Magnetophonon spectroscopy of Dirac fermion scattering by transverse and longitudinal acoustic phonons in graphene

Recently observed magnetophonon resonances in the magnetoresistance of graphene are investigated using the Kubo formalism. This analysis provides a quantitative fit to the magnetophonon resonances over a wide range of carrier densities. It demonstrates the predominance of carrier scattering by low-energy transverse acoustic (TA) mode phonons: the magnetophonon resonance amplitude is significantly stronger for the TA modes than for the longitudinal acoustic (LA) modes. We demonstrate that the LA and TA phonon speeds and the electron-phonon coupling strengths determined from the magnetophonon resonance measurements also provide an excellent fit to the measured dependence of the resistivity at zero magnetic field over a temperature range of 4--150 K. A semiclassical description of magnetophonon resonance in graphene is shown to provide a simple physical explanation for the dependence of the magneto-oscillation period on carrier density. The correspondence between the quantum calculation and the semiclassical model is discussed.