vacuum thickness along the z axis is 16 ˚ A to avoid the interaction between graphene layers of adjacent supercells. 

We considered the ˜ A -B Bernal stacking structure for bilayer graphene. Top-view for the bilayer graphene is shown in Fig. 1(a), in which violet color is for the lower layer, and gray color is for the upper layer. Seen from the top-view, ‘ ˜ A’ position in the lower layer coincides with ‘B’ position in the upper layer, ‘A’ position in the upper layer is exactly the center of the hexagon of the lower graphene layer from the top-view, and ‘ ˜ B’ position in the lower layer is right the center of the hexagon of the upper graphene layer. The foreign atom is intercalated between the upper and lower graphene layers and is initially positioned in the middle position of the bilayer distance. Three kinds of initial positions are considered for each intercalated atom: bridge, top and hollow positions, which are noted in the following by using subscript $^{“}$Bri”, “Top”, and “Hol” when needed, for example, we use N$_{Bri}$ to indicates the bilayer system with N atom positioned at the bridge site. Bridge site is above the carbon-carbon bonding in the lower graphene layer, top site indicates the middle position between the coinciding positions ‘ ˜ A’ and ‘B’, and hollow site is just above a carbon atom of the lower graphene layer and simultaneously below the center of a carbon hexagon of the upper layer. The structure relaxation calculations show that, if the intercalated atom is initially positioned at the bridge or hollow site, it will finally be adsorbed to one graphene layer and away from the other layer. While for the top site, the foreign atom will keep being located in t he middle position of the bilayer interval. 

The binding energy is defined as: dE = E$_{graphene}$ + E$_{atom}$$_{−}$ E$_{total}$, where E$_{graphene}$ is the energy of the clean bilayer graphene, E$_{atom}$ stands for the energy of the single foreign atom, and E$_{total}$ is the total energy of the bilayer graphene with the intercalated atom. The binding energy, the distance between the foreign atom and its nearest C atom, and the interlayer distance of the doped bilayer graphene are illustrated in Table I. Comparing the data in Table I, we find both N and O atoms favor the bridge site, while the C atom prefers the hollow site. No intercalated atom is stable at the top site. At the top position, the relaxation calculations show that nearest C-N bonding is about 1.83 ˚ A , and C-O bonding is about 1.74 ˚ A , which is much larger than the typical lengths of C-N (1.47 ˚ A )and C-O (1.42 ˚ A ) [20], implying the physisorption rather than the chemisorption. For the hollow site, O atom is adsorbed to the layer which provides the nearest C atom, and away from the hexagonal 

