Direct measurement of the quantum metric of moire flat bands
In plain words
The quantum metric measures how fast electron wavefunctions change across momentum space and is central to flat-band theories, but it has not been measured for the flat bands of moire graphene.
Precise statement
Measure the Brillouin-zone-integrated quantum metric of the magic-angle graphene flat bands, for example through the optical sum rule that relates the frequency integral of $\operatorname{Re}\sigma_{xx}(\omega)/\omega$ for transitions out of a filled band to the integral of its quantum metric, or through polarization-resolved photoemission. An answer is the integrated tr g with uncertainty, compared with continuum-model predictions.
What would settle it
Broadband infrared absorption sum-rule or polarization-resolved photoemission measurements on gated devices compared with continuum-model quantum metric.