Theory of triangulene two-dimensional crystals

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.

Automated summary

We present a unified theory for the electronic properties of a family of two-dimensional honeycomb lattices containing a pair of triangulenes with dimensions n(a),n(b). Our calculations reveal various half-filled narrow bands, including a graphene-like spectrum, spin-1 Dirac electrons, p(x,y)-orbital physics, and a gapped system with flat valence and conduction bands. These results can be rationalized with a class of effective Hamiltonians acting on the subspace of the zero-energy states.