Hypersound Absorption of Acoustic Phonons in a degenerate Carbon Nanotube

Hypersound Absorption of acoustic phonons having $ql>>1$ in a degenerate Carbon Nanotube (CNT) with linear energy dispersion near the Fermi level was theoretically studied. The general expression for the absorption coefficient ($\Gamma$) under a non-quantizing electric field ($E$) with drift velocity ($V_D$)was obtained. At $T = 10K$ and scattering angle $\theta > 0$, the dependence of $\Gamma$ on acoustic wave number ($\vec{q}$), frequency ($\omega_q$), and $\gamma = 1-\frac{V_D}{V_s}$, ($V_s$ being the speed of sound) were analysed numerically at $n = 0, \pm 1, \pm 2$ (where $n$ represent the various harmonics) and presented graphically. In a $3D$ representation, when $\gamma < 0$, the maximum amplification was attained at $V_D = 1.1V_s$ which occurred at $E = 51.7Vcm^{-1}$. In the second harmonics, ($n =\pm 2$), the absorption obtained was compared to experimental measurement of acoustoelectric current via the Weinreich relation. From the graphs, the observed amplification of acoustic phonons caused by intraband transition shows CNT as a promising hypersound generator (SASER).