Flat bands and broken symmetry phases in 2D graphene triangulene crystals

Equilateral triangle-shaped graphene nanoislands with lateral dimension of n benzene rings are known as [n]-triangulenes. Individual [n]-triangulenes are open-shell molecules, with single-particle spectra that feature n-1 zero modes at half-filling, and a many-body ground state with total spin S=(n-1)/2. Their on-surface synthesis has been demonstrated for n=2,3,4,5,7. The Haldane phase for 1D chains of spin-1 [3]-triangulenes has been recently observed, showing the potential of triangulenes to create nontrivial quantum states. Here we present mean-field Hubbard calculations of several honeycomb triangulene 2D crystals. In the noninteracting limit, all these crystals feature narrow bands at the Fermi level. We study the emergence of broken symmetry phases as interactions are ramped up.