Abstract:
Based on the Hamiltonian for charge carriers in carbon nanotubes with finite lengths, we obtain eigenvalues and eigenfunctions in a neighborhood of the Dirac points (wave functions written analogously to the two-component Dirac wave function are expressed in terms of Hermite polynomials, and the spectrum is equidistant) in the presence of a longitudinal electric field. We express the solution in terms of the Hermite functions in the case of carbon nanotubes with infinite lengths. Based on the obtained wave function for an elongated nanotube, we consider the problem of determining the coefficient of charge carrier transport through the nanotube. The results of finding the transport coefficient can also be applied to other nanoparticles, in particular, to carbon chains and nanotapes. We propose to use the eigenvalues and eigenfunctions of nanotubes with finite lengths to consider the problem of radiation generation in a nonlinear medium based on an array of such noninteracting nanotubes.
Keywords:
two-wave Dirac wave function, nanotube array, nanotape,
transport coefficient.
Citation:
N. R. Sadykov, “Wave functions and eigenvalues of charge carriers in a nanotube in a neighborhood of the Dirac point in the presence of a longitudinal electric field”, TMF, 180:3 (2014), 368–381; Theoret. and Math. Phys., 180:3 (2014), 1073–1085
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\paper Wave functions and eigenvalues of charge carriers in a~nanotube in a~neighborhood of the~Dirac point in the~presence of a~longitudinal electric field
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\yr 2014
\vol 180
\issue 3
\pages 368--381
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\jour Theoret. and Math. Phys.
\yr 2014
\vol 180
\issue 3
\pages 1073--1085
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Linking options:
https://www.mathnet.ru/eng/tmf8642
https://doi.org/10.4213/tmf8642
https://www.mathnet.ru/eng/tmf/v180/i3/p368
This publication is cited in the following 10 articles:
N. R. Sadykov, Yu. A. Petrova, I. A. Pilipenko, R. S. Khrabrov, S. N. Skryabin, “Effect of a Geometric Potential on the Eigenfunction and Eigenvalue of the Energy of State in a Twisted Graphene Nanoribbon”, Russian Journal of Physical Chemistry, 97:2 (2023), 252
N. R. Sadykov, Yu. A. Petrova, I. A. Pilipenko, R. S. Khrabrov, S. N. Skryabin, “Effect of a Geometric Potential on the Eigenfunction and Eigenvalue of the Energy of State in a Twisted Graphene Nanoribbon”, Russ. J. Phys. Chem., 97:2 (2023), 367
N. R. Sadykov, R. S. Khrabrov, I. A. Pilipenko, “Field emission in an array of homogeneous identical nanometer-long nanotubes”, Eur. Phys. J. D, 77:1 (2023)
Sadykov N.R., Pilipenko I.A., Jolnirov S.E., “Terahertz Radiation Generation Process in the Medium Based on the Array of the Elongated Nanoparticles”, Opt. Quantum Electron., 54:1 (2022), 36
Sadykov N.R., Zholnirov S.E., Pilipenko I.A., “The Nordheim Function in An Array of Homogeneous Identical Nanotubes Under Field Emission”, Tech. Phys., 66:9 (2021), 1032–1040
Sadykov N.R., Peshkov D.A., Aporoski V A., Belonenko M.B., “Decay, Amplification and Absorption of Initial Terahertz Pulse in Resonant Two-Level Medium Based on Noninteracting Array of Zigzag Nanotubes and Armchair Nanoribbons”, Int. J. Mod. Phys. B, 34:21 (2020), 2050202
Sadykov N.R., Muratov E.T., Pilipenko I.A., Aporoski A.V., “Wavefunctions and Energy Eigenvalues of Charge Carriers in Zigzag Carbon Nanotubes and in Armchair Nanoribbons in the Vicinity of Dirac Point Under the Influence of Longitudinal Electric Field”, Physica E, 120 (2020), 114071
N. R. Sadykov, D. A. Peshkov, P. N. D'yachkov, “Combined effect of external periodic and constant electric fields on electron transport in carbon nanotubes and nanoribbons with metallic conductivity”, J. Phys. Soc. Jpn., 86:3 (2017), 034712
N. R. Sadykov, A. V. Aporoski, “Majorana fermion wavefunctions in carbon nanotubes and carbynes”, Int. J. Mod. Phys. B, 31:4 (2017), 1750017
N. R. Sadykov, A. V. Aporoski, D. A. Peshkov, “Terahertz radiation generation process in the medium based on the array of the noninteracting nanotubes”, Opt. Quantum Electron., 48:7 (2016), 358
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