Magnetoplasma waves on the surface of a semiconductor nanotube with a superlattice

Abstract

The effective mass approximation is used to consider plasma and magnetoplasma waves in an electron system on the surface of the semiconductor cylindrical nanotube. The electron-electron coupling is taken into account in the random phase approach. In the case of a degenerate electron gas the spectral windows on the wavevector-frequency plane and the spectra of the waves are obtained. Their frequencies undergo quantum oscillations of the de Haas-van Alfven type which are attributed to the Fermi level traversing the sub-zone boundaries in the electron energy spectrum. The spectrum and the damping of waves in the non-degenerate electron gas were found. In a magnetic field parallel to the cylinder axis the frequencies of the magnetoplasma waves sustain the Aharonov-Bohm type oscillations that appear with changing magnetic field strength.

The Effect of Umklapp Processes on Magnetoplasma Waves on the Surface of a Semiconductor Nanotube with a Superlattice

“…In Ref. [22], the spectrum of magnetoplasma waves in an electron gas on the surface of a semiconductor nanotube with a longitudinal superlattice in a magnetic field parallel to the axis of the tube and superlattice is calculated on the basis of the effective mass model and the strong-binding method of electrons in the random phase approximation. In the quantum and quasiclassical cases, the frequencies of long-wavelength intraband and interband magnetoplasmons in a degenerate electron gas were calculated.…”

“…In Refs. [22][23][24], the magnetoplasmons are investigated in nanotubes with a superlattice, but without the influence of umklapp processes. In these papers, a plane wave is used as the basic wave function of longitudinal motion on the tube.…”

“…It is assumed that the longitudinal effective mass of an electron is equal to the transverse mass. Thus, the energy of an electron on a tube with a longitudinal tunnel superlattice is [22][23][24]:…”

“…This approach is based on the theory of linear response, in which the collective states appear as resonances in the linear response of the gas to an external perturbation [16,28]. We start by considering an electron gas on the surface of a semiconductor nanotube in a longitudinal (along the axis of the tube) uniform magnetic field, initially in thermal equilibrium, which is subsequently perturbed by a weak external field, whose dependence on coordinates and time in a cylindrical coordinate system is represented in the form [22][23][24]:…”

“…which is the cylindrical harmonics of the Coulomb potential of electrons on the tube [22], I m and K m are modified Bessel functions. Small longitudinal oscillations of the electron gas on the tube can be described with the help of the linearized Liouville equation for the density matrix [28] with a selfconsistent field (6):…”