Dichotomy of Thermodynamic and Transport Properties in Twisted Double-Bilayer Graphene*

The emergence of controlled, two-dimensional moiré materials has uncovered a new platform for investigating topological physics. 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. However, it can be difficult to diagnose topological states using a single measurement. The challenge lies in probing the bulk and edge properties at the same time. A combination of chemical potential measurements, transport measurements, and theoretical calculations provides insight to the band topology of twisted double bilayer graphene. The thermodynamic gap extracted from chemical potential measurements shows that twisted double bilayer graphene is a bulk insulator under an applied transverse electric field, while transport measurements show metallic edge transport. A Landauer-Büttiker analysis of measurements on multi-terminal samples allows us to quantitatively assess edge state scattering. We interpret these results as signatures of the predicted topological phase at charge neutrality.