The Recursive Green's Function Method To Study The Band Of The Low-dimensional Carbon Nanomaterials

Carbon nanomaterials are a new type of materials for Mesoscopic Physics study, and have become one of the important regions of condensed-matter physics. Due to the quantum confinement effect, carbon nanomaterials have unique mechanical, electronic and optical properties. So carbon nanomaterials have a bright future in application.Based on the recursive green’s function technique, in ZGNRs and AGNRs the influence of boundary structure on the band structure is studied detailed. And the conclusions are consistent with previous findings. For AGNRs, we first made a detailed theory analysis of the band structure by taking the tight-binding model, and employing the hard-wall boundary condition. It is found that only when its width are n=3p+2, the AGNRs show metallic properties. And the properties of semiconducting AGNRs are investigated by complex band structures which are calculated by the recursive green’s function technique. The properties of evanescent states are described by e-k_imagx x.The band structure of multilayer ZGNRs,AGNRs and SWCNs are calculated by the recursive green’s function technique also. With the increased number of layers, the band gap of semiconducting AGNRs is reduced. For GNRs, the influence of periodic boundary conditions is explained by tight-binding model theory also.At last we study the influence of carbon vacancy defect. For ZGNRs with width n=7, we found single carbon vacancy did not change the metallic properties of ZGNRs. The band structure in the Fermi level changes a lot when the vacancy located at the boundary. The structures of B-H-ZGNRs、π-ZGNRs are investigated also. For B-H-ZGNRs, band gap appears. The value of the band gap depends on the number of Benzene ring.