The Effect of Umklapp Processes on Magnetoplasma Waves on the Surface of a Semiconductor Nanotube with a Superlattice
G. Rashba
Kharkiv National University named after V.N. Karazin, 4 Svobody Sq., Kharkiv, 61022, Ukraine
Received: January 25, 2019; revised version March 15, 2019; in final form March 15, 2019
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The spectra of plasma waves in the electron gas on the surface of a semiconductor nanotube with a superlattice in a parallel magnetic field have been studied using the self-consistent field method. The analytical results for the dispersion relation of the plasmon branch are derived in a tight-binding approximation which takes into account the umklapp effects in the superlattice direction. The long-wave intra- and interband magnetoplasmon frequencies in a degenerate electron gas are calculated both in quasiclassical and in quantum limits. In case of a large number of the filled electron levels, associated with the orbital motion of electrons, the magnetoplasmon frequencies exhibit the oscillations, which are similar to the de Haas-van Alphen oscillations upon variation of nanotube parameters and the Aharonov-Bohm oscillations upon variation of the magnetic flux through the nanotube cross-section.

topics: nanotube, superlattice, magnetoplasmon, Aharonov-Bohm oscillations, de Haas-van Alphen \\m{oscillations}, umklapp effects