Spectral properties of incommensurate double-walled carbon nanotubes

Incommensurate double-walled carbon nanotubes (iDWCNTs) are one of the simplest nanostructures where we can study the role of incommensurability in quantum transport. We investigate the dynamics of electrons via spectral statistics for different interwall interactions in iDWCNTs. The spectral properties of iDWCNTs are described by Poisson, Wigner–Dyson, and semi-Poisson distributions, depending on the energy regime, implying that the transport nature might be ballistic, diffusive, and intermediate between them. The spectral distribution is found to change from Poisson to Wigner–Dyson as the interwall interaction strength increases. We also analyze the characteristics of wave functions for the three different energy regimes, in conjunction with the transport behavior.