Effects of antidots on the transport properties of graphene nanoribbons

Abstract

Effects of magnetic antidots on the transport properties of zigzag-edged graphene nanoribbons ZGNRs are investigated by spin-polarized first-principles calculations combined with a nonequilibrium Green’s-function technique. Specifically, the effects of antidots or holes with regular shapes rectangular and triangular are studied. It is found that rectangular holes with a zero total spin S0 and triangular holes with a finite spin S0 cause different effects on the equilibrium conductance of ZGNRs. A rectangular hole with zigzag edges parallel to the ribbon edges blocks the transmission of the band edges of both the valence band and the conduction band from both the spin-up channel and the spin-down channel. Thus a much wider transmission gap than the pristine ZGNRs can be observed. However, a triangular hole with zigzag edges blocks transmission from only one spin channel in either the valence-band edge or the conduction-band edge. Thus the gap width in the total conductance is not affected in this case. The difference originates from the different energy shift of the valence band and conduction band relative to Fermi energy as a result of two effects: finite-size effect and spin splitting from the antidot-induced effective internal magnetic field. Graphene nanostructures are supposed to be very important building blocks in future nanoelectronic devices due to their remarkable structural and electronic properties. Among them, graphene nanoribbons GNRs have attracted intensive attention 1–12 and it is found that the properties of GNRs are highly dependent on their sizes and edge shapes. Tightbinding calculations show that armchair-edged GNRs AGNRs can be either metallic or semiconducting depending on their widths 8,12 while first-principles calculations show that AGNRs are always semiconducting with an energy-gap scaling inversely to the GNR width. 8–10 More interestingly, in the zigzag-edged GNRs ZGNRs, magnetic ordering is formed due to the unpaired - and -edge electrons. Two most stable spin configurations have been observed: ferromagnetic FM and antiferromagnetic AF, 13 which mean that the localized edge states on the two sides are FM coupled or AF coupled. Tight-binding calculations show that the ZGNRs are always metallic 12 while first-principles calculations show that it is metallic only in the FM configuration. There is always an energy gap in the AF configuration. Calculations also show that the most stable configuration is the AF state with the states of different spins in the valence bands and conduction bands localized on different edges while the energy of the states with different spins is degenerate. 5,8 Meanwhile, quantum dots and antidots made by graphene are another kind of graphene nanostructures which initiate great interests. 14–20 The dots are just graphene molecules with finite size in all directions while antidots are holes in graphene with some kinds of dots cut away from it. Just like in ZGNRs, magnetism can also be formed in graphene molecules with zigzag edges. 15 In a graphene molecule with rectangular or hexagonal edges, magnetic moments with the same magnitude and different signs are always formed on the two opposite zigzag edges. Thus the total spin S0 in such systems is exactly zero. However, in a molecule with triangular zigzag edges, exactly the same magnetic moments are observed on all edges. So the total spin S0 is nonzero. Like in ZGNRs, the local magnetism in graphene molecules arises from the spin-polarized edge states localized on the zigzag edges. The local magnetism in graphene nanostructures may qualify graphene nanoribbons and molecules with zigzag edges as promising candidates for application in the spintronic devices. Therefore, the study of spin-polarized transport through these nanostructures are quite interesting. In this work, we build graphene-based devices by combining graphene nanoribbons and antidots with zigzag edges and investigate the electron transport in them. Specifically, we study the effects of graphene antidots or holes on the transport properties of ZGNRs. Two kinds of antidots will be considered: rectangular hole and triangular hole. The model structure is constructed as follows: the scatter