Electron-Phonon Interactions for Optical Phonon Modes in Few-Layer Graphene

We present a first-principles study of the electron-phonon (e-ph) interactions and their contributions to the linewidths for the optical phonon modes at $\Gamma$ and K in one to three-layer graphene. It is found that due to the interlayer coupling and the stacking geometry, the high-frequency optical phonon modes in few-layer graphene couple with different valence and conduction bands, giving rise to different e-ph interaction strengths for these modes. Some of the multilayer optical modes derived from the $\Gamma$-$E_{2g}$ mode of monolayer graphene exhibit slightly higher frequencies and much reduced linewidths. In addition, the linewidths of K-$A'_1$ related modes in multilayers depend on the stacking pattern and decrease with increasing layer numbers.