Stability and electronic properties of two-dimensional silicene and germanene on graphene

We present first-principles calculations of silicene/graphene and germanene/graphene bilayers. Various supercell models are constructed in the calculations in order to reduce the strain of the lattice-mismatched bilayer systems. Our energetics analysis and electronic structure results suggest that graphene can be used as a substrate to synthesize monolayer silicene and germanene. Multiple phases of single crystalline silicene and germanene with different orientations relative to the substrate could coexist at room temperature. The weak interaction between the overlayer and the substrate preserves the low-buckled structure of silicene and germanene, as well as their linear energy bands. The gap induced by breaking the sublattice symmetry in silicene on graphene can be up to 57 meV.

Figure 1

(a) Top and side views of the atomic structure of Si($\sqrt{3}$)/G($\sqrt{7}$) (see text for the definition of the supercell notation), where red and yellow atoms represent the two sublattices of Si atoms separated by $\Delta$ $=$ 0.62 $\AA$ vertically, and the grey spheres represent carbon atoms in the graphene layer at a separation of $D=3.3$ $\AA$ from the lower silicon layer. The lattice vectors ${\vec{a}}_{\text{Si}}$ and ${\vec{a}}_{\text{G}}$ of the (1$\times$1) unit cell of silicene and graphene, respectively, have a relative rotational angle of $10.9^{\circ }$ between them. (b) The first Brillouin zones of Si($\sqrt{3}$)/G($\sqrt{7}$) (orange), 1$\times$1 silicene (white), and 1$\times$1 graphene (purple) are plotted. The blue triangle indicates the path $\Gamma MK$ of the band structure.

Figure 2

Interlayer binding energy per Si atom of the Si($\sqrt{7}$)/G(4) bilayer as a function of interlayer spacing. Results using different exchange-correlation functionals are show. See text for the geometry and the binding energy definition.

Figure 3

Energy per Si or Ge with reference to the bulk value for silicene or germanene on graphene obtained using different supercell models in Table . The results are plotted as a function of strain in the layer.

Figure 4

The relative energy per Si atom (compared with the bulk value) in monolayer silicene, Si($\sqrt{21}$)/G($2\sqrt{13}$), Si${}_n$ cluster, Si${}_n$, and Si${}_n$/G.

Figure 5

Band structure of Si($\sqrt{3}$)/G($\sqrt{7}$): (a) the projected states on Si are highlighted; (b) the projected states on C are highlighted; and (c) the projected bands in (a) and (b) are combined. The substrate-induced gap is about 26 meV for Si ($\Gamma$) and 2 meV for graphene ($K$), respectively.

Figure 6

Band structure of (a) Si(4)/G($\sqrt{39}$), the Dirac point of silicene (graphene) is located at $K$ ($\Gamma$), and (b) Ge($\sqrt{39}$)/G($\sqrt{103}$), the Dirac point of germanene (graphene) is located at $\Gamma$ ($K$).

Figure 7

The angle distribution of silicene bonds over unit cell and the energy gap of Si/G as a function of local strain.