Abstract
Applying an external electric field to gapped armchair graphene nanoribbons (AGNRs) would lead to the splitting of subbands with opposite valleys (K and K’) due to the valley-orbit interaction (VOI). Moreover, the boundary scattering couples K and K’ states giving the formation of a pseudo-gap. We can set the incident electron energy inside the pseudo-gap, so that the above AGNR configuration can filter the K’ or K valley state, resulting in a device called the valley filter. This thesis presents a transport study of such an all-electrical valley filtering structure based on the recursive Green’s function method, which particularly focuses on three parts: the effect of the channel length, electric field strength, and dependence on the incident electron energy. The valley filter needs enough channel length to reduce the transmission through the channel of evanescent waves, which passes electrons without any valley filtering effect. Fano resonance and Fabry-Perot resonance can occur in the structure of, for example, three valley filters in series, which happens due to the coupling between the two channels – one via the bound state and the other via evanescent waves in the middle valley filter. The transmittance would vary rapidly with the length of the middle filter due to the resonance. Our study confirms that the ability of filtering in a valley filter can be truly controlled by applying an external electric field. Variation of transmission with incident energy has yet to be clarified.