Scattering of plasmons at the intersection of two metallic nanotubes: implications for tunneling

We study theoretically the plasmon scattering at the intersection of two metallic carbon nanotubes. We demonstrate that, for a small angle of crossing θ « 1, the transmission coefficient is an oscillatory function of λ / θ where λ is the interaction parameter of the Luttinger liquid in an individual nanotube.We calculate the tunnel density of states v(ω, x) as a function of energy ω and distance x from the intersection. In contrast with a single nanotube, we find that, in the geometry of crossed nanotubes, conventional ‘‘rapid'' oscillations in v(ω, x) due to the plasmon scattering acquire an aperiodic ‘‘slowbreathing'' envelope which has λ / θ nodes.