Revealing quantum geometry in nonlinear quantum materials

Abstract: This review provides a modern framework for understanding how quantum geometric quantities—such as the quantum metric, Berry curvature, and quantum connection—govern nonlinear responses in quantum materials. We demonstrate how these geometric tensors naturally arise in nonlinear optical effects, subgap responses, and nonlinear transport. Distinguishing responses by energy scale allows a unified physical understanding of excitation processes, lifetimes, and symmetry constraints, revealing the geometric foundations of electron dynamics beyond linear order.

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