Thermoelectric Amplification of Phonons in Graphene

Amplification of acoustic phonons due to an external temperature gredient ($\nabla T$) in Graphene was studied theoretically. The threshold temperature gradient $(\nabla T)_0^{g}$ at which absorption switches over to amplification in Graphene was evaluated at various frequencies $\omega_q$ and temperatures $T$. For $T = 77K$ and frequency $\omega_q = 12THz$, $(\nabla T)_0^{g} = 0.37Km^{-1}$. The calculation was done in the regime at $ql >> 1$. The dependence of the normalized ($\Gamma/\Gamma_0$) on the frequency $\omega_q$ and the temperature gradient $(\nabla T/T)$ are evaluated numerically and presented graphically. The calculated $(\nabla T)_0^{g}$ for Graphene is lower than that obtained for homogeneous semiconductors ($n-InSb$) $(\nabla T)_0^{hom} \approx 10^3Kcm^{-1}$, Superlattices $(\nabla T)_0^{SL} = 384Kcm^{-1}$, Cylindrical Quantum Wire $(\nabla T)_0^{cqw} \approx 10^2Kcm^{-1}$. This makes Graphene a much better material for thermoelectric phonon amplifier.