Quantum Diagrammatic Theory of the Extrinsic Spin Hall Effect in Graphene

TL;DR

This paper develops a comprehensive quantum diagrammatic theory for the extrinsic spin Hall effect in disordered graphene, revealing how skew scattering and quantum corrections influence spin transport, with implications for experiments.

Contribution

It introduces a nonperturbative, self-consistent diagrammatic approach that captures skew scattering, quantum corrections, and the effects of graphene's sublattice structure on the spin Hall effect.

Findings

Quantitative agreement with Boltzmann theory for skew scattering.

Skewness from impurities significantly affects the anomalous spin Hall component.

Quantum interference corrections, especially $ ext{Psi}$ diagrams, dominate away from the Dirac point.

Abstract

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.