Imaging bulk and edge transport near the Dirac point in graphene moir\'e superlattices

Van der Waals structures formed by aligning monolayer graphene with insulating layers of hexagonal boron nitride exhibit a moir\'e superlattice that is expected to break sublattice symmetry. Despite an energy gap of several tens of millielectron volts opening in the Dirac spectrum, electrical resistivity remains lower than expected at low temperature and varies between devices. While subgap states are likely to play a role in this behavior, their precise nature is unclear. We present a scanning gate microscopy study of moir\'e superlattice devices with comparable activation energy but with different charge disorder levels. In the device with higher charge impurity (~${10}^{10}$ $cm^{-2}$) and lower resistivity (~$10$ $k{\Omega}$) at the Dirac point we observe current flow along the graphene edges. Combined with simulations, our measurements suggest that enhanced edge doping is responsible for this effect. In addition, a device with low charge impurity (~$10^9$ $cm^{-2}$) and higher resistivity (~$100$ $k{\Omega}$) shows subgap states in the bulk, consistent with the absence of shunting by edge currents.