Intrinsic crystal fields and electronic polarizabilities of multilayer graphene with and without twist

We use an original approach combining ab initio calculations and Wannier function formalism to analyze intrinsic crystal fields in multilayer graphene of various stacking configurations. We find that Bernal- and rhombohedral-stacked multilayer graphene features a pronounced out-of-plane intrinsic polarization of the order of 10 mV/Å, which is directed towards the outer layers of the structure. Upon twisting the multilayers, the out-of-plane crystal field weakens significantly and reverses its direction. Twisted multilayer graphene also features a pronounced in-plane crystal field of the order of 10 meV, strongly modulated by the moiré pattern in these structures. We further include explicitly applied external electric field in our ab initio calculations and show that graphene without a twist has highly nonlinear electric-field screening, with its permittivity reaching a pronounced minimum of 2.0–2.5 at certain electric fields. On the contrary, twisted multilayer graphene is found to have a field-independent dielectric response. Overall, our study provides a highly accurate parametrization of intrinsic fields and dielectric properties of graphene multilayers and will enable accurate modelling of devices based on twisted bilayer graphene and other multilayer configurations.