Two-dimensional Kagome Lattices Made of Hetero Triangulenes are Dirac Semimetals or Single-Band Semiconductors

In two dimensions, 11 lattice types are mathematically possible, the Kepler nets, but nature offers only few of them in dense crystals. Two-dimensional covalent organic frameworks (2D COFs) offer to overcome this limitation and to provide nets that are to date only possible as photonic lattices or atom-by-atom engineered surface structures. Here we discuss, based on first-principles calculations, 2D kagome lattices composed of polymerized hetero-triangulene units, planar molecules with D3h point group containing a B, C or N center atom and CH₂, O or CO bridges. We explore the design principles for a functional lattice made of COFs, which involves control of π-conjugation and electronic structure of the knots. The former is achieved by the chemical potential of the bridge groups, while the latter is controlled by the heteroatom. The resulting 2D kagome COFs have a characteristic electronic structure with a Dirac band sandwiched by two flat bands and are either Dirac semimetals (C center), or single-band semiconductors - materials with either exclusively electrons (B center) or holes (N center) as charge carriers of very high mobility, reaching values of up to ~8×10³ cm²V^-1s^-1, which is comparable to crystalline silicon. The flat bands show a delocalized electronic structure with no contribution from the center atoms, and their curvature is modulated by the bridge atoms. This suggests that the flat bands are inherent features of the kagome lattice.