Quantum Chaotic Behavior in Zigzag Graphene Nanoribbon: Effect of Impurity and Electric Field

Metal-insulator transition in zigzag graphene nanoribbon has been studied using random matrix theory. By employing inverse participation ratio and spectral analysis, our results show that metal-insulator transition occurs in the presence of a random distribution of substitutional nitrogen atoms. We have observed quantum chaotic Wigner energy levelstatistics distribution for low nitrogen concentration. At sufficiently high doping, system is at the begging of transition from Wigner to Poisson distribution. For doped graphene, our calculations indicate that this transition becomes fast by applying transverse electric field. Additionally, a threshold value for the transverse electric field is reported. For this threshold value, the change of the conductivity is drastically and Poisson level-spacing sets in. More interestingly, a negative differential resistance and quasi-ohmic behavior can be found for various values of impurity and electric field, such that for these values quantum chaotic predicts Wigner distribution.