Resonance Transitions in the Cylindrical Barrier as Related Carbon Nanotube States

Authors

  • Yury. I. Bokhan *

    Belarusian State Academy of Communications, Vitebsk Branch Ilyinsky, 45, Vitebsk 210001, Belarus

DOI:

https://doi.org/10.55121/nefm.v4i1.388

Keywords:

Carbon Nanotube , Potential Barrier , Cylindrical Coordinates , Energy States , Current

Abstract

The solution of the Schrödinger equation in a cylindrical coordinate system is considered. The carbon nanotube is modeled by a cylindrical tunnel barrier with periodic boundary conditions. An expression is obtained for the charge current depending on the radius and length of the nanotube. Shown that the current vector has a radial component that changes the sign for certain transitions with large index values. The occurrence of negative values of the current component indicates the presence of negative differential conductivity for these transitions. The appearance of additional current peaks serves as an indication of the excitation of the tunnel system by the external field. This makes it possible to further tune into resonance, which can be carried out by adjusting the “longitudinal” component of the current, depending on the length of the nanotube.

References

[1] Abraham, J., Thomas, S., Kalarikkal, N., 2022. Handbook of Carbon Nanotubes. Springer Nature: Cham, Switzerland. pp. 1–2112. DOI: https://doi.org/10.1007/978-3-030-91346-5

[2] Schants, H.G., 2015. The Art and Science of Ultrawideband Antennas. Artech House: London, UK. pp. 1–593.

[3] Eatemadi, A., Daraee, H., Karimkhanloo, H., et al., 2014. Carbon nanotubes: properties, synthesis, purification, and medical applications. Nanoscale Research Letters. 9, 393.

[4] Babu, A.M., Prabu, N.M., Balasubramanian, K., 2015. Investigation on carbon nanotubes over review on other heat transfer nanofluids. International Journal of Applied Engineering Research, 10(62), 112–117.

[5] Amtate,D., Goro. G., 2017. Carbon nanotubes: synthesis, properties and technological applications. International Journal Advanced Research (IJAR). 5(3), pp.1549-1565 DOI: https://dx.doi.org/10.21474/IJAR01/3664

[6] Narayanan, M.R., Logeshwaran, J., 2017. Synthesis and machining characterization of copper-multiwalled carbon nanotubes-graphene hybrid composite using SEM and ANOVA. Journal of Nano Research. 50, 105–115. DOI:https://doi.org/10.4028/www.scientific.net/JNanoR.50.105

[7] Vigneau, F., Monsel, J., Tabanera, J., et al., 2022. Ultrastrong coupling between electron tunneling and mechanical motion. arXiv preprint. DOI:https://doi.org/10.48550/arXiv.2103.15219

[8] Chen, A., Chatterjee, S., 2013. Nanomaterials based electrochemical sensors for biomedical applications. Chemical Society Reviews. 42(12), 5425–5438. DOI: https://doi.org/10.1039/C3CS35518G

[9] Conle, K., Karttunen, A. J., 2022. Bridging the Junction: Electrical Conductivity of Carbon Nanotube. The Journal of Physical Chemistry C. 126(40), 17266–17274. DOI: https://doi.org/10.1021/acs.jpcc.2c03904.

[10] Dyachkov, P.N., Bochkov, I.A., 2013. The energy-band structure of nanotubes with spiral and rotary symmetry axes. Inorganic Materials: Applied Research. 4, 328–335. DOI: https://doi.org/10.1134/S2075113313040023

[11] Wang, H., Song, Z., Liu, D., Energy band calculation of spiral single-walled carbon nanotubes. Advanced Materials Research. 2012. 535, 341–344. DOI:https://doi.org/10.4028/www.scientific.net/AMR.535-537.341

[12] Belonenko, M.B., Lebedev, N.G., Zhukov, A.V., et al., 2011. Electron Spectrum and Tunneling Current of the Toroidal and Helical Graphene Nanoribbon-Quantum Dots Contact. International Scholarly Research Network ISRN Nanotechnology. Article ID 161849, 5 pages. DOI: https://doi.org/10.5402/2011/161849.

[13] Charlier, J.-C., Blase, X., Roche, S., 2007. Electronic and transport properties of nanotubes. Reviews of Modern Physics. 79(2), 677–732. DOI: https://doi.org/10.1103/RevModPhys.79.677

[14] Razavy, M., 2014. Quantum Theory of Tunneling, 2nd ed. World Scientific Publishing Co.: Singapore. pp. 1–792.

[15] Watson, G., 1966. A Treatise on the Theory of Bessel Functions. University Press: Cambridge, UK. pp. 1–816.

[16] Tapaszto, L., Mark, G., Koos, A.A., et al., 2006. Apparent diameter of carbon nanotubes in scanning tunnelling microscopy measurements. Journal of Physics: Condensed Matter 18, 5793–5805. DOI: https://doi.org/10.1088/0953-8984/18/26/001

[17] Belonenko, M.B., Lebedev, N.G., Yanyushkina, N.N., 2010. Tunneling through the carbon nanotube/graphene interface exposed to a strong oscillating electric field. Journal of Nanophotonics. 4, 041670. DOI:https://doi.org/10.1117/1.3398501

[18] Bokhan Y.I., System carbon nanotube for reception terahertz radiations. In: Fedosyuk VM, editor. Actual Problems of Solid State Physics: Proceedings of the X International Scientific Conference; May 22-26; 2023.Minsk, Belarus. pp. 494-496.

Downloads

How to Cite

I. Bokhan, Y. (2025). Resonance Transitions in the Cylindrical Barrier as Related Carbon Nanotube States. New Environmentally-Friendly Materials, 4(1), 67–73. https://doi.org/10.55121/nefm.v4i1.388

Issue

Section

Communication