General scattering and electronic states in a quantum-wire network of moiré systems

We investigate electronic states in a two-dimensional network consisting of interacting quantum wires, a model adopted for twisted bilayer systems. We construct general operators which describe various scattering processes in the system. In a twisted bilayer structure, the moiré periodicity allows for generalized umklapp scatterings, leading to a class of correlated states at certain fractional fillings. We identify scattering processes which can lead to an insulating gapped bulk with gapless chiral edge modes at fractional fillings, resembling the quantum anomalous Hall effect recently observed in twisted bilayer graphene. Finally, we demonstrate that the description can be useful in predicting spectroscopic and transport features to detect and characterize the chiral edge modes in the moiré-induced correlated states.