Anomalous diffusion and elastic mean free path in disorder-free multi-walled carbon nanotubes

Abstract

We explore the nature of anomalous diffusion of wave packets in disorder-free incommensurate multi-walled carbon nanotubes. The spectrum-averaged diffusion exponent is obtained by calculating the multifractal dimension of the energy spectrum. Depending on the shell chirality, the exponent is found to lie within the range $1/2\le \eta <1$. For large unit cell mismatch between incommensurate shells, $\eta$ approaches the value 1/2 for diffusive motion. The energy-dependent quantum spreading reveals a complex density-of-states-dependent pattern with ballistic, super-diffusive or diffusive character.

4 pages, 4 figures

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