Non-diffusion theory of weak localization in graphene

Abstract: We put forward a theory of the weak localization in two dimensional graphene layers which explains experimentally observable transition between positive and negative magnetoresistance. Calculations are performed for the whole range of classically weak magnetic field with account on intervalley transitions. Contribution to the quantum correction which stems from closed trajectories with few scatterers is carefully taken into account. We show that intervalley transitions lead not only to the transition from weak antilocalization to the weak localization, but also to the non-monotonous dependence of the conductivity on the magnetic field.