Crossover to the Anomalous Quantum Regime in the Extrinsic Spin Hall Effect of Graphene

Recent reports of spin-orbit coupling enhancement in chemically modified graphene have opened doors to studies of the spin Hall effect with massless chiral fermions. Here, we theoretically investigate the interaction and impurity density dependence of the extrinsic spin Hall effect in spin-orbit coupled graphene. We present a nonperturbative quantum diagrammatic calculation of the spin Hall response function in the strong-coupling regime that incorporates skew scattering and anomalous impurity density-independent contributions on equal footing. The spin Hall conductivity dependence on Fermi energy and electron-impurity interaction strength reveals the existence of experimentally accessible regions where anomalous quantum processes dominate. Our findings suggest that spin-orbit-coupled graphene is an ideal model system for probing the competition between semiclassical and bona fide quantum scattering mechanisms underlying the spin Hall effect

Quantum Diagrammatic Theory of the Extrinsic Spin Hall Effect in Graphene

We present a rigorous microscopic theory of the extrinsic spin Hall effect in disordered graphene based on a nonperturbative quantum diagrammatic treatment incorporating skew scattering and anomalous---impurity concentration-independent---quantum corrections on equal footing. The leading skew scattering contribution to the spin Hall conductivity is shown to quantitatively agree with Boltzmann transport theory over a wide range of parameters. Our self-consistent approach---where all topologically equivalent noncrossing diagrams are resummed---unveils that the skewness generated by spin--orbit-active impurities deeply influences the anomalous component of the spin Hall conductivity, even in the weak scattering regime. This seemingly counterintuitive result is explained by the rich sublattice structure of scattering potentials in graphene, for which traditional Gaussian disorder approximations fail to capture the intricate correlations between skew scattering and side jumps generated through diffusion. Finally, we assess the role of quantum interference corrections by evaluating an important subclass of crossing diagrams recently considered in the context of the anomalous Hall effect, the $X$ and $\Psi$ diagrams [Ado et al., EPL 111, 37004 (2015)]. We show that $\Psi$ diagrams---encoding quantum coherent skew scattering---display a strong Fermi energy dependence, dominating the anomalous spin Hall component away from the Dirac point. Our findings have direct implications for nonlocal transport experiments in spin--orbit-coupled graphene systems

Spin Hall effect in a 2DEG in the presence of magnetic couplings

It is now well established that the peculiar linear-in-momentum dependence of the Rashba (and of the Dresselhaus) spin-orbit coupling leads to the vanishing of the spin Hall conductivity in the bulk of a two-dimensional electron gas (2DEG). In this paper we discuss how generic magnetic couplings change this behaviour providing then a potential handle on the spin Hall effect. In particular we examine the influence of magnetic impurities and an in-plane magnetic field. We find that in both cases there is a finite spin Hall effect and we provide explicit expressions for the spin Hall conductivity. The results can be obtained by means of the quasiclassical Green function approach, that we have recently extended to spin-orbit coupled electron systems