Quantum Size Effect Of Triangular Graphene With Zigzag Edges

2D graphene was prepared successfully in experiment by Geim’s research group from Mancheter University in2004. Its unique electronic properties, such as anomalous quantum hall effect,special electron mobility and so on, have received wide attention. The nanostructures of graphene with boundary and finite size was made by mechanical stripping, surface epitaxial growing, seal extrusion, and chemical separation.The quantum size effect of triangular grapheme with zigzag edges was investigated by tight-binding approach and the reliability of Dirac equation in calculating the electronic structure of the finite-size triangular graphene with zigzag edges was also tested. The results showed as follows:(a) The energy level is quantization and the energy bands are disperstion when the size of triangular graphene is small.(b) While the size is increasing, the energy level becomes continuous and the gap decreases gradually, more energy bands were found and the electronic states near the Fermi surface increases gradually.(c) When the size of the graphene nanostructure is large enough (up to10nm), DOS is similar to2D graphene and the energy bands spread all over the space.(d) Compared with the tight-binding appoach, Dirac method have no clear results on degeneracies of zero-energy states and the outcome of the energy gap is relatively small when the size of graphene is small. On the contrary, the results of the two calculation methods are anastomosis to each other.As for the edge deformation effect, the relaxation time of the small size triangular graphene with zigzag edges is quite large,which leads to the changes of the c-c chemical bond and hopping integral and affects the electronic structure of graphene nanostructures. we construced the edge deformation model in this way and calculated the effects of edge deformation on electronic structure by tight-binding approach.In this paper, The edge deformation effect of small size Triangular Graphene is investigated.when the hopping integral decrease,the bands width and the gap both become small.On the contrary, the bands width and the gap both increase.we pay more attention to the energy bands near Fermi Surface,finding the energy bands which include edge states and standing wave states became steep when the hopping integral was changed.