Raman spectroscopy of graphene edges.

Graphene edges are of particular interest since their orientation determines the electronic properties. Here we present a detailed Raman investigation of graphene flakes with edges oriented at different crystallographic directions. We also develop a real space theory for Raman scattering to analyze the general case of disordered edges. The position, width, and intensity of G and D peaks are studied as a function of the incident light polarization. The D-band is strongest for polarization parallel to the edge and minimum for perpendicular. Raman mapping shows that the D peak is localized in proximity of the edge. For ideal edges, the D peak is zero for zigzag orientation and large for armchair, allowing in principle the use of Raman spectroscopy as a sensitive tool for edge orientation. However, for real samples, the D to G ratio does not always show a significant dependence on edge orientation. Thus, even though edges can appear macroscopically smooth and oriented at well-defined angles, they are not necessarily microscopically ordered.