Hot Electron Terahertz Oscillations in Graphene: Crater and Terraces in the Carrier Distribution Function

Abstract

In graphene, after the electric field is turned-on, the ballistic acceleration of charge carriers up to the monochromatic optic phonon energy generates a back-and-forth motion of the whole distribution function between the zero point energy and the phonon energy. This effect is predicted to manifest in damped terahertz oscillations of the carrier drift velocity and average energy. The most dramatic feature of this transient phenomenon is the onset of momentum-free areas surrounded by high momentum probability in phase space, and smooth steps or terraces in the distribution function. This dynamical effect that only takes place within a voltage and sample length window, is the direct consequence of the interplay between the electric force and the randomizing nature of deformation potential optic phonons in the linear band structure of graphene.

Appearance of Negative Differential Conductivity in Graphene Nanoribbons at High-Harmonics

“…We consider a classical limit in which energy levels could be excited due to thermal fluctuations, i.e ∆E << K B T << E C . This condition is also necessary for large enough field, so that charge carriers can escape low energy scattering 16 . The energy level spacing ∆E = πW γ 0 l/A, E C is the charging energy, K B is the Boltzmann constant, T is the lattice temperature and W is the graphene width.…”