Moiré pattern assisted commensuration resonance in disordered twisted bilayer graphene

We investigate the mesoscopic transport through a twisted bilayer graphene (TBG) consisting of a clean graphene nanoribbon on the bottom and a disordered graphene disk on the top. We show that, with strong top-layer disorder, the transmission through such a device shows a sequence of resonant peaks with respect to the rotation angle θ, where at the resonant angles θc the disk region contains one giant hexagonal moir\'e supercell. A further investigation shows that the value of θc shows negligible dependence on the disorder strength, the Fermi energy, and the shape distortion, indicating the resonance is a robust commensuration feature of the moir\'e supercell. We explain this commensuration resonance based on the bound states formed inside TBG disk as a result of the nonuniform interlayer coupling, with their average local density of states dominating at the AA stacking region while minimizing at the AB/BA stacking regions. By increasing the interlayer distance, the peak becomes less pronounced which further confirms the role of interlayer coupling. The results presented here suggest a new mechanism to tune the quantum transport signal through the twist angle in disordered moir\'e systems.