Polarization dependence of Raman spectra in strained graphene

The polarization dependences of the G, D, and 2D $\left({\text{G}}^{\prime }\right)$ bands in Raman spectra at graphene bulk and edge are examined theoretically. The 2D and D bands have different selection rules at bulk and edge. At bulk, the 2D band intensity is maximum when the polarization of the scattered light is parallel to that of incident light, whereas the D band intensity does not have a polarization dependence. At edge, the 2D and D bands exhibit a selection rule similar to that of the G band proposed in a previous paper. We suggest that a constraint equation on the axial velocity caused by the graphene edge is essential for the dependence of the G band on the crystallographic orientation observed in the bulk of strained graphene. This is indicative of that the pseudospin and valley spin in the bulk of graphene can not be completely free from the effect of surrounding edge. The status of the experiments on the G and D bands at the graphene edge is mentioned.

Figure 1

(a) The coordinate system represents the crystal reference system. The zigzag edge is parallel to the $x$ axis while the armchair edge is parallel to the $y$ axis. (b) A graphene system with rectangle shape enclosed by the zigzag and armchair edges.

Figure 2

(a) The strain is at the angle ${\phi }_s$ with respect to the $x$ axis. The direction of strain is parallel to ${\mathbf{A}}_{+}^{\text{q}}$. The angle between the strain and the incident (scattered) laser polarization is denoted by ${\theta }_{\text{in}}\left({\theta }_{\text{out}}\right)$. The axial vector ${\mathbf{A}}_{+}^{\text{q}}$ corresponds to the ${\text{G}}^{+}$ mode while ${\mathbf{A}}_{-}^{\text{q}}$ corresponds to the ${\text{G}}^{-}$ mode. (b) A hexagonal graphene with zigzag edges (top) and that with armchair edges (bottom).

Figure 3

Kohn anomaly effect at the bulk and edge. In the bulk, the intermediate electron-hole state consists of the Bloch plane wave, while at the edge, the intermediate state consists of the standing wave. The spin of the Bloch state can point arbitrary direction while that of the standing wave can not have a component parallel to ${\sigma }_y{\tau }_z$.