Ab initio investigation of graphene-based one-dimensional superlattices and their interfaces

We investigate structural and electronic properties of graphene-based one-dimensional (1D) superlattices by means of first-principles calculations. The 1D superlattices are modeled by three different chemical and structural modifications of the carbon lattice. We study partial hydrogenation of graphene, substitution of carbon-atom pairs by boron and nitrogen atoms, and incorporation of ribbons of the recently discovered silicene. Our investigations based on density functional theory provide accurate predictions of structural and electronic properties of all systems under consideration. In detail, the formation of 1D interfaces between two-dimensional honeycomb crystals is studied, including the construction of a coincidence lattice. The importance of the interface for the energy alignment and the Fermi-level position is proven. Finally, we discuss the results in light of the possible realization of a quasi-1D metal.

Figure 1

Superlattice of graphene (black) with $N=5$ boron nitride pairs (green and gray) that substitute 10 carbon atoms (top view). The rectangular unit cell of the superlattice is indicated by solid lines.

Figure 2

Band structure of graphene-BN superlattice with $N=5$ stripes of BN. The band-gap region is clearly distinguished from the regions of the allowed bands.

Figure 3

Rectangular BZ of the superlattice [brown (dark) rectangle] compared with the hexagonal BZ of the original honeycomb crystal [yellow (bright) area]. High-symmetry points in the irreducible part of the BZ as well as one (for $N=5$) folded Dirac point $\overline{\text{K}}$ are indicated.

Figure 4

Band gap of graphene-BN superlattices as a function of the number $N$ of BN stripes. Filled circles correspond to three classes of superlattices, with $N=3n$ (red), $N=3n-1$ (black), and $N=3n-2$ (blue) dimer lines of BN ($n=0,1,...,6$).

Figure 5

Side view of a superlattice of graphene (carbon atoms are dark, hydrogen atoms are bright) with $N=5$ graphane stripes. The lattice period of the superlattice in the $\left[10\overline{1}0\right]$ direction is indicated by vertical lines.

Figure 6

Band structure of a graphene-graphane superlattice with $N=5$ stripes of graphane.

Figure 7

DFT band gap of graphene-graphane superlattices as a function of the number of graphane stripes $N$. The coloring of the filled symbols is analogous to that in Fig. 4

Figure 8

Superlattice of graphene and silicene in top view (a) and side view (b). Plane-averaged charge-density redistribution (c) and corresponding changes of the local potential (d) between the superlattice and the individual materials.

Figure 9

(a) The BZ of graphene, silicene, and the superlattice structure, respectively. Small gray (blue) circles indicate positions of expected Dirac cones of graphene (silicene) in the superlattice BZ. (b) Band structure of the graphene-silicene superlattice along high-symmetry directions. Dirac points found therein are indicated by larger (green) circles. The Fermi level is used as energy 0. The density of states is also given.

Figure 10

(a) Plot of the 2D Dirac cone at the $\Gamma X^{\prime }$ line. The energy at which the two cones touch each other is about 0.45 eV above the Fermi level. (b) A contour plot of the upper band.

Figure 11

Band structure of the graphene-silicene superlattice in Fig. 8 near the short axis $\Gamma X^{\prime }$ of the BZ. Bands around the Fermi level at 0 eV including corresponding Dirac points are displayed. The character of each band state with a certain band index at a given $\mathbf{k}$ vector is described by the atomic $p_z$ orbital contribution and the group IV element. Circles (triangles) describe carbon (silicon) atoms, while the size of the symbol describes the $p_z$ strength.