Weak localisation magnetoresistance and valley symmetry in graphene

Due to the chiral nature of electrons in a monolayer of graphite (graphene) one can expect weak antilocalisation and a positive weak-field magnetoresistance in it. However, trigonal warping (which breaks p/-p symmetry of the Fermi line in each valley) suppresses antilocalisation, while inter-valley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore conventional negative magnetoresistance. We show this by evaluating the dependence of the magnetoresistance of graphene on relaxation rates associated with various possible ways of breaking a 'hidden' valley symmetry of the system.