Electronic and magnetic properties of graphane nanoribbons

In this study, we investigate the electronic and magnetic properties of graphane nanoribbons. We find that zigzag and armchair graphane nanoribbons with H-passivated edges are nonmagnetic semiconductors. While bare armchair nanoribbons are also nonmagnetic, adjacent dangling bonds of bare zigzag nanoribbons have antiferromagnetic ordering at the same edge. Band gaps of the H-passivated zigzag and armchair nanoribbons exponentially depend on their width. Detailed analysis of adsorption of C, O, Si, Ti, V, Fe, Ge, and Pt atoms on the graphane ribbon surface reveal that functionalization of graphane nanoribbons is possible via these adatoms. It is found that C, O, V, and Pt atoms have tendency to replace H atoms of graphane. We showed that significant spin polarizations in graphane can be achieved through creation of domains of H vacancies and CH divacancies.

Figure 1

(Color online) (a) Top and perspective view of the atomic structure of infinite 2D graphane sheet having honeycomb structure. Two sublattices of graphane are indicated by A and B. Black (dark) and blue (light) balls are for carbon and hydrogen atoms, respectively. (b) Charge density contour plots of diamond and graphane are shown on a plane passing through C-C-C-C and H-C-C-H bonds, respectively. The tetrahedral angle of the diamond ${\theta }_{\text{C}}=109.47°$. Arrows indicate the direction of increasing charge density. The calculated values of ${\theta }_{\text{C}}$ and ${\theta }_{\text{H}}$, namely, C-C-C and H-C-C bond angles in graphane, respectively, are given in Table . Contour spacings are $0.0286\text{e}/{\text{Å}}^3$. (c) The LDA energy-band structure where the orbital character of specific bands is also given. The band gap is shaded yellow/gray.

Figure 2

(Color online) (a) Atomic structure of bare armchair graphane NR having $N=11$. The double unit cell of the nanoribbon is delineated by red/dashed lines with the lattice constant $2a$. Large/black and small/light blue balls indicate carbon and hydrogen atoms. Energy-band structure corresponding to the armchair graphane NR and charge density of selected bands are shown in the panels at the righthand side. (b) Atomic structure of bare zigzag graphane NR having $N=6$ with double unit cell delineated by red/dashed lines and with lattice constant $2a$. Energy-band structure and isosurface charge density of selected states corresponding to zigzag graphane NR are indicated. Bands shown by red/dotted lines are derived from edge states. Zero of energy is set to the Fermi level, shown by dashed-dotted lines, of the nanoribbons with H-passivated edges. In spin polarized calculations double unit cell is used to allow antiferromagnetic order along the edges.

Figure 3

(Color online) Total energies of possible magnetic orderings at the edges of bare zigzag graphane nanoribbons. Calculations are performed in double unit cell delineated by red/dashed lines. Spin-up and spin-down states are shown by green/dark and gray/light isosurfaces of the difference charge density, $\Delta \rho$.

Figure 4

(Color online) Variation in the energy band gap of H-passivated zigzag and armchair NRs of graphane as a function of width given by $N$. The variation in the band gap with $N$ is fitted to the curve given by continuous line. (See text.)

Figure 5

(Color online) Schematic representations of possible positions of adatoms on a large H-passivated armchair graphane nanoribbon. Positions of adatoms obtained after the structure optimization through minimization of total energy and forces exerting on the atoms are also shown.

Figure 6

(Color online) Atomic structures corresponding to single H, double-sided triangular shaped $\Delta 2$ and $\Delta 3$, double-sided rectangular shaped ◻2, CH and ${\text{C}}_2{\text{H}}_2$ vacancies and resulting difference charge density, $\Delta \rho ={\rho }^{(\uparrow )}-{\rho }^{(\downarrow )}$, surfaces for a bare armchair graphane NR. Large/black and small/light blue-gray balls indicate C and H atoms, respectively. Only a small part which includes vacancy region and its nearby atoms, of the armchair graphane NR with $N=15$ is shown.

Figure 7

(Color online) Energy-band diagram and band projected charge-density isosurfaces of various states for bare zigzag graphane NR including edge roughness. The band gap between edge states are shaded yellow/gray. Zero of the band energy is set to the Fermi level.