All-optical probe of the local quantum geometry in a two-dimensional semiconductor

Quantum geometry, which governs many transport and interaction phenomena in solid matter, has become a foundational concept in physics. It plays a crucial role in a wide range of effects, including the quantum Hall effect and resonant optical responses [1]. The quantum geometric tensor provides a direct way to quantify this geometry by describing the distance between quantum states. Its imaginary part corresponds to the Berry curvature, which is directly related to a system’s Chern number and thus to its topology [1]. To date, measurements of the local quantum geometry have been possible only via angle-resolved photoemission spectroscopy [2,3]. However, in one of our recent works [4] we have established a link between linear circular dichroism and derivatives of the Berry curvature in 3D crystals where time-reversal symmetry is preserved.

In the present work, we use a two-dimensional semiconductor to demonstrate both experimentally and with analytical expressions for the nonlinear optical susceptibility that second-harmonic circular dichroism, which arises when time-reversal symmetry is broken, is a direct probe of the Berry curvature differences between opposite momenta of the Brillouin zone. This provides a novel and powerful approach for an all-optical measurements of the local quantum geometry.

[1] Törmä, P., PRL 131, 240001 (2023)

[2] Schüler, M. et al., Sci. Adv. 6, eaaay2730 (2020)

[3] Kang, M. and Kim, S. et al., Nat. Phys. 21, 110–117 (2025)

[4] Soavi, G. and Wilhelm, J., arXiv:2501.03684 (2025)