Exotic behavior of the dielectric function and the plasmons of an electron gas on a tubule

The dielectric response of an electron gas confined to the surface of a hollow infinitely long cylinder is calculated in the random-phase approximation. The frequency dependence of the imaginary part of the dielectric function shows a steplike behavior. The dielectric function shows the dimensional crossover from two-dimensional to one-dimensional behavior with decreasing cylinder radius. In the quasi-one-dimensional case, our model does not need any artificial cutoff parameters for the Coulomb potential.