Strain-activated edge reconstruction of graphene nanoribbons

The edge structure and width of graphene nanoribbons (GNRs) are crucial factors for the electronic properties. A combination of experiment and first-principles calculations allows us to determine the mechanism of the hexagon-hexagon to pentagon-heptagon transformation. GNRs thinner than 2 nm have been fabricated by bombardment of graphene with high-energetic Au clusters. The edges of the GNRs are modified in situ by electron irradiation. Tensile strain along the edge decreases the transformation energy barrier. Antiferromagnetism and a direct band gap are found for a zigzag GNR, while a fully reconstructed GNR shows an indirect band gap. A GNR reconstructed on only one edge exhibits ferromagnetism. We propose that strain is an effective method to tune the edge and, therefore, the electronic structure of thin GNRs for graphene-based electronics.

Figure 1

(a) Schematic illustration of a GNR formed by two nearby holes. (b) GNR of width $w=8$ in the $x$ direction. Calculations have been performed for $w=2,\cdots ,15$. By periodic boundary conditions the length of the GNR is infinite, where $a$ is the lattice parameter along the edge in the $y$ direction. (c) GNRs generated by bombardment with Au clusters using a pulsed high-power laser. The scale bar is 2 nm. In (a) and (c) the red arrows indicate the GNRs.

Figure 2

Aberration corrected high-resolution TEM image of a reconstructed zigzag GNR of about 1.5-nm width. The C atoms are resolved as gray spots. The scale bar is 2 nm. (a) Zigzag GNR between two holes ($w=6$). (b) Left side of the GNR ($w=6$) reconstructed to a pentagon-heptagon pair series. (c) Right side of the GNR ($w=5$) reconstructed. (d and e) Both sides reconstructed and the width reduced to $w=4$ and 3, respectively. (f and g) GNR transferred to a double and single C chain, respectively. (h) Single C chain finally breaking. (i) Exemplary strain map resulting from the geometric phase analysis of image (c). (j–l) TEM simulations of zigzag edges with pentagon-heptagon pairs, point defects, and stone-wales defects (acceleration voltage 60 kV, spherical aberration 1 $\mu$m, chromatic aberration 1.5 mm, defocus $-3$ nm, convergence angle 0.15 mrad[30]).

Figure 3

(a) Stress along the GNR edge and (b) band gap for fixed lattice parameter $a_0$ and width $w=2,...,15$. The insets in (a) show that the zigzag GNR ($w=2$) turns into a double chain and the FR GNR ($w=2$) resembles an armchair GNR. (c) Energy diagram of the initial state, transition state, and final state. (d) Transition barrier for the transformation of the first hexagon-hexagon pair into a pentagon-heptagon pair ($w=4$) for strain between $-5$ and 5%. The insets show the structures of the three states.

Figure 4

Phonon-dispersion relations of the (a) zigzag, (b) FR, and (c) SR GNRs for $w=4$. (d and e) Atomic displacements of the two FR GNR modes with frequency around 2000 cm${}^{-1}$.

Figure 5

Band structures: (a) AFM $w=4$ zigzag GNR, (b) FM $w=4$ zigzag GNR, (c) nonmagnetic $w=4$ FR GNR, (d) FM $w=4$ SR GNR, and (e) nonmagnetic $w=5$ FR GNR. The energy zero is set to be the Fermi energy.