Quantum Hydrodynamic Analysis of Electrostatic Waves in Carbon Nanotubes

The linearized quantum hydrodynamic model (QHD) is employed to investigate the dispersion relation of electrostatic waves propagating through Single Walled Carbon Nanotubes (SWCN) subjected to an axial magnetic field. Previously, we theoretically computed the conditions for exciting quantum electrostatic modes in a CNT filled with electrons and exposed to an axial magnetic field, utilizing wavelengths spanning the microwave to visible spectrum range [۱, ۲]. In this paper, we present the dispersion relations, unveiling the magnetic field's influence on the excitation of quantum acoustical and optical waves. We establish that weak magnetic fields hinder the propagation of quantum acoustical waves, while strong magnetic fields permit it. Additionally, the excitation of quantum optical waves across all magnetic field strengths requires wavelengths from the microwave to visible spectrum. Lastly, we depict the dispersion relations of acoustical and optical modes as a logarithmic function of the magnetic field’s base ۱۰. Through a comparative analysis using two models, we reveal intriguing disparities between these two modes. This study might provide a platform to create new finite transverse cross section quantum magnetized plasmas and to devise nanometer dusty plasmas based on the metallic carbon nanotubes in the absence of either a drift or a thermal electronic velocity and their existence could be experimentally examined.