Magnetoplasmons and persistent currents in cylindrical tubules

The quasi-one-dimensional (1D) magnetoplasmons of a graphene tubule threaded by a magnetic field (B) have been evaluated exactly within the random-phase approximation. The plasmon frequency ${\mathit{w}}_{\mathit{p}}$ exhibits a very rich structure as a function of the magnetic flux through the tubule (φ)—including many cusps. The φ-dependent part of ${\mathit{w}}_{\mathit{p}}$ is shown to be proportional to the induced persistent-current density (J) in the tubule. Measurements on ${\mathit{w}}_{\mathit{p}}$ and J are expected to reveal insights regarding the band properties of the quasi-1D system. The structure near the cusps has been examined and is found to be related to important band parameters (e.g., the effective mass of the electrons). The results of this study may be easily generalized to systems composed of several coaxial tubules. The importance of the spin-B interaction in graphene tubules is indicated.