  Crystal fields occur due to a potential difference between chemically
different atomic species. In Van-der-Waals heterostructures such fields are
naturally present perpendicular to the planes. It has been realized recently
that twisted graphene multilayers provide powerful playgrounds to engineer
electronic properties by the number of layers, the twist angle, applied
electric biases, electronic interactions and elastic relaxations, but crystal
fields have not received the attention they deserve. Here we show that the
bandstructure of large-angle twisted double bilayer graphene is strongly
modified by crystal fields. In particular, we experimentally demonstrate that
twisted double bilayer graphene, encapsulated between hBN layers, exhibits an
intrinsic bandgap. By the application of an external 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 of -0.13 V/nm (0.12 V/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 twisted double bilayer graphene, suggesting that such
contributions must be taken into account in other regimes to faithfully predict
the electronic properties of twisted graphene multilayers.
