Carbon Nanotube Ballistic Thermal Conductance and Its Limits

Calculations of the quantum-mechanical ballistic thermal conductance of single-walled carbon nanotubes, graphene, and graphite are presented, which explain previous experimental results, and directly disprove earlier theoretical calculations. The ballistic thermal conductances are smaller than had been previously thought, whereas the maximum sample lengths in which phonon transport remains ballistic are orders of magnitude larger than previously suggested. Good agreement with previous experiments is obtained, which shows that measured lower bounds to the thermal conductance of multiwalled carbon nanotubes are very close to the upper theoretical bounds for graphite. The bounds shown here draw a line between what is physical and unphysical in any measurements or calculations of carbon nanotube thermal conductance, and constitute a necessary test to their validity.