (Harvard University) and Y. Zhang (Massachusetts Institute of Technology) for discussions and critical reading of the manuscript. K.S.B. is grateful for the primary support of the US Department of Energy, Office of Science, Office of Basic Energy Sciences under award no. DE-SC0018675. Q.M. is supported by the Center for the Advancement of Topological Semimetals, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, through the Ames Laboratory under contract DE-AC02-07CH11358 (manuscript preparation and writing). A.G.G. is supported by the ANR under the grant ANR-18-CE30-0001-01 and by the European Union Horizon 2020 research and innovation programme under grant agreement no. 829044 (SCHINES).

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Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Qiong Ma

  2. Department of Physics, Boston College, Chestnut Hill, MA, USA

    Qiong Ma & Kenneth S. Burch

  3. Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France

    Adolfo G. Grushin

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  1. Qiong Ma
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K.S.B. conceived of the project. All authors wrote the manuscript together.

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Correspondence to Kenneth S. Burch.

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Ma, Q., Grushin, A.G. & Burch, K.S. Topology and geometry under the nonlinear electromagnetic spotlight. Nat. Mater. 20, 1601–1614 (2021). https://doi.org/10.1038/s41563-021-00992-7

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