Thermoelectric properties of finite graphene antidot lattices

Abstract

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 $\ensuremath{\pi}$-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 ($\ensuremath{\simeq}$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 ${S}^{2}{G}_{e}$ ($S$ is the Seebeck coefficient and ${G}_{e}$ is the electric conductance).