Theory of triangulene two-dimensional crystals

Abstract

Equilateral triangle-shaped graphene nanoislands with a lateral dimension of n benzene rings are known as [n]triangulenes. Individual [n]triangulenes are open-shell molecules, with single-particle electronic spectra that host n−1 half-filled zero modes and a many-body ground state with spin S = (n−1)/2. The on-surface synthesis of triangulenes has been demonstrated for n = 3, 4, 5, 7 and the observation of a Haldane symmetry-protected topological phase has been reported in chains of [3]triangulenes. Here, we provide a unified theory for the electronic properties of a family of two-dimensional honeycomb lattices whose unit cell contains a pair of triangulenes with dimensions na, nb. Combining density functional theory and tight-binding calculations, we find a wealth of half-filled narrow bands, including a graphene-like spectrum (for na = nb = 2), spin-1 Dirac electrons (for na = 2, nb = 3), px,y-orbital physics (for na = nb = 3), as well as a gapped system with flat valence and conduction bands (for na = nb = 4). All these results are rationalized with a class of effective Hamiltonians acting on the subspace of the zero-energy states that generalize the graphene honeycomb model to the case of fermions with an internal pseudospin degree of freedom with C3 symmetry.