Anomalous thermal transport in disordered harmonic chains and carbon nanotubes

We report the coherent potential approximation method of treating quantum thermal transport properties of nanoscale systems with mass disorder. Instead of massive efforts required in brute-force calculations, configuration averaging of disordered systems can be efficiently handled in a self-consistent manner by setting up the phonon version of nonequilibrium vertex correction theory. The accuracy of the method is verified by comparing with the exact results and Monte Carlo experiments in one-dimensional atomic chains. Results obtained for disordered harmonic chains and carbon nanotubes provide evidence of anomalous thermal transport in such systems. We also observe crossover in the transport where phonon scattering by disorder becomes important. Our results show that disorder plays a role in thermal conductance reduction.