▎ 摘　　要

In this paper,we study the quantum size effects in multilayer graphene sheets using first principles methods within the framework of density functional theory. Four different types of functionals are adopted respectively to describe the van der Waals interactions between graphene layer sheets: the DFT-GGA(PBE), the DFT-D2, the vdW-DF and the optPBE-vdW. By inspecting the binding energy as a function of increasing graphene layers, we find that the PBE functional can not well describe the van der Waals interactions between different layers of graphene sheets. In contrast, the other three methods exhibit similar results with monotonic increasing binding energy as a function of graphene layers towards the bulk limit, concluding that the layered graphene structure is stabilized by van der Waals interactions. The density of states at zero temperature indicate that the multilayer graphene sheets is a semi-metal, which is independent of sheet layers number. The finite temperature (about 200 K) density of states at Fermi surface are studied as a function of the number of stacking graphene layers. The systematic oscillating behavior of finite temperature density of states between odd and even number of layers is a demonstration of quantum size effects. The Fermi wavelength will converge to two times the inter-layer distance of graphite, which is consistent with the theory describing the motion of particles in a quantum well. Finally, we study the adsorption of single H atom on multilayer graphene sheets to test the role of quantum size effects. The adsorption energies and the vibration frequencies are calculated for comparison with experiments. Our results shed light on understanding the stacking process of multilayer graphene in vacuum both theoretically and experimentally.