Thermoelectric Amplification of Phonons in Graphene

TL;DR

This paper theoretically investigates how a temperature gradient can amplify acoustic phonons in graphene, identifying conditions and thresholds for phonon amplification, and comparing graphene's efficiency with other materials.

Contribution

It provides the first theoretical analysis of thermoelectric phonon amplification in graphene, including threshold gradients and frequency dependence, highlighting graphene's superior potential as a phonon amplifier.

Findings

Threshold temperature gradient for amplification at 77K and 12THz is 0.37 Km^{-1}.

Graphene's amplification threshold is lower than in other semiconductors and superlattices.

Graphene is identified as a highly effective material for thermoelectric phonon amplification.

Abstract

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.