Weak localization in monolayer and bilayer graphene

We describe the weak localization correction to conductivity in ultrathin graphene films, taking into account disorder scattering and the influence of trigonal warping of the Fermi surface. A possible manifestation of the chiral nature of electrons in the localization properties is hampered by trigonal warping, resulting in a suppression of the weak anti-localization effect in monolayer graphene and of weak localization in bilayer graphene. Intervalley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore weak localization resulting in negative magnetoresistance in both materials.