How to measure the quantum geometric tensors of Bloch electrons in solids

The geometric properties of quantum states are characterized by the quantum geometric tensors whose real and imaginary parts correspond to the quantum metric and Berry curvature, respectively. Despite its fundamental importance, it is quite challenging to directly visualize their momentum space distribution. Recently, using the circular-dichroic (CD) angle resolved photoemission spectroscopy (ARPES), the momentum space distribution of the local angular momentum was measured. As the local angular momentum is closely related to the local Berry curvature, it was possible to visualize the momentum space distribution of the Berry curvature. However, the distribution of the quantum metric in momentum space has never been observed in solids yet. In this talk, I will explain how the quantum metric as well as the Berry curvature can be measured using the APRES data. Apply this idea to CoSn, I'll show the corresponding distribution of the quantum geometric tensors probed in recent CD-APRES measurement.