Tight-binding Based Calculations On Electronic Structure For Blue Phosphorene

The two-dimensional material is the 2D plane material with the thickness of one or a few atoms.After the preparation of graphene,they have been springed up.Although these materials have been successfully prepared in recent years,these materials attracted considerable attention rapidly because of their unique physical and the potential applications in spin electronics.In the academic dissertation,we systematically used the tight binding model to investigate the establishment of the Hamiltonian and the calculation of the band dispersion of the blue phosphorous,a kind of 2D semiconductor.There are four chapters in this paper,in which the third chapter is our own work.The first chapter is the introduction.In this section,we introduce the the basic concepts of 2D materials,the rise of these materials in the field of science and some of the typical 2D materials.Graphene is the most simple 2D material,with two non-equivalent atoms in the same plane.Its Brillouin zone is the regular hexagon.Similared to the graphene,there is a tiny difference in height between two non-equivalent atoms in silicene,which has the warped structure.The height of MoS2 is the height of three atoms.And black phosphorous is the hexagonal structure,with four atoms in each primitive cell.Blue phosphorous,the allotrope of black phosphorous,is predicted that which has similar advantage to the black phosphorous.In the second chapter,we introduce the usual way to the tight binding method,which used in the calculation of band.The configuration of Extranuclear electrons follows the electronic band theory.The integral between the different atomic orbit agree with Slater-Koster parameter when the electrons in the different atom orbits to form the bonding.The hybridization between the s orbit and p orbit can form the sigma bonds,which can't form the pi bonds.There are three main methods to form covalent bonding among the three nearest neighbor atoms,named sp,sp2 and sp3 hybridization.The main idea of the tight binding is the linear combination of atomic orbits and we can obtain by calculation the general expression of Hamilton.In the third chapter,we take the blue phosphorus for the model to discuss the sp3 hybridization.We gained the the Hamiltonian matrix through the tight binding,and compared with the result of DFT.We find that,the influence of hybridization between the two s orbits is weak.The influence of hybridization of sp is following.The material's energy band is decided by hybridization between the two p orbits.From the point of view of chemical bonding,nearest neighbor calculation better description of the conduction band is well,but it is not accurate in the description of the valence band.So we added the next-nearest-neighbor hoppings with the basis of the Hamiltonian matrix mentioned above,indicate that,the analytic expression and band structure obtained are in good agreement with the results performed by DFT.In the last chapter,a short summary of this paper and some remarks on future developments in forthcoming years is given.