Filling-Factor-Dependent Magnetophonon Resonance in Graphene

We describe a peculiar fine structure acquired by the in-plane optical phonon at the $\Gamma$-point in graphene when it is brought into resonance with one of the inter-Landau-level transitions in the material. The effect is most pronounced when this lattice mode is in resonance with inter-Landau-level transitions $-,1\Rightarrow 0 $ and $0\Rightarrow+,1$ at a magnetic field $B_0 \approx 30$ T. The predicted mode splitting may be used to measure directly the strength of the electron-phonon coupling, and also to distinguish between circularly (left- and right-hand) polarized lattice modes. A similar effect is predicted in bilayer graphene in lower magnetic fields. \newline \newline [1] M.O. Goerbig, J.-N. Fuchs, K. Kechedzhi, V. I. Fal'ko, PRL 98, 087402 (2007).