Weak localization in graphene.

We review the recently-developed theory of weak localization in monolayer and bilayer graphene. For high-density monolayer graphene and for any-density bilayers, the dominant factor affecting weak localization properties is trigonal warping of graphene bands, which reflects asymmetry of the carrier dispersion with respect to the center of the corresponding valley. The suppression of weak localization by trigonal warping is accompanied by a similar effect caused by random-bond disorder (due to bending of a graphene sheet) and by dislocation/antidislocation pairs. As a result, weak localization in graphene can be observed only in samples with sufficiently strong inter-valley scattering, which is reflected by a characteristic form of negative magnetoresistance in graphene-based structures