Magnetic distillation of intrinsic electric dipoles in mixed-stacking tetralayer graphene

Polytypes of tetralayer graphene (TLG: Bernal, rhombohedral and mixed stacking) offer a choice of crystalline structures with different symmetries. Among those, mixed-stacking tetralayers lack inversion symmetry, which allows for intrinsic spontaneous out-of-plane electrical polarisation, inverted in the mirror-image pair, ABCB and ABAC stackings. Here, we compare the intrinsic polarisation with the symmetry-breaking effect of a substrate. We find that a potential induced by the substrate on the bottom layer of the TLG can generate out-of-plane electric dipole moments with different sizes in all four polytypes and, also, different for the ABCB and ABAC pair. This undermines a straightforward interpretation of experimentally measured Kelvin probe microscopy maps of tetralayer flakes in terms of their intrinsic polarisation. To overcome this difficulty, we analyse the influence of an external magnetic field on electrical polarisation of all four TLGs and find that Landau level quantisation highlights the intrinsic asymmetry of mixed stacking polytypes, making the difference between ABCB and ABAC polarisations almost independent of the substrate effect. We also notice a non-monotonic (hump-like) feature in the polarisation in a magnetic field range of 0.5-3 Tesla, caused by the interplay between time inversion symmetry breaking and spatial inversion symmetry breaking specific for those two polytypes.