Stabilizing the Zigzag Edge: Graphene Nanoribbons with Sterically Constrained Terminations

The zigzag edge of a graphene nanoribbon is predicted to support a spin-polarized edge state. However, this edge state only survives under a pure $s{p}^2$ termination, and it is difficult to produce thermodynamic conditions that favor a pure $s{p}^2$ termination of a graphene edge, since the edge carbons generally prefer to bond to two hydrogen atoms in $s{p}^3$ hybridization, rather than one hydrogen, as $s{p}^2$. We describe how to use the steric effects of large, bulky ligands to modify the thermodynamics of edge termination and favor the $s{p}^2$ edge during, e.g., chemical vapor deposition. Ab initio calculations demonstrate that these alternative terminations can support robust edge states across a broad range of thermodynamic conditions. This method of exploiting steric crowding effects along the one-dimensional edge of a two-dimensional system may be a general way to control edge reconstructions across a range of emerging single-layer systems.

Figure 1

Top: Three possible edge terminations for a zigzag graphene nanoribbon: pure $s{p}^2$ ($Z_1$), pure $s{p}^3$ ($Z_2$), and a mixed state ($Z_{21}$) with alternating configurations. Center: A reconstructed zigzag edge with alternating pentagon and heptagon rings. Bottom: Other kinds of defective zigzag edges. All distances are in units of angstroms.

Figure 2

A schematic diagram showing the distances between terminating groups on neighboring edge atoms or the same edge atom for an $s{p}^3$-terminated zigzag graphene edge. The right side shows the stagger induced on an $s{p}^2$ edge for sufficiently large capping ligands.

Figure 3

Side view of a tert-butyl terminated carbon nanoribbon with $N=6$. The edge carbon atoms of the nanoribbon (labeled C1 and C2) stagger alternately up and down to accommodate the bulky tert-butyl capping ligands.

Figure 4

Calculated spin-polarized density of states projected onto the carbon atoms along one edge of an antiferromagnetic, tert-butyl terminated $N=12$ nanoribbon.

Figure 5

The band structures of a tert-butyl terminated $N=12$ zigzag nanoribbon in different magnetic states (left), as compared to a similar nanoribbon terminated with simple hydrogen atoms (right). Blue solid lines and red dashed lines represent opposite spin states.

Figure 6

Left: Projected density of the state of the $p$ orbital on single side edge carbon atom ($N=12$) for the non-spin-polarized calculation. Right: ${\Theta }_R$ measures the tilt angle of the edge carbon atom in terms of the location of the attached tert-butyl group. ${\Theta }_p$ measures this angle in terms of the rotation of the atom’s $\pi$ orbital.