Magnetoplasma oscillations in nanoscale tubules with helical symmetry

The collective excitations associated with density fluctuations of a system of electrons on nanoscale tubules when a constant magnetic field is present along the tube axes are presented. Several types of acoustic and optical magnetoplasma modes are found. The Kohn anomalies associated with the static density response for appropriate particle-hole excitations across the Fermi surface are also discussed. When the spin-paramagnetic contribution is ignored, it is found that the Fermi energy, magnetization, magnetic susceptibility, and the collective properties are periodic in the magnetic flux enclosed by the cylinder. For these to be relevant to graphitic tubules, which are thought to be obtained by rolling two-dimensional graphite sheets into cylinders, their inherent helical structures must be incorporated into the theory. It is shown that a transformation of the cylindrical wave states to helical wave states allows these results to be made relevant to nanoscale tubules with helical symmetry.