Quasiperiodicity enabled quasi-fractal order in 1D narrow-band moiré systems

We demonstrate that quasiperiodicity can modify the ground-state properties of one-dimensional moiré systems compared to their periodic counterparts. We show that although narrow bands enhance the effects of interactions in both commensurate and incommensurate structures, only quasiperiodicity can extend the ordered phase down to an infinitesimal interaction strength. At small interactions, an exotic correlated regime - here dubbed quasi-fractal - can be stabilized. This regime is characterized by charge order at a very large number of wavevectors and cannot be stabilized in the commensurate case, even in the presence of a narrow band. Our findings suggest that quasiperiodicity can be a crucial factor in stabilizing new and interesting types of ordered phases in interacting moiré structures, highlighting multifractal non-interacting phases as particularly promising parent states.