Thermoelectric properties of finite graphene antidot lattices

We present calculations of the electronic and thermal transport properties of graphene antidot lattices with a finite length along the transport direction. The calculations are based on the π-tight-binding model and the Brenner potential. We show that both electronic and thermal transport properties converge fast toward the bulk limit with increasing length of the lattice: only a few repetitions (≃6) of the fundamental unit cell are required to recover the electronic band gap of the infinite lattice as a transport gap for the finite lattice. We investigate how different antidot shapes and sizes affect the thermoelectric properties. The resulting thermoelectric figure of merit, ZT, can exceed 0.25, and it is highly sensitive to the atomic arrangement of the antidot edges. Specifically, hexagonal holes with pure armchair edges lead to an order-of-magnitude larger ZT as compared to pure zigzag edges. We explain this behavior as a consequence of the localization of states, which predominantly occurs for zigzag edges, and of an increased splitting of the electronic minibands, which reduces the power factor S²G_e (S is the Seebeck coefficient and G_e is the electric conductance).