Regulation Of Zigzag Graphene Nanoribbons Boundary Bands

Due to the peculiar electronic properties of monolayer graphene more and more attention have been attracted by more and more people in recent years.A lot of theoretical research on band structure and electrical transport properties have been done.The early theoretical work proposed the zero-gap energy dispersion of Dirac particles without mass.In zigzag graphene nanoribbons(ZGNRs)there are edge bands having zero gap,which restricts the application to electronic devices.So many scientists continually explore ways to open the band gap in graphene and ZGNRs.In this thesis,based on the tight binding Kane-Mele model involving self-consistant on-site Coulomb potential,we try to investigate one way to control the band structure of four edge bands in narrow ZGNR.Firstly,considering the influence of enviroment on the bond length between two nearest-neighbor atoms at the two edges,we simulate the effect of environment on the band structure of four edge bands by changing the hopping coefficients between two nearest-neighbor atoms at the edges.When two edges are under the same environment,through adjusting both of the hopping coefficient at two edge sides,the theoretical simulations show that the band structure still is symmetry in k-space.With the increase of the hopping coefficient,the two Fermi wave vectors of the two sub-band stuctures are close to 0.5,respectively.The energy band gap decreases linearly.When two edge sides are under different environments,through adjusting the hopping coefficient at one edge side,the theoretical simulations show that band structure symmetry is broken.With the decrease of the hopping coefficient,the region of the edge states on this edge side enlarges.Therefore,we can change the hopping coefficients at the edges to tune the characteristics of sub-band structure corresponding to different edges.Next,by applying transverse electric field in plane of ZGNR,we study in detail the change process of the band structure of four edge bands with the strength of field.The theoretical results show that when applying weak electric field intensity,the direction of electric field can adjust these two spin-down edge bands moving along the different directions in one-dimensional q space,which leads to the two different types of degenerative breakdown of two pure spin-down edge states at q=0.5.When applying positive electric field the energy of spin-down edge band at edge site 1 is higher than that at edge site 8.On the contrary,when applying negative electric field the energy of spin-down edge band at edge site 8 is higher than that at edge site 1.It shows that we can use the direction of electric field to control the two spin-down edge currents occurring at two different energies.Further,when the electric field intensity increases above 0.69 V/nm,the increased large band gap between the two spin-down edge bands leads to the inversion of these two spin-down edge bands.That is to say,there is a spin-down band gap,however,there is not a band gap for spin-up edge band in the region of spin-down band gap.Thus the system becomes half-metallic,and the QSH does not belong in the type B any longer.Specially,when the electric field intensity reaches 1.17 V/nm in the region of spin-down band gap,the pure spin-up edge state appears at q=0.5,which shows that the strong pure spin-up edge current along the edge site 8 can occur.With increasing the intensity of electric field,the QSH system undergoes three processes from the type B to the type C.When the electric field intensity is more than 1.42 V/nm,the two spin-up edge bands also present band inversion and turn into the conduction band and the valence band,respectively.Thus the system becomes semiconducting and the QSH system does not belong in 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 transverse electric field in plane we can adjust the properties of edge current,and control the type of QSH system varying from the type B to the type C.