| The two-Dimensional(2D) materials have many exciting properties, such as the high carrier mobility and mechanical property, the superconductivity of Fe Se, etc. The 2D materials have many different geometric structures, such as the hexagonal structure of MoS2, the pentagon structure of penta-graphene, the tetragonal structure of T graphene, the triangular structures of CuSi2, etc. Besides, the electronic properties are also different from each other, from semiconductor to semimetal to metal. Recently, people find that the intercalated three-Dimensional(3D) structures constructed from 2D materials possessing exotic properties, such as the superconductivity of Ca C6, the excellent optical properties, etc. specially, they find that the intercalation compounds may possess 3D semimetal properties.The article be divided into five parts. In chapter one, we introduced some representative 2D structures such as graphene, silicene, hexagonal 2D silicon carbide and T-graphene. Besides, we also introduced the electronic properties of the 3D materials such as the CKL carbon foam and CaC6 graphite intercalations.In chapter two, the density functional methods are introduced.In chapter three, we studied the versatile electronic properties and exotic edge states in single-layer tetragonal silicon carbides.Threesingle-layer tetragonal silicon carbides(SiC),termed as T1,T2 and T3, are proposed by density functional theory(DFT) computations. Although the three structures have the same topological geometry, they show versatile electronic properties from semiconductor(T1), semimetal(T2) to metal(T3). The versatile properties are originated from the rich bonds between Si and C atoms. The nanoribbons of the three SiC also show interesting electronic properties. Especially, T1 nanoribbons possess exotic edge states, where electrons only distribute on one edge’s silicon or carbon atoms. The band gaps of the T1 nanoribbons are constant because of no interaction between the edge states.In chapter four, we studied the 3D Dirac point in graphite intercalation MC6(M is the transition metals). The structures are constructed by AA stacking graphene and intercalate transition metals between each graphene layers. We find the only intercalate Ni family atoms into the AA stacking 3D graphene can obtain 3D Dirac point in the direction of Z. That is because the d-cahracter 3D Dirac point spectrum arising on the Fermi surface is result from the d orbitals of transition metals coupled with the pz orbitals of graphene. Besides, we find that randomly arrange the transition metals have no effect on the 3D Dirac point..In capter five, summary is given to our study and we also explicitly described the studies in the future. |