Ballistic transport and electrostatics in metallic carbon nanotubes

We calculate the current and electrostatic potential drop in metallic carbon nanotube wires self-consistently, by solving the Green's function and electrostatics equations in the ballistic case. About one tenth of the applied voltage drops across the bulk of a nanowire, independent of the lengths considered here. The remaining nine tenths of the bias drops near the contacts, thereby creating a non linear potential drop. The scaling of the electric field at the center of the nanotube with length (L) is faster than 1/L (roughly $1/L^{1.25-1.75}$). At room temperature, the low bias conductance of large diameter nanotubes is larger than $4e^2/h$ due to occupation of non crossing subbands. The physics of conductance evolution with bias due to the transmission Zener tunneling in non crossing subbands is discussed.