Hot-electron transient and terahertz oscillations in graphene

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. It only takes place within a voltage and sample length window as 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.

Terahertz harmonic generation in graphene

“…5 to the steady state-homogenous equation for f h = f h 0 . [13] A similar analysis on the harmonics f m1 , m > 1 shows that solutions exist only, for mqv F = ω, so f m1 also reduces to f h 0 . Since f mn are related to f (m−1)(n−1) by Eq.…”

“…where f h ( k) = f 00 is the solution to the homogeneous, steady state problem, [13] f mn ( k) are the harmonic amplitudes, and the summation excludes all terms with m = 0 and n = 0, since they would result either in homogenous (m = 0) or state-state (n = 0) terms that are already taken into account in f h ( k) = f 00 ( k). On substituting Eq.…”

“…[12] This stop-and-go motion of carriers can occur over long distances during picosecond flight times. [13] An interesting effect could arise if the carriers are placed in periodic long range and time varying scattering to achieve transport resonance as well as possible frequency mixing. This kind of situation could be realized in free standing graphene sheets lying over periodically spaced narrow electric gates that would be regulated by an a-c field of appropriate frequency to modulate coulomb scattering of remote oxide impurities when carriers pass in front of the gates (Fig.…”

“…In low electron concentration (n < 10 12 /cm 2 ), most of the electron population is stretched along the fields (streaming case), so that the majority of carriers have their velocity pointing in that direction. [13] If the fields are applied along the x-direction, the time and space dependent BTE in both regions reads…”

“…Also, in the streaming case, we assume v x ∼ v F . Low energy elastic collisions in region I with impurities and APs are accounted for within a local and time dependent relaxation time approximation [13]τ (x, t) with the same periodicity as the gate spacing and applied a-c field i.e.…”