Intrinsic Bandgap in Twisted Doublebilayer graphene due to Crystal Fields

Electronic properties of twisted graphene multilayers can be engineered by tuning several parameters such as the number of layers, the twist angle, applied electric and magnetic biases, electronic interactions and elastic lattice relaxations. Here, we present an additional parameter: the crystal field. This field occurs due to a potential difference between chemically different atomic species. We experimentally demonstrate that twisted double bilayer graphene (tDBG), encapsulated between hBN layers, exhibits an intrinsic bandgap. By applying an electric field, the gaps in the individual bilayers can be closed, allowing to determine the crystal fields. We find that crystal fields point from the outer to the inner layers with strengths in the bottom/top bilayer Eb = 0.13V/nm ≈ −Et = 0.12V/nm. We show both by means of first principles calculations and low energy models that crystal fields open a band gap in the groundstate. Our results put forward a physical scenario in which a crystal field effect in carbon substantially impacts the low energy properties of tDBG, suggesting that such contributions must be taken into account in other regimes to faithfully predict the electronic properties of twisted graphene multilayers.
[1] P. Rickhaus, Nano Lett. (2019) 19(12) 8821-8829