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Graphene pn junction is the brick to build up variety of graphenenano-structures. The analytical formula of the conductance of graphene gradualpn junctions in the whole bipolar region has been absent up to now. In thispaper, we analytically calculated that pn conductance with the spin-orbitcoupling and stagger potential taken into account. Our analytical expressionindicates that the energy gap causes the conductance to drop a constant valuewith respect to that without gap in a certain parameter region, and manifeststhat the curve of the conductance versus the stagger potential consists of twoGaussian peaks -- one valley contributes one peak. The latter feature allowsone to detect the valley polarization without using double-interface resonantdevices.

Valley detection using a graphene gradual pn junction with spin-orbit coupling: an analytical conductance calculation