A Clarification on Quantum‐Metric‐Induced Nonlinear Transport

How does the quantum metric truly govern the nonlinear transport? The longstanding theoretical discrepancies are resolved in quantum‐metric‐induced nonlinear transport and the correct intrinsic nonlinear conductivity is identified. Furthermore, a toy model is engineered to suppress the competing effects, uniquely highlighting the role of quantum metric and enabling the future detection of quantum metric in quantum materials. Abstract Over the years, Berry curvature, which is associated with the imaginary part of the quantum geometric tensor, has profoundly impacted many branches of physics. Recently, quantum metric, the real part of the quantum geometric tensor, has been recognized as an indispensable part in comprehensively characterizing the intrinsic properties of condensed matter systems. The intrinsic second‐order nonlinear conductivity induced by the quantum metric has attracted significant recent interest. However, its expression varies across the literature. Here, this discrepancy is reconciled by systematically examining the nonlinear conductivity using the standard perturbation theory, the wave packet dynamics, and the Luttinger–Kohn approach. Moreover, inspired by the Dirac model, a toy model is proposed that suppresses the Berry‐curvature‐induced nonlinear transport, making it suitable for studying the quantum‐metric‐induced nonlinear conductivity. This work provides a clearer and more unified understanding of the quantum‐metric contribution to nonlinear transport. It also establishes a solid foundation for future theoretical developments and experimental explorations in this highly active and rapidly evolving field. How does the quantum metric truly govern the nonlinear transport? The longstanding theoretical discrepancies are resolved in quantum-metric-induced nonlinear transport and the correct intrinsic nonlinear conductivity is identified. Furthermore, a toy model is engineered to suppress the competing effects, uniquely highlighting the role of quantum metric and enabling the future detection of quantum metric in quantum materials. Abstract Over the years, Berry curvature, which is associated with the imaginary part of the quantum geometric tensor, has profoundly impacted many branches of physics. Recently, quantum metric, the real part of the quantum geometric tensor, has been recognized as an indispensable part in comprehensively characterizing the intrinsic properties of condensed matter systems. The intrinsic second-order nonlinear conductivity induced by the quantum metric has attracted significant recent interest. However, its expression varies across the literature. Here, this discrepancy is reconciled by systematically examining the nonlinear conductivity using the standard perturbation theory, the wave packet dynamics, and the Luttinger–Kohn approach. Moreover, inspired by the Dirac model, a toy model is proposed that suppresses the Berry-curvature-induced nonlinear transport, making it suitable for studying the quantum-metric-induced nonlinear conductivity. This work provides a clearer and more unified understanding of the quantum-metric contribution to nonlinear transport. It also establishes a solid foundation for future theoretical developments and experimental explorations in this highly active and rapidly evolving field. Advanced Science, EarlyView.