The topology of electronic band structures


The study of topology as it relates to physical systems has rapidly accelerated during the past decade. Critical to the realization of new topological phases is an understanding of the materials that exhibit them and precise control of the materials chemistry. The convergence of new theoretical methods using symmetry indicators to identify topological material candidates and the synthesis of high-quality single crystals plays a key role, warranting discussion and context at an accessible level. This Perspective provides a broad introduction to topological phases, their known properties, and material realizations. We focus on recent work in topological Weyl and Dirac semimetals, with a particular emphasis on magnetic Weyl semimetals and emergent fermions in chiral crystals and their extreme responses to excitations, and we highlight areas where the field can continue to make remarkable discoveries. We further examine open questions and directions for the topological materials science community to pursue, including exploration of non-equilibrium properties of Weyl semimetals and cavity-dressed topological materials.

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Fig. 1: Dirac and Weyl physics.
Fig. 2: Large responses of topological materials.


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We thank M. Hopkins (Harvard University), D. Nenno (Harvard University), Y. Wang (Harvard University) and J. Gooth (Max Planck) for fruitful discussions and feedback. P.N. acknowledges helpful discussions with D. Basov (Columbia University) and S. Parkin (Max Planck) on various aspects of this work. This work was supported by the DOE Photonics at Thermodynamic Limits Energy Frontier Research Center under grant no. DE-SC0019140. C.A.C.G. is supported by the NSF Graduate Research Fellowship Program under grant no. DGE-1745303. P.N. is a Moore Inventor Fellow and gratefully acknowledges support through grant GBMF8048 from the Gordon and Betty Moore Foundation, and support as a CIFAR Azrieli Global Scholar.

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P.N., C.A.C.G. and C.F. have all contributed equally to this Perspective, the writing and the ideas presented here.

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Correspondence to Prineha Narang.

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Narang, P., Garcia, C.A.C. & Felser, C. The topology of electronic band structures. Nat. Mater. (2020).

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