Localization – Weak Antilocalization Crossover in Two-Dimensional Materials with Spin-Orbit Interaction

In this paper, the patterns of manifestation of weak localization and antilocalization in graphene with enhanced spin-orbit interaction, as well as in a topological insulator with a gap in surface states induced by magnetic impurities are studied. The parameters characterizing the manifestation of weak localization, antilocalization and crossover between them are established. Quantum corrections to the conductivity of graphene are determined in units of e 2 /h = 38.64 μS for various ratios between the characteristic dephasing time and spin-orbit scattering time. It has been established that with a relatively long spin-orbit scattering time, not less than 10 –10 s, it does not affect the correction to conductivity and its value is determined by the dephasing time and the times of intervalley and intravalley scattering. The effect of the spin-orbit scattering is to suppress weak antilocalization. It leads to a spin flip of the conduction electron during elastic scattering, and the interference pattern of weak localization becomes more complicated due to the mixing of spin states. The sign of the quantum correction depends on which spin state contributes the most.