Quantum Hydrodynamic Study of Electron Electrostatic Waves in Single-Walled Carbon Nanotubes

This study presents a comprehensive theoretical investigation of electron electrostatic (plasmon) wave propagation۲۶۵ in single-walled carbon nanotubes (SWCNTs) using an advanced quantum hydrodynamic (QHD) framework. We develop a sophisticated model that rigorously incorporates essential quantum mechanical effects, including the Bohm potential (accounting for electron tunneling phenomena) and Fermi pressure (arising from electron degeneracy). Through systematic linearization of the QHD equations coupled with Poisson’s equation, we derive a generalized dispersion relation that accurately describes plasmon behavior across different wavelength regimes. Our analysis reveals the existence of highly tunable plasmon resonances in SWCNTs, with frequencies spanning from the terahertz to the near-infrared range; this broad tunability makes them potentially relevant for optoelectronic and plasmonic applications. The plasmonic characteristics exhibit exquisite sensitivity to fundamental parameters such as nanotube radius, electron density, doping levels, and the surrounding dielectric environment. Notably, we identify a critical transition wavevector (𝑘𝑐≈۰.۱ /nm) where quantum effects become dominant, fundamentally altering the plasmon dispersion. The theoretical predictions show good consistency with experimentally reported plasmon energies and propagation lengths. Furthermore, we provide a detailed analysis of damping mechanisms and propagation characteristics, estimating room-temperature propagation lengths of approximately ۱۰۰ nm, with significant enhancement at cryogenic temperatures. This work establishes a robust theoretical foundation for understanding and engineering quantum plasmonic excitations in low-dimensional carbon-based materials, with substantial implications for next-generation nano-optoelectronic devices, quantum sensors, and advanced photonic systems.

کلیدواژه ها:

Single-walled carbon nanotubes ، Quantum hydrodynamic model ، Plasmons