摘要 (Abstract)：

Quantum geometry interprets the Hilbert space of quantum states. In this talk, I will cover how quantum geometry can be probed by nonlinear transport and nonlinear magnetization. We survey all the geometric and disorder mechanisms in the second- and third-order nonlinear Hall effects and how they can be distinguished by performing a scaling analysis that expresses the nonlinear Hall conductivity as a polynomial function of the linear longitudinal conductivity. We discover a nonlinear magnetization induced by electric field, described by the Christoffel symbol of Einstein’s general theory of relativity. This quantum Christoffel nonlinear magnetization can be probed by the lock-in magneto-optical Kerr spectroscopy in many 2D materials and gives a paradigm of how geometry dictates physics.

References: Sci. Bull. 71, 4422 (2026); PRX 16, 031012 (2026); PRL 136, 056302 (2026); PRL 135, 216703 (2025); NSR 12, nwae334 (2025).