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In this paper, we study the electronic conductance of armchair and zigzag graphene nanoribbons in the presence of a local magnetic field by using Green’s function technique at the nearest neighbor tight-binding approach. The results show that the existence of magnetic flux in an armchair nanoribbon causes that the intrinsic gap of the nanoribbon becomes smaller and two anti-resonances are created in the conductance spectrum. Whenever, all rings contain the uniform magnetic flux, a part of resonance region can be converted to a tunneling region which represent a new gap energy. Moreover, in a zigzag nanoribbon which is connected to two simple leads through the trans connection, some Fano resonances can exist at the conductance spectrum in the absence of magnetic flux. 

Keywords: : Green’s function, Tight-binding, Graphene nanoribbons, Aharonov-Bohm

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