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 this material. The effect is most pronounced when this lattice mode (associated with the $G$ band in graphene Raman spectrum) is in resonance with inter-Landau-level transitions $0\Rightarrow +$, 1 and $-,1\Rightarrow 0$, at a magnetic field $B_0\simeq 30\mathrm{T}$. It can be used to measure the strength of the electron-phonon coupling directly, and its filling-factor dependence can be used experimentally to detect circularly polarized lattice vibrations.