Topology and geometry under the nonlinear electromagnetic spotlight

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. This Review focuses on nonlinear electromagnetic responses that arise from quantum geometry and topology.

Automated summary

This review highlights recent advances in understanding nonlinear electromagnetic responses that originate from quantum geometry and topology. It focuses on theoretical ideas, experiments, and materials driving this research, with a goal of identifying and controlling quantum properties to explore and ultimately manipulate emergent topological and correlated properties.