Half-metallic Dirac cone in zigzag graphene nanoribbons on graphene

The Dirac electrons of graphene, an intrinsic zero gap semiconductor, uniquely carry spin and pseudospin that give rise to many fascinating electronic and transport properties. While isolated zigzag graphene nanoribbons are antiferromagnetic semiconductors, we show by means of first-principles and tight-binding calculations that zigzag graphene nanoribbons supported on graphene are half metallic as a result of spin- and pseudospin-symmetry breaking. In particular, half-metallic Dirac cones are formed at $K \left(K^{\prime }\right)$ near the Fermi level. The present results demonstrate that the unique combination of spin and pseudospin in zigzag graphene nanoribbons may be used to manipulate the electronic properties of graphene, and may have practical implications for potential graphene-based nanoelectronic applications.

Figure 1

Top view of AB stacking hydrogen-terminated AFM-ZGNR on graphene. Green and brown balls represent carbon atoms in the nanoribbon and graphene, respectively. Red arrows denote spins on the edge atoms. The black box represents the unit cell for calculations. A ZGNR with $n$ zigzag chains is denoted by $n$-ZGNR. The nanoribbon here is 8-ZGNR.

Figure 2

DFT-derived electronic bands for AA stacking of 8-ZGNR on graphene. The Fermi level is represented by a dashed line.

Figure 3

DFT bands for AB stacked AFM-ZGNR on graphene for (a) for 8-ZGNR on graphene, and the corresponding (b) graphene- and (c) nanoribbon-weighted bands. (d)–(f) Corresponding bands for 32-ZGNR on graphene. Bands for the freestanding AFM ZGNR are overlaid as blue solid lines for comparison in (b), (c), (e), and (f). Letters L and R stand for the left side and the right side of the nanoribbon, respectively.

Figure 4

Electronic bands around $K$. (a) $k$-projected bands along $\mathrm{\Gamma }\text{−}K$ [cut A in (e)] and (b) perpendicular to $\mathrm{\Gamma }\text{−}K$ [cut B in (e)] for 8-ZGNR on graphene. (c) and (d) Corresponding $k$-projected bands for 32-ZGNR on graphene. (e) BZs of 8-ZGNR on graphene and $1\times 1$ graphene. High symmetry points in each cell are also shown. A and B indicate different cuts about $K$. (f) Schematic illustration of half-metallic Dirac cone in the BZ of graphene.

Figure 5

Electronic bands along $\mathrm{\Gamma }\text{−}X$ near the point where the half-metallic behavior occurs for an 8-AFM-ZGNR on graphene with different supercells corresponding to the ratio (1.75 and 3.5) of the area of the graphene substrate to that of the nanoribbon.

Figure 6

TB calculations of AFM-ZGNRs on graphene for (a) 8-ZGNR and (b) 32-ZGNR. (c) Band structure for 32-ZGNR on graphene when the on-site energies for the top and hollow sites are treated differently and (d) when weak magnetism is induced in the substrate.

Figure 7

Interaction between bands of AFM-ZGNR and graphene. (a) DFT-derived band structures for AFM 32-ZGNR on graphene with respect to different interlayer separations (4.0–5.0 Å). Gap openings at $k_1$ and $k_2$ are labeled by ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$, respectively. (b) TB bands for the isolated systems before interaction. Bands 1 and 2 are the graphene substrate linear dispersions. Bands 3 and 4 are the valence and conduction bands, respectively, of AFM 32-ZGNR. (c) and (d) ${\gamma }_{14}$ and ${\gamma }_{23}$ derived from Eq. (6) for (c) spin up and (d) spin down. The two blue solid lines show the difference between ${\gamma }_{14}$ at $k_1$ and ${\gamma }_{23}$ at $k_2$.

Figure 8

Band-decomposed charge density at $k_2$ for an isolated AFM 32-ZGNR. VB and CB denote the valence band and the conduction band [labeled by 3 and 4, respectively, in Fig. 7]. The two sublattices are colored differently.