Valley-valve effect and even-odd parity in p-n graphene junctions

We address the current blocking by a p-n junction in a zigzag graphene ribbon by means of numerical and analytic investigations. Ribbons with superimposed gate potentials perfectly block the current in the energy range, where a single energy band is active in both the n and the p regions, if the number of carbon chains is even. In the same conditions, an odd number of chains allows current transmission. We interpret this even-odd valley-valve effect in terms of the underlying honeycomb topology and crystal structure symmetry.