Theory of triangulene two-dimensional crystals

Abstract

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 n a , n b . Combining density functional theory and tight-binding calculations, we find a wealth of half-filled narrow bands, including a graphene-like spectrum (for n a = n b = 2 ), spin-1 Dirac electrons (for n a = 2 , n b = 3 ), p x , y -orbital physics (for n a = n b = 3 ), as well as a gapped system with flat valence and conduction bands (for n a = n b = 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 C 3 symmetry.