Substrate, temperature and magnetic field dependence of electric polarisation in mixed-stacking tetralayer graphenes.

Polytypes of tetralayer graphene (TLG: Bernal, rhombohedral and mixed stacking) are 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 [1].

We compare the intrinsic polarisation of such TLGs with the symmetry-breaking effect of a substrate, which can also generate out-of-plane electric dipole moments with different sizes in all four polytypes, including the ABCB and ABAC twins. We analyse their temperature and magnetic field dependence, in view of understanding the origin of the recently measured Kelvin probe force microscopy maps of tetralayer flakes [2], and notice that the intrinsic contribution could be singled out based the unusual magnetic field dependence of polarisation measured at low temperatures.

[1] S. S. Atri, et al. Spontaneous electric polarization in graphene polytypes. Advanced Physics Research, page 2300095, 2023.

[2] A. Garcia-Ruiz, et al. Mixed-Stacking Few-Layer Graphene as an Elemental Weak Ferroelectric Material. Nano Letters, 23(10):4120–4125, 2023.