On the role of long-wavelength disorder near a continuous bandwidth-tuned metal-insulator transition

Recent experiments in moiré transition metal dichalcogenide materials have reported the observation of a continuous bandwidth-tuned transition from a Fermi liquid metal to a paramagnetic Mott insulator at fixed filling of one electron per moiré unit cell. While interactions play a dominant role in driving the Mott transition and in the disappearance of the electronic Fermi surface, the effects of long-wavelength disorder due to twist-angle inhomogeneities cannot be ignored near the critical point. Building on the theory of a continuous metal-insulator transition at fixed filling in the clean limit, we study the effects of meso-scale inhomogeneities near the critical point on transport and related quantities using the framework of random resistor networks. The results will be placed in the context of recent and ongoing experiments.