Hypersound absorption of acoustic phonons in a degenerate carbon nanotube

Abstract

Absorption of acoustic phonons was studied in degenerate Carbon Nanotube (i.e. where the electrons are found close to the Fermi level). The calculation of the hypersound absorption coefficient (Γ) was done in the regime where ql >> 1 (q is the acoustic phonon number and l is the electron mean free path). At T = 10K and θ > 0 (θ being scattering angle), the dependence of Γ on acoustic wave number (~), frequency (ωq), and γ = 1 − VD, (Vs and VD being the speed of sound and the drift velocity respectively) were analysed numerically at n = 0, ±1, ±2 (where n is an integer ) and presented graphically. It was observed that when γ < 0, the maximum amplification was attained at VD = 1.1Vs which occurred at E = 51.7V cm −1. In the second harmonics, (n = ±2), the absorption obtained was compared to experimental measurement of acoustoelectric current via the Weinreich relation and the results qualitatively agreed with each other