$z\ensuremath{\rightarrow}\ensuremath{-}z$ Symmetry of Spin-Orbit Coupling and Weak Localization in Graphene

$z \to - z$ Symmetry of Spin-Orbit Coupling and Weak Localization in Graphene

Edward McCann and Vladimir I. Fal’ko

Phys. Rev. Lett. 108, 166606 – Published 20 April 2012

Abstract

We show that the influence of spin-orbit (SO) coupling on the weak-localization effect for electrons in graphene depends on the lack or presence of $z \to - z$ symmetry in the system. While, for $z \to - z$ asymmetric SO coupling, disordered graphene should display a weak antilocalization behavior at lowest temperature, $z \to - z$ symmetric coupling leads to an effective saturation of decoherence time which can be partially lifted by an in-plane magnetic field, thus tending to restore the weak-localization effect.