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Abstract

Our previous understanding of transport in disordered system depends on the assumption that there is a well-defined Fermi velocity. The Fermi velocity determines important length scales in the system such as the diffusion length and localization length. However, nearly flat band materials with vanishing Fermi velocity, it is uncertain how to understand the disorder effects and what quantities determine the characteristic length scales in the system. In the clean limit, it is expected that the bulk transport is absent. In this work, we demonstrate, with a 1D Lieb lattice, that disorder can induce diffusion transport in a flat-band system with finite quantum metric. As disorder increases, the bulk transmission channels are activated, and the conductance reaches a maximum before decays inversely with disorder strength. Importantly, via the calculation of the wave-packet dynamics numerically, we show that the quantum metric determines the diffusion length of the system. Analytically, we show that the interplay between the disorder and quantum geometry gives rise to an effective Fermi velocity, as captured by the self-consistent Born approximation. The diffusion coefficient is identified from the Bethe-Salpeter equation under the ladder approximation. Our results reveal a disorder-driven delocalization mechanism in flat-band systems with finite quantum metric which cannot be understood by well-established theories of quantum diffusion. Our theory is important for understanding the disorder effects and transport properties of flat band materials such as twisted bilayer graphene which are current under intense investigation.