Spectral Correlation in Incommensurate Multi-Walled Carbon Nanotubes

We investigate the energy spectra of clean incommensurate double-walled carbon nanotubes, and find that the overall spectral properties are described by the so-called critical statistics of Anderson metal-insulator transition. In the energy spectra, there exist three different regimes characterized by Wigner-Dyson, Poisson, and semi-Poisson distributions. This feature implies that the electron transport in incommensurate multi-walled nanotubes can be either diffusive, ballistic, or intermediate between them, depending on the position of the Fermi energy.