The Effect of the Disorder on the Longitudinal Resistance of a Graphene p-n Junction in Quantum Hall Regime

The longitudinal resistances of a six-terminal graphene p-n junction under a perpendicular magnetic field are investigated. Because of the chirality of the Hall edge states, the longitudinal resistances on top and bottom edges of the graphene ribbon are not equal. In the presence of suitable disorder, the top-edge and bottom-edge resistances well show the plateau structures in the both unipolar and bipolar regimes and the plateau values are determined by the Landau filling factors only. These plateau structures are in excellent agreement with the recent experiment. For the unipolar junction, the resistance plateaus emerge in the absence of impurity and they are destroyed by strong disorder. But for the bipolar junction, the resistances are very large without the plateau structures in the clean junction. The disorder can strongly reduce the resistances and leads the formation of the resistance plateaus, due to the mixture of the Hall edge states in virtue of the disorder. In addition, the size effect of the junction on the resistances is studied and some extra resistance plateaus are found in the long graphene junction case. This is explained by the fact that only part of the edge states participate in the full mixing.