Alright, this one is pretty interesting but, as usual, it needs some amount of background to appreciate it properly. Let me try to make an elementary summary.

Alright, this one is pretty interesting but, as usual, it needs some amount of background to appreciate it properly. Let me try to make an elementary summary. Electrons in a crystal are partially governed by a "quantum metric" on the "Brillouin zone manifold" [1]. Metric tensors on manifolds famously appear in general relativity, and are a central object in differential geometry (hence the accurate moniker "quantum geometry"). "Quantum geometry" is a hot topic in condensed matter physics in the last few years, and governs or is connected to many important quantities. For instance, the integral of the quantum metric is proportional to the conductivity (in the disorder-free regime) [2]. This paper makes a more-or-less direct measurement of the quantum metric in the material CoSn. [1] https://doi.org/10.1007/BF02193559 https://doi.org/10.1007/BF02193559 [2] https://doi.org/10.1103/PhysRev.133.A171 https://doi.org/10.1103/PhysRev.133.A171, https://doi.org/10.1103/PhysRevB.62.1666 https://doi.org/10.1103/PhysRevB.62.1666