The geometry of an object indicates its shape or the relationship of its parts to each other. Did you know that the electrons in solids also have geometric structures? In quantum mechanics, an electron in solids takes the form of a wave with periodicity so that the periodic electronic state, so-called the Bloch state, can be characterized by specifying its energy and crystal momentum which is proportional to its wave number. The relationship between the energy and the crystal momentum of electrons is called the band structure of solids. For electrons in solids, the Berry curvature and the quantum metric of Bloch states take the role of the curvature and the distance of an object in geometry.
Source:
https://phys.org/news/2020-08-manifestation-quantum-distance-flat-band.html