Phonon Cerenkov amplification in graphene

A model of phonon Cerenkov amplification in graphene is used to explain the observed superlinear growth of resistivity for drift velocities above the speed of sound. When the electronic drift velocity exceeds the speed of sound, the phonon population is amplified by the electron-phonon coupling, with a positive amplification rate in a cone centered about the direction of the drift velocity. The resulting position-dependent nonequilibrium phonon population gives rise to a resistivity that increases exponentially along the length of the graphene sample, with a growth rate equal to the maximum phonon amplification rate divided by the speed of sound. This effect increases in magnitude linearly with both the drift velocity and the carrier density. Our theoretical calculations agree qualitatively with experimental results and pave the way for a more sophisticated model which includes self-consistently the out-of-equilibrium distributions of electrons and phonons.