Effects of coupling on plasmon modes and drift-induced instabilities in a pair of cylindrical nanotubes

We develop a theory of collective plasma excitations in a pair of parallel nonoverlapping cylindrical nanotubes. A general dispersion equation is obtained as a function of the angular momentum and linear momentum transfer. We use our results to calculate the phase velocity of the plasmon excitations when current flows parallel to the axis of the nanotube in either the same or neighboring nanotube as the plasma excitations. We demonstrate that the less energetic undamped plasmon excitations may have a phase velocity which is smaller than the Fermi velocity. The plasmons with the largest frequencies have phase velocities which decrease with increasing wave vector. We discuss the instabilities which may arise when the drift velocity of the electrons lies within a range which is determined by the phase velocity for the plasmon modes of the pair of cylindrical nanotubes.