Quantum diagrammatic theory of the extrinsic spin Hall effect in graphene

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 (impurityconcentration-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 diagrams [A. Ado et al., Europhys. Lett. 111, 37004 (2015)]. We show that 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.

Microscopic Linear Response Theory of Spin Relaxation and Relativistic Transport Phenomena in Graphene

“…It is not surprising that the spin lifetime dependences are found to be nonphysical as → 0: vanishingly small for the Gaussian limit and divergent for the unitary limit. To overcome this limitation, one needs to evaluate crossing diagrams encoding quantum coherent processes, which includes weak localization corrections and diffractive skew-scattering from two or more impurities [54,69,70]. However, here, we are mostly interested in the diffusive regime away from the Dirac point τ 1, thus neglecting interference effects that can correct the standard DP relation [32,33,71].…”

“…In the weak scattering regime, it suffices to only take into account the "rainbow" diagram with two impurity lines in the Dyson expansion (see Figure 2b). For scalar disorder, this approximation is equivalent to assuming that the disorder potential satisfies white-noise statistics [54] …”

“…Note that charge current relaxation is regulated by the transport time τ tr ≡ 2τ, indicating the absence of backscattering [43,54,55]. …”

Direct coupling between charge current and spin polarization by extrinsic mechanisms in graphene

“…If Rasba SOC is absent, the "skewness ratio" σ cisc /σ D reduces to θ sH , conventionally known as the spin Hall angle. Note that both terms are independent of the impurity density, unlike the quantum side-jump contribution to the spin Hall current 36,37 . (Side-jump is not included in the present theory.)…”

“…In particular, the ASP scattering contribution is distinct from side-jump scattering 36,37 , which is another mechanism that contributes to the SHE in graphene. ASP scattering also gives important corrections to spin relaxation processes, and particularly the D'yakonov-Perel (DP) relaxation time.…”