Ring current effects on the dielectric function of cylindrical   nano-organic materials
  We review recent results on the behaviour of the dielectric function of cylindrical nano-organic materials at very low frequencies in a magnetic field. For cylindrical structures - such as carbon nanotubes - the polarisability is shown to be a discontinuous function of a longitudinal magnetic field where plateau-like regions are separated by sudden jumps or peaks. A relation is pointed out between each discontinuity in the polarisability and the cross-over between ground and first excited states induced by the magnetic field. This one to one correspondence suggests to use measurements of the dielectric function in an applied magnetic field in order to obtain informations about the electronic structures of cylindrical nanostructures. In addition, it is shown, by studying finite graphene layers, that the measurement of the polarisability in a magnetic field could be a powerful way for detecting possible edge-states in amorphous carbon materials such as activated carbon fibres. Finally, the importance of the electron-electron interaction is emphasised by discussing examples of strongly interacting electrons on rings or cylinders, in the limit of infinite interaction. 
S. Pleutin and A.A. Ovchinnikov