Heat superdiffusion in carbon nanotubes

Like many one-dimensional systems, carbon nanotubes are known to exhibit a divergent thermal conductivity as the length of the nanotube is increased, but the precise form of this divergence has so far been disputed, some even arguing for a final convergent conductivity. In this work, the solution given by mode-coupling theory, which precisely describes the heat divergence as a power law for sufficiently large lengths, is clearly revealed in molecular dynamics simulations where the tubes' ends are kept at different temperatures. The precise localization of such an asymptotic power law explains why it has not been found before and helps resolve a long-standing puzzle in nanoscale heat transport. It is estimated to show up in carbon nanotubes of macroscopic lengths, currently achievable experimentally.