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. For single wall nanotubes, we find that there are two qualitatively different regimes corresponding to low and high biases. In the low bias regime (100 mV), 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. In the high voltage regime, the potential drops primarily across the bulk of the nanowire. The electric field at the nanotube center increases with increase in nanotube diameter for low biases. 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 low biases, and 1/L at high biases. At room temperature, the low bias conductance of large diameter nanotubes is larger than 4e²/h due to occupation of non crossing subbands. The physics of conductance evolution with bias due to the competing factors of transmission into non crossing subbands and phonon scattering is discussed.