Abstract Analytical studies of the effect of edge decoration on the energy spectrum of semi-infinite one-dimensional (1D) model and zigzag edged graphene (ZEG) are presented by means of transfer matrix method, in the frame of which the conditions for the existence of edge states are determined. For 1D model, the zero-energy surface state occurs regardless of whether the decorations exist or not, while the non-zero-energy surface states can be induced and manipulated through adjusting the edge decoration. On the other hand, the case for the semi-infinite ZEG model with nearest-neighbour interaction is discussed in the analogous way. The non-zero-energy surface states can be induced by the edge decoration and moreover, the ratio between the edge hopping and the bulk hopping amplitudes should be within a certain threshold.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10847001) and the National Basic Research Program of China (Grant Nos. 2009CB929204 and 2011CB921803).
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