Bulk and edge properties of twisted double bilayer graphene

The emergence of controlled, two-dimensional moiré materials^1–6 has uncovered a new platform for investigating topological physics^7–9. Twisted double bilayer graphene has been predicted to host a topologically non-trivial gapped phase with Chern number equal to two at charge neutrality, when half the flat bands are filled^8,9. However, it can be difficult to diagnose topological states using a single measurement because it is ideal to probe the bulk and edge properties at the same time. Here we report a combination of chemical potential measurements, transport measurements and theoretical calculations that show that twisted double bilayer graphene can host metallic edge transport in addition to simultaneously being insulating in the bulk. A Landauer–Büttiker analysis of the measurements on multi-terminal samples allows us to quantitatively assess the edge-state scattering. We interpret these results as signatures of the predicted topological phase at charge neutrality, but further characterization of the edge transport is required to be certain.