On the amplification of acoustic phonons in carbon nanotube

TL;DR

This paper theoretically investigates the amplification of acoustic phonons in carbon nanotubes via Cerenkov emission, revealing conditions for phonon amplification and potential for SASER development.

Contribution

It introduces a novel theoretical framework for acoustic phonon amplification in CNTs through Cerenkov emission, with specific threshold fields and amplification ratios.

Findings

Amplification significantly exceeds absorption in CNTs under certain conditions.

Threshold electric field for phonon amplification is much lower than Bloch oscillation estimates.

Potential application in developing SASER devices using CNTs.

Abstract

We present a theoretical study of acoustic phonons amplification in Carbon Nanotubes (CNT). The phenomenon is via Cerenkov emission (CE) of acoustic phonons using intraband transitions proposed by Mensah et. al.,~\cite{1} in Semiconductor Superlattices (SSL) and confirmed in ~\cite{2}. From this, an asymmetric graph of $\Gamma^{CNT}$ on $\frac{V_d}{V_s}$ and $\Omega\tau$ were obtained where amplification ($\Gamma_{amp}^{CNT}$) $>>$ absorption ($\Gamma_{abs}^{CNT}$). The ratio, $\frac{\vert \Gamma_{amp}^{CNT}\vert}{\vert\Gamma_{abs}^{CNT}\vert}\approx 3.5$, at $V_d = 1.02V_s$, $\omega_q = 3.0\ \mathrm{THz}$ and $T = 85\ K$ for scattering angle $\theta > 0$ . A threshold field at which $\Gamma_{abs}^{CNT}$ switches over to $\Gamma_{amp}^{CNT}$ was calculated to be $E_{z}^{dc} = 6.2\times 10^3\ \mathrm{V/m}$. This field is far less than that deduced using Bloch-Type Oscillation (BTO)~\cite{3} which is $E_{BTO}^{dc} = 3.0\times 10^5\ \mathrm{V/m}$. The obtained $\Gamma_{amp}^{CNT}$ would enable the use of CNT for the production of SASER.