Localized Edge Vibrations and Edge Reconstruction by Joule Heating in Graphene Nanostructures

Control of the edge topology of graphene nanostructures is critical to graphene-based electronics. A means of producing atomically smooth zigzag edges using electronic current has recently been demonstrated in experiments [Jia et al., Science 323, 1701 (2009)]. We develop a microscopic theory for current-induced edge reconstruction using density functional theory. Our calculations provide evidence for localized vibrations at edge interfaces involving unpassivated armchair edges. We demonstrate that these vibrations couple to the current, estimate their excitation by Joule heating, and argue that they are the likely cause of the reconstructions observed in the experiments.

Figure 1

(Top) The ZAZ structure. (Middle) The two modes lying outside of the bulk bands, labeled (a) and (b), respectively. Atomic displacements of less than 5% of the total amplitude are not shown. (Bottom) The energies of the two localized modes compared with the local vibrational DOS of the outermost carbon atoms on infinite graphene edges. For H-passivated edges, additional 1D bands are found at $\sim 380\mathrm{meV}$ (not shown).

Figure 2

(Top) The ZAZZZ structure. (Bottom) The three ADMs, labeled (c), (d), and (e), respectively. Atomic displacements of less than 5% of the total amplitude are not shown.

Figure 3

The absolute square of the minority spin left-to-right scattering states at the Fermi level for a large ZAZ system, corresponding to a transmission of 0.15.

Figure 4

The effective temperature as a function of bias for the localized modes for the ZAZ (full curves) and the ZAZZZ system (dashed curves). The horizontal line indicates the uniform temperature where the decay rate of the outer C-C dimer of an armchair reaches 1 Hz.