Superlattice on the surface of a nanotube (Review Article)

The results of theoretical studies of the thermodynamic, kinetic, and high-frequency properties of the electron gas on the surface of a nanotube in a magnetic field in the presence of a longitudinal superlattice are presented. Nano-dimensions of the motion area lead to energy quantization. Its multiply connected structure in the presence of a magnetic field leads to effects that are derived from the Aharonov–Bohm effect. It is shown that the curvature of a nanotube, even in the absence of a magnetic field, causes new macroscopic oscillation effects such as de Haas–van Alphen oscillations, which are associated with the quantization of the transverse electron motion energy and with the root peculiarities of the density of electron states on the nanotube surface. Thermodynamic potentials and heat capacity of the electron gas on the tube are calculated in the gas approximation. The Kubo formula for the conductivity tensor of the electron gas on the nanotube surface is obtained. The Landau damping regions of electromagnetic waves on a tube are determined and the beats are theoretically predicted on the graph of the dependence of conductivity on tube parameters. In the hydrodynamic approximation, the plasma waves on the surface of a semiconductor nanotube with a superlattice are considered. It is shown that optical and acoustic plasmons can propagate along a tube with one kind of carrier. Electron spin waves on the surface of a semiconductor nanotube with a superlattice in a magnetic field are studied. The spectra and areas of collisionless damping of these waves are found. We have shown that the spin wave damping is ab-sent in these areas if the tubes with a degenerate electron gas have small radius.

Key words: nanotubes, superlattice, magnetic field, thermodynamic functions, dynamic conductivity, plasma waves, electron spin waves.

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