We have theoretically investigated the properties of electronic transport in graphene heterostructures, which consist of two different graphene superlattices with one-dimensional periodic potentials. It is found that such heterostructures possess an unusual tunneling state occurring inside the original forbidden gaps, the electronic conductance is greatly enhanced and additionally, the Fano factor is strongly suppressed near the energy of the tunneling state. Finally, we present the matching condition of the impedance of the pseudospin wave for occurring the tunneling state by using the Bloch-wave expansion method.
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