Quantum chaos in weakly disordered graphene

We have studied numerically the statistics for electronic states (level spacings and participation ratios) from disordered graphene dots of finite size, described by the aspect ratio W/L and various geometries, corresponding to finite chiral or achiral carbon nanotubes. Quantum chaotic Wigner energy level-spacing distribution is found for weak disorder, even infinitesimally small disorder for wide and short tight-binding samples (W/L > 1), while for strong disorder, Anderson localization with Poisson level-statistics always sets in. Although pure graphene near the Dirac point corresponds to integrable ballistic statistics diffusive chaotic behavior seems more common for realistic (weakly disordered) finite samples.