Spontaneous Electric Polarization in Graphene Polytypes

Spontaneous electric polarization is recently observed in multilayered van der Waals stacked materials, arising from a symmetry breaking in a unit cell with two or more constituent species, or non-centrosymmetric intra-layer atom displacement in single-atom-species materials. Here, it is shown that even elemental crystals, consisting of one type of atom and composed of non-polar and centrosymmetric layers, exhibit electric polarization if arranged in an appropriate three-dimensional architecture. This concept is demonstrated here for mixed-stacking tetra-layer polytypes of non-polar graphene sheets. Surprisingly, it is find that the room temperature out-of-plane electric polarization increases with external electrostatic hole doping, rather than decreases with it owing to screening. Using first-principles calculations, as well as a self-consistent tight-binding model, the emergence of polarization is explain in terms of inter-layer charge rearrangement and the doping dependence in terms of gating-induced inter-layer charge transfer. This newly discovered intrinsic polarization may therefore offer new venues for designing the electronic response of graphene-based polytypes to external fields.