Interfaces between buckling phases in silicene: Ab initio density functional theory calculations

The buckled structure of silicene leads to the possibility of new kinds of line defects that separate regions with reversed buckled phases. In the present work we show that these new grain boundaries have very low formation energies, one order of magnitude smaller than grain boundaries in graphene. These defects are stable along different orientations, and they can all be differentiated by scanning tunneling microscopy images. All these defects present local dimerization between the Si atoms, with the formation of $\pi$ bonds. As a result, these defects are preferential adsorption sites when compared to the pristine region. Thus, the combination of low formation energy and higher reactivity of these defects may be cleverly used to design new nanostructures embedded in silicene.

Figure 1

Fully relaxed geometries for the (a) zz-1 interface in the zigzag direction, (b) zz-2 interface in the zigzag direction, (c) arm-1 interface in the armchair direction, and (d) arm-2 interface in the armchair direction. The atoms are colored according to their out-of-plane dislocation ($y$). The gray rectangles emphasize the interface region. Below each structure are presented the bond-length deviations from the pristine silicene ($d^{\text{bulk}}-d$).

Figure 2

DOS and LDOS for the $\alpha$-$\beta$ interfaces: (a) zz-1, (b) zz-2, (c) arm-1, and (d) arm-2. For (a) and (b) the LDOS were calculated around the peaks localized at $-0.814$ and $-0.918$ eV below the Fermi energy, respectively. An energy window of $\pm 0.025$ eV was adopted. For (c) and (d) the LDOS were calculated integrating the states within the energy range $-0.9\le E-E_f\le -0.4$ eV.

Figure 3

(a) Black circles highlighting the rehybridized sites where $U_i$ must be modified for the zz-1, zz-2, arm-1, and arm-2 defects. Energy bands are for the zz-1 structure calculated with (a) DFT and (b) our tight-binding model; (c) and (d) show similar calculations for the arm-1 structure. Tight-binding wave functions for the highest occupied energy band ($k_x=0$) for the (e) zz-1 and (f) arm-1 structures. Here, the tight-binding calculations consider a total of 80 sites ($N=80$).

Figure 4

Images of the STM simulations for the buckling phase interfaces: (a-1) and (a-2) zz-1 interface, (b-1) and (b-2) zz-2 interface, (c) arm-1 interface, and (d) arm-2 interface. The filled (nonfilled) circles represent Si atoms with up (down) shifts. The lines are guides to the eye. The scale bar represent the tip height in Å.

Figure 5

Geometry for a chiral line defect. The angle between the defect direction and the pure zigzag direction is $19.{11}^{\circ }$. Here, the atoms are colored according to their out-of-plane dislocation. The arrow represents the lattice vector along the defect direction.

Figure 6

Schematic representation of the most stable adsorption site of Au over the (a) zz-1, (b) zz-2, (c) arm-1, and (d) arm-2 interfaces.

Figure 7

(a) Diagrammatic representation of the Hamiltonian coupling terms. (b) and (c) Building blocks for the zigzag and armchair structures, enclosed with dashed lines.

Figure 8

(a) Density of states (DOS) of silicene with the arm-2 defect varying the distance between the line defect and its lateral image. For $N=40$ the distance is $3.8$ nm, whereas for $N=400$ the distance is 38 nm. We normalize the absolute value or the DOS by the respective number of sites of the system. Inset: Zoom of the DOS. Also considering the arm-2 defect we show in (b) the modulus square of the wave function of the valence band at $k_x=0$ and $k_z=\pi$. Here, the system has 400 sites ($N=400$). The defect lies in sites 201–204.