Frustrated magnetism in a cyclacene crystal*

We consider a triangular lattice of short carbon nanorings (cyclacenes). In the single molecule limit, each unit has 2 topologically protected zero modes. As a result, we could expect the low energy bands of the cyclacene crystal to be formed by such zero modes. When Coulomb repulsion is added into this picture, the low energy physics of this system should be similar to a Hubbard model of two weakly coupled triangular lattices. In the strong coupling limit, every ring should host 2 localized electrons, correlated antiferromagnetically with each other, and with the first neighbour ciclacene's, producing antiferromagnetically coupled frustrated S=1/2 triangular lattices. We carry out DFT calculations that confirm the main features of this scenario and show a non-collinear 120 antiferromagnetic phase ground state. Our results show a bottom-up route to engineer correlated electronic phases with narrow bands in carbon-based crystals, complementary to the top-bottom twisted bilayer approach.