Theory of the valley-valve effect in graphene nanoribbons

A potential step in a graphene nanoribbon with zigzag edges is shown to be an intrinsic source of intervalley scattering-no matter how smooth the step is on the scale of the lattice constant a. The valleys are coupled by a pair of localized states at the opposite edges, which act as an attractor and/or repellor for the edge states propagating in valley K/K'. The relative displacement A along the ribbon of the localized states determines the conductance G. Our result G = (e(2)/h)[1-cos(N pi+2 pi Delta/3a)] explains why the valley-valve effect (the blocking of the current by a p-n junction) depends on the parity of the number N of carbon atoms across the ribbon.