Breakdown of Fourier's law in nanotube thermal conductors

We present experimental evidence that the room temperature thermal conductivity ($\kappa )$ of individual multiwall carbon nanotubes and boron-nitride nanotubes does not obey Fourier's law as do ordinary thermal conductors. By varying the length (L) of the nanotube, we find that $\kappa $ diverges as L$^{0.6\sim 0.9}$. Our results show that Fourier's law is violated despite the fact that the ballistic phonon condition is not satisfied and large isotopic disorder is present.