Research On Boundary States In Low-dimensional Carbon Nanomaterials

Low dimensional carbon nanomaterials have been considered as promising materials since the breakthrough experimental discovery of carbon tubes and monolayer graphene.In recent years,topological states induced by Dirac particles in graphene have become a hot topic in condensed matter physics.For zigzag graphene nanoribbon?ZGNR?,we apply the tight binding Kane-Mele model combining with the self-consistent on-site Coulomb interactions?O-CIs?to study the influence of different vertical electric field on the different regions of ZGNR on the edge band structure in order to investigate the way to control the type of quantum spin Hall?QSH?system.The theoretical results show that when applying weak electric field,the direction of electric field can control these two spin-down edge bands moving along the opposite directions in one-dimensional k space.When the electric field intensity is over 0.21 eV,at the right Fermi wave vector the spin-down top edge band crosses over the the spin-up bottom edge band,the QSH is not the closed loop of the type B any longer,and becomes a mixed flow loop.Further,when the electric field intensity is up to 0.25 eV,at the left Fermi wave vector the spin-down top edge band also crosses over the the spin-up bottom edge band,at the same time the QSH becomes one new closed loop forming by two edge bands with opposite spin at the same edge side.When the electric field intensity is over 0.78 eV,because the larger band gap appears,the four edge bands occur flipping,in which the top edge bands and the top edge bands become the conduction band and the valence band,respectively.Thus the system becomes semiconducting and the QSH system becomes the type C,ordinary quantum Hall system.Finally,according to the results discussed above,we can expect that using the direction and the intensity of the vertieal eleetrie field we can adjust the properties of edge current,and eontrol the type of QSH system varying from the type B to the type C.For bilayer zigzag graphene nanoribbon?ZGNR?,we apply the tight binding Kane-Mele model combining with the self-consistent on-site Coulomb interactions?O-CIs?to study the influence of different horizon electric field on the different layer of bilayer ZGNR on the edge band structure and density of states.lt is found that the bilayer ZGNR stacked with AB does not appear a band gap.When the electric field intensity is over 3.5eV,eight bands enter into the energy zone of other bands.When the electric field intensity is over 6eV,eight bands are degenerate in four bands.When the electric field intensity is over 0.7eV,the bilayer ZGNR stacked with AA appears a band gap,but the band structure does not change significantly with the electric field continues to increase.In order to study the electronic structure of other low-dimensional carbon nanomaterials,we through the first principles caculated the band structure of a assemble structure assembled by a carbon nanotube and three zigzag graphene nanoribbons,we found the band structure of ZW₃-CNT is very unique,the boundary bands are not enter into the energy region of other bands,three boundary bands are degenerate near the point of ?,two of three boundary bands degenerate wave vectors between 0.1 and 0.9.Subsequently,we construct a quasi-three-dimensional by translating the ZW₃-CNT structure in the XY plane and calculate the energy band of the point k_x=k_y=0 in the XY plane.In the energy structure of the quasi-three-dimensional structure of ZW₃-CNT,we found six boundary bands.At kz=0,the boundary band intersects the body band,and the wave vectors between 0,2 and 0.8,four of the six boundary bands degenerate below the Fermi energy;the wave vectors between 0.25 and 0.75,the remaining two boundary bands degenerate above the Fermi energy.Then we consider the electronic structure of C7 with large vacancies in 2D graphene.By substitutional doping,? and V elements such as B and N are formed into A₃B₄ structure.First-principles calculations show that C₃N₄ and N₃B₄ appear energy gaps.The conduction and valence bands near Fermi energy do not cross with other energy bands,and the energy bands are relatively flat.Compared with C₃N₄,N₃B₄ is a direct semiconductor with larger energy gap.