  The current carrying capacity of ballistic electrons in carbon nanotubes that
are coupled to ideal contacts is analyzed. At small applied voltages, where
electrons are injected only into crossing subbands, the differential
conductance is $4e^2/h$. At applied voltages larger than $\Delta E_{NC}/2e$
($\Delta E_{NC}$ is the energy level spacing of first non crossing subbands),
electrons are injected into non crossing subbands. The contribution of these
electrons to current is determined by the competing processes of Bragg
reflection and Zener type inter subband tunneling. In small diameter nanotubes,
Bragg reflection dominates, and the maximum differential conductance is
comparable to $4e^2/h$. Inter subband Zener tunneling can be non negligible as
the nanotube diameter increases because $\Delta E_{NC}$ is inversely
proportional to the diameter. As a result, with increasing nanotube diameter,
the differential conductance becomes larger than $4e^2/h$, though not
comparable to the large number of subbands into which electrons are injected
from the contacts. These results may be relevant to recent experiments in large
diameter multi-wall nanotubes that observed conductances larger than $4e^2/h$.
