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

Document Type : Original Article

Authors

1 Department of Physics, K. N. Toosi University of Technology, Tehran, Iran

2 Department of Physics, Razi University, Kermanshah, Iran

10.22075/ppam.2026.39657.1185

Abstract

This study presents a comprehensive theoretical investigation of electron electrostatic (plasmon) wave propagation265 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 (๐‘˜๐‘≈0.1 /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 100 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.

Keywords

Main Subjects

© 2026 The Author(s). Progress in Physics of Applied Materials published by Semnan University Press. This is an open access article under the CC-BY 4.0 license. (https://creativecommons.org/licenses/by/4.0/)

References

[1] Mansouri, M., Rezagholipour Dizaji, H., Saeidi, M. R., and Vaezzadeh, M., 2022. Electron gas hardness of individual carbon nanotubes. Progress in Physics and Applied Materials, 2, p.27.
[2] Habisreutinger, S. N., Nicholas, R. J., and Snaith, H. J., 2017. Carbon nanotubes in perovskite solar cells. Advanced Energy Materials, 7, p.1601839.
[3] Jeon, I., Matsuo, Y., and Maruyama, S., 2018. Single-walled carbon nanotubes in solar cells. Single-Walled Carbon Nanotubes: Preparation, Properties and Applications, pp.271–298.
[4] Batmunkh, M., Shearer, C. J., Bat-Erdene, M., Biggs, M. J., and Shapter, J. G., 2017. Single-walled carbon nanotubes enhance the efficiency and stability of mesoscopic perovskite solar cells. ACS Applied Materials & Interfaces, 9, pp.19945–19954.
[5] Bachilo, S. M., Strano, M. S., Kittrell, C., Hauge, R. H., Smalley, R. E., and Weisman, R. B., 2002. Structure-assigned optical spectra of single-walled carbon nanotubes. Science, 298, pp.2361–2366.
[6] Lin, M. F., and Shung, K. W. K., 1994. Plasmons and optical properties of carbon nanotubes. Physical Review B, 50, p.17744.
[7] Avouris, P., Freitag, M., and Perebeinos, V., 2008. Carbon-nanotube photonics and optoelectronics. Nature Photonics, 2, pp.341–350.
[8] Bursill, L. A., Stadelmann, P. A., Peng, J. L., and Prawer, S., 1994. Surface plasmon observed for carbon nanotubes. Physical Review B, 49, p.2882.
[9] Stauber, T., 2014. Plasmonics in Dirac systems: from graphene to topological insulators. Journal of Physics: Condensed Matter, 26(12), p.123201.‏
[10] Dyakonov, M., and Shur, M. S., 2001. Plasma wave electronics for terahertz applications. Terahertz Sources and Systems, pp.187–207.
[11] Perez, R., and Que, W., 2006. Plasmons in isolated single-walled carbon nanotubes. Journal of Physics: Condensed Matter, 18, p.3197.
[12] Adhikari, C.M., 2025. Optoplasmonics of single-walled carbon nanotube thin films. Photonics, 12, p.298.
[13] Zhao, Y. M., Hu, X. G., Chen, C., Wang, Z. H., Wu, A. P., Zhang, H. W., ... and Cheng, H. M., 2024. Plasmon-enhanced ultra-high photoresponse of single-wall carbon nanotube/copper/silicon near-infrared photodetectors. Nano Research. 17, pp.5930-5936.
[14] Martín-Luna, P., and Resta-López, J., 2025. Plasmonic excitations in carbon nanostructures: Carbon nanotubes vs. graphene. In: Electromagnetic Field – From Atomic Level to Engineering Applications.
[15] Annamalai, S. and Ramasamy, R.P., 2023. Chitosan–carbon nanotube–maghemite nanocomposites: A flexible negative dielectric constant material. Progress in Physics and Applied Materials, 3, p.147.
[16] Toscano, G., Straubel, J., Kwiatkowski, A., Rockstuhl, C., Evers, F., Xu, H., ... and Wubs, M., 2015. Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics. Nature Communications, 6, p.7132.
[17] Ciraci, C., 2019. Nonlinear quantum plasmonics: A quantum hydrodynamic approach. EOARD–AFRL–AFOSR UK Technical Report, No. TR20190062.
[18] Wang, Y., Sun, G., Zhang, X., Zhang, X., and Cui, Z., 2024. Advancement in carbon nanotubes optoelectronic devices for terahertz and infrared applications. Advanced Electronic Materials, 10, p.2400124.
[19] Popov, V.N., 2004. Carbon nanotubes: Properties and application. Materials Science and Engineering: R: Reports, 43, pp.61–102.
Progress in Physics of Applied Materials
Volume 6, Issue 4
In Progress
December 2026
Pages 265-271

Files

History

  • Receive Date: 23 November 2025
  • Revise Date: 10 February 2026
  • Accept Date: 14 February 2026

Share

How to cite

Statistics