Electron Transport and Hot Phonons in Carbon Nanotubes

We demonstrate the key role of phonon occupation in limiting the high-field ballistic transport in metallic carbon nanotubes. In particular, we provide a simple analytic formula for the electron transport scattering length, which we validate by accurate first principles calculations on $(6,6)$ and $(11,11)$ nanotubes. The comparison of our results with the scattering lengths fitted from experimental $I\mathrm{\text{−}}V$ curves indicates the presence of a nonequilibrium optical phonon heating induced by electron transport. We predict an effective temperature for optical phonons of thousands Kelvin.