Unexpected Reconstruction of the $\alpha$-Boron (111) Surface

We report a novel reconstruction of the $\alpha$-boron (111) surface, discovered using ab initio evolutionary structure prediction, and show that this unexpected neat structure has a much lower energy than the recently proposed (111)-$I_{R,(a)}$ surface. In this reconstruction, all single interstitial boron atoms bridge neighboring $B_{12}$ icosahedra by polar covalent bonds, and this satisfies the electron counting rule, leading to the reconstruction-induced metal-semiconductor transition. The peculiar charge transfer between the interstitial atoms and the icosahedra plays an important role in stabilizing the surface.

Figure 1

(a) Projection of the $2\times 2\times 1$ supercell of the (111)-$I_{R,(z)}$ structure along the $[111]$ direction. (b) Projection of the $2\times 2\times 1$ supercell of the (111)-$I_{R,(z)}$ structure along the $[\overline{1}\overline{1}2]$ direction. The inequivalent surface atoms are shown by different colors.

Figure 2

Band structures of (a) (111)-I and (b) (111)-$I_{R,(z)}$, the special $k$ points are labeled as $\mathrm{\Gamma }(000)$, $Y(00.50)$, $S(-0.50.50)$, and $X(-0.500)$, respectively.

Figure 3

[(a) and (b)] PDOS of the (111)-I and (111)-$I_{R,(z)}$ structures. [(c) and (d)] PDOS of the $B_p$ and $B_i$ atoms in (111)-$I_{R,(z)}$ structure.

Figure 4

Charge density difference isosurface [45] showing bonding between the adsorbed boron atoms and the substrate. (a) Top view (for clarity, only the adsorbed atoms are shown), (b) side view (showing the substrate).