Instability of capacitance mode in multi-walled nanotubes

Conditions for intra and inter layer Coulomb interactions in multi-walled carbon nanotubes are derived from stability of capacitance excitations. It is pointed out, supposing the stability conditions are not satisfied, that the system has unstable modes which correspond to a charge transfer between layers or charge density oscillation in each layer depending on zero mode or non-zero modes. It is argued that the stability conditions can be broken when the vacuum polarization processes due to the massive bands are taken into account.