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Russia Izhevsk
Section Mathematics
Title Electron scattering in a carbon nanotube
Author(-s) Morozova L.E.a
Affiliations Izhevsk State Technical Universitya
Abstract Carbon nanotubes are being actively studied in the physics literature in the last two decades. Their unique physical properties, in particular high strength and conductivity, are the reason of the promising applications for their use in microelectronics. Despite the relevance of these physical problems, such structures are poorly mathematically studied. In this paper, within the tight-binding approximation, we consider the Hamiltonian of an electron in a single-walled zigzag nanotube with an impurity, evenly distributed in the cross section of the nanotube. Using the Lippmann-Schwinger equation, we investigate the scattering problem for this Hamiltonian in the case of small impurity potential and slow electrons. Since the electronic conductance is proportional to the transmission probability, we actually study the problem of conductance in a nanotube. Simple formulas for the reflection and transmission coefficients are obtained. The conditions of total reflection and total transmission, as well as the conditions of increasing and decreasing the transmission probability are found.
Keywords carbon nanotube, Lippmann-Shwinger equation, scattering, reflection and transmission probabilities
UDC 517.958, 530.145.6
MSC 81Q10, 81Q15
DOI 10.20537/vm160210
Received 29 April 2016
Language Russian
Citation Morozova L.E. Electron scattering in a carbon nanotube, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 239-244.
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