Exploring unconventional transport in flat-band systems by quantum geometry

Characterization of the ground state and its excitations is fundamental to understanding the transport properties of any quantum material. Until recently, this mostly meant studying the dispersive features of the band structure and the topological features of the quantum state manifold. The featureless dispersion of flat-band materials challenges this approach since all transport quantities proportional to the quasiparticle velocity vanish. We show how quantum geometry, an emerging field of study with remarkable power to capture the parameter-local properties of the quantum states, can be used to analyze unconventional transport phenomena in flat-band systems. This talk will discuss the role in transport of quantum geometric quantities other than the Berry curvature, such as the quantum metric. Given its broad applicability, quantum geometry is a promising tool for characterizing and understanding multiband systems with non-trivial quantum geometry even beyond flat-band systems.