Weak Localization and Spin-Orbit Coupling in Monolayer and Bilayer Graphene

Abstract

The effective Hamiltonian of low-energy electrons in monolayer and bilayer graphene is described, taking into account static disorder and spin-orbit coupling. We review different regimes of weak localization in these materials that arise from an interplay between lattice, valley, and spin degrees of freedom and the relative strength of different types of symmetry-breaking scattering. At very low temperature, weak localization may be sensitive to the presence and nature of spin-orbit coupling, and we derive formulae for the corresponding low-field magnetoresistance. If Bychkov-Rashba spin-orbit coupling is present, it tends to induce weak anti-localization in both monolayers and bilayers—as in semiconductors and metals—but, if intrinsic spin-orbit coupling prevails, it results in a suppression of weak localization.