Cluster Sliding Ferroelectricity in Trilayer Quasi-Hexagonal C$_{60}$
Electric polarization typically originates from non-centrosymmetric charge distributions in compounds. In elemental crystalline materials, chemical bonds between atoms of the same element favor symmetrically distributed electron charges and centrosymmetric structures, making elemental ferroelectrics rare. Compared to atoms, elemental clusters are intrinsically less symmetric and can have various preferred orientations when they are assembled to form crystals. Consequently, the assembly of clusters with different orientations tends to break the inversion symmetry. By exploiting this concept, we show that sliding ferroelectricity naturally emerges in trilayer quasi-hexagonal phase (qHP) C$_{60}$, a cluster-assembled carbon allotrope recently synthesized. Compared to many metallic or semi-metallic elemental ferroelectrics, trilayer qHP C$_{60}$'s have sizable band gaps and several ferroelectric structures, which are distinguishable by measuring their second-harmonic generation (SHG) responses. Some of these phases show both switchable out-of-plane and in-plane polarizations on the order of 0.2 pC/m. The out-of-plane and in-plane polarizations can be switched independently and enable an easy-to-implement construction of Van der Waals homostructures with ferroelectrically switchable chirality.