Electronic Structure of Carbon Nanotube Ropes
  We present a tight binding theory to analyze the motion of electrons between carbon nanotubes bundled into a carbon nanotube rope. The theory is developed starting from a description of the propagating Bloch waves on ideal tubes, and the effects of intertube motion are treated perturbatively in this basis. Expressions for the interwall tunneling amplitudes between states on neighboring tubes are derived which show the dependence on chiral angles and intratube crystal momenta. We find that conservation of crystal momentum along the tube direction suppresses interwall coherence in a carbon nanorope containing tubes with random chiralities. Numerical calculations are presented which indicate that electronic states in a rope are localized in the transverse direction with a coherence length corresponding to a tube diameter. 
Ahmed A. Maarouf, Charles L. Kane and Eugene J. Mele