Theoretical Researches On Optical Conductivity And Light Transmission Spectrum In Graphene

Graphene is a two-dimensional new material with perfect properties. In 2004, graphene was isolated by Geim and coworkers using a method of micro-mechanical stripping. The unique electrical and optical properties in graphene attract many scientists interest. In this paper, based on quantum mechanics and the energy band theory, using the tight-binding approximation method, the band structure was calculated in graphene. Including the interaction between the second nearest neighbor atoms, the nonlinear spectroscopy in graphene was obtained. The optical conductivity in graphene was obtained analytically and numerically with the dependence of the electron concentration, the broadening width, and the nonlinear energy spectrum. The optical conductivity can be tuned by the electron density. With increasing the broadening width, the optical mutation induced by the inter-band transition was more gradual and the intra-band contribution is increasing. The turning point of inter-band transition can be obtained at two times the Fermi energy. The more obvious contribution from intra-band transition was observed when nonlinear energy dispersion was included. Klein tunneling was observed in graphene. Then we investigated the tunneling characteristics in monolayer graphene with applied barrier structures. The number and shape of the barrier can be adjusted. Using transfer matrix method, the tunneling probability, energy band strucutre and conductivity are obtained in graphene with barrier structure. We found that the tunneling probability and conductance in graphene not only dependent on the barrier height, the barrier width, the angle of incidence and the incident energy, but also dependent on the shape of the barrier. The results show that the tunneling probability and conductance can be tuned by the structural parameters of the barrier. These properties can be analyzed by the energy band structure with the corresponding periodic barrier structure. Based on previous studies, we also made a preliminary theoretical analysis of light transmissibility in graphene with periodic barrier structure, which will provide a theoretical reference for graphene-based optoelectronic nano devices.