Quantum ion-acoustic waves in single-walled carbon nanotubes studied with a quantum hydrodynamic model

The quantum ion-acoustic waves in single-wall carbon nanotubes are studied with the quantum hydrodynamic model, in which the electron and ion components of the nanotubes are regarded as a two-species quantum plasma system. An analytical expression of the dispersion relation is obtained for the linear disturbance. Numerical results show that the frequency of the ion-acoustic wave strongly depends on the nanotube’s radius in the long-wavelength cases.

Figure 1

The dispersion relation $\omega ∕{\omega }_s$ of the quantum ion-acoustic wave for the discrete azimuthal quantum numbers $m=2$ and different nanotube’s radii: $a=2a_B$, $a=5a_B$, $a=8a_B$, and $a=10a_B$.

Figure 2

The dispersion relation $\omega ∕{\omega }_s$ of the quantum ion-acoustic wave for the nanotube’s radius $a=5a_B$ and different azimuthal quantum numbers $m=0$, 1, 2, 3, and 4.