Velocity and momentum fluctuations in suspended monolayer graphene

In this work, the instantaneous velocity and momentum fluctuations in suspended monolayer graphene are investigated by means of an ensemble Monte Carlo simulator. Due to the particular properties of graphene band structure (conical dispersion relationship near the Dirac points), instantaneous velocity fluctuations show a non-linear dependence with time during free flights, being limited by the maximum value set by the Fermi velocity. On the other hand, momentum fluctuations follow the linear dependence expected by the laws of motion. Particular attention is paid to the auto-correlation function of velocity fluctuations and the power spectral density at high frequencies (from which the axial diffusion coefficient is obtained), studying their relation to microscopic transport phenomena (scattering events undergone and relaxation times).