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

TL;DR

This paper investigates anomalous wave packet diffusion in disorder-free multi-walled carbon nanotubes, revealing how shell chirality and incommensurability influence diffusion behavior and quantum spreading patterns.

Contribution

It introduces a method to analyze anomalous diffusion in disorder-free nanotubes using multifractal spectrum analysis and characterizes the diffusion exponent's dependence on structural parameters.

Findings

Diffusion exponent ranges from 1/2 to 1 depending on chirality.

Large incommensurability leads to diffusive behavior with exponent near 1/2.

Quantum spreading varies with energy, showing ballistic, super-diffusive, or diffusive patterns.

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 $1/2 \leq \eta < 1$. 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.