Quantum Chaos Analysis of a Nano-crystal’s Electronic Transport Properties

The electronic transport through a nano-scale device is an interesting topic for both experimental and theoretical physicists, addressing development of new nano-devices. Among the synthesized carbon nanostructures as the materia prima for development of nano-devices, graphene sheets has attracted a lot of attention among researchers. Exceptional properties including carriers with extremely large mobilities and truly two dimensional geometry have made graphene as a promising candidate for replacing semiconductors in the future of nanotechnology. It seems that for a more comprehensive insight of electronic transport properties of the graphene, we could use new frames. The electronic properties of graphene can be well described using a 2-D tight-binding model. The tight-binding is a quantum model to describe electron motion within an atomic lattice, so graphene and other synthesized carbon nanostructure dynamics can be well studied through quantum chaos theory. Present study discusses different regimes of conductivity in a 2-D tight-binding model of a graphene sheet. For this purpose, we apply quantum chaos theory. Spectral statistics of energy levels are used to get consecutive level spacing distribution as an identifier of electronic properties of the device. In order to find best configuration of the crystal for metallic regime, different arrays of onsite energies and hopping constants are analyzed. Also, we discuss the obtained results through multi-fractal analysis. Our results can report different regimes of conductivity and transition between metallic and insulator phases.