Extrinsic Spin Hall Effect Induced by Resonant Skew Scattering in Graphene

We show that the extrinsic spin Hall effect can be engineered in monolayer graphene by decoration with small doses of adatoms, molecules, or nanoparticles originating local spin-orbit perturbations. The analysis of the single impurity scattering problem shows that intrinsic and Rashba spin-orbit local couplings enhance the spin Hall effect via skew scattering of charge carriers in the resonant regime. The solution of the transport equations for a random ensemble of spin-orbit impurities reveals that giant spin Hall currents are within the reach of the current state of the art in device fabrication. The spin Hall effect is robust with respect to thermal fluctuations and disorder averaging.

Figure 1

Schematic picture of extrinsic spin Hall effect generated by transport skewness. An impurity (sphere) near the graphene sheet causes a local spin-orbit field with range $R$. The scattering of components with positive (negative) angular momentum is enhanced (suppressed) for charge carriers with $s_z=1$ ($s_z=-1$), resulting in a net spin Hall current.

Figure 2

Skew scattering induced by SOC impurities close to a resonance in the cross section. (a) Skeweness $\gamma ={\mathrm{\Sigma }}_{\perp }^s/{\mathrm{\Sigma }}_{\parallel }^s$ as a function of $V_0$ for an intrinsic (Rashba)-type SOC scatterer [solid black line (dashed blue line)]. Even larger values of $\gamma$ are found near sharper resonances occurring at larger $V_0$ (not shown). (b) Transport cross section versus $V_0$. These panels have $R=4\mathrm{nm}$, $\hslash v_{F}k=0.1\mathrm{eV}$, and $\mathrm{\Delta }=25\mathrm{meV}$. (c) Dispersion relation inside the SOC disk scatterer. Dashed orange lines are guidelines to the eye representing the bulk band structure of monolayer graphene.

Figure 3

Spin Hall angle as a function of Fermi energy for a dilute random distribution of intrinsic SOC scatterers. (a) ${\theta }_{\text{sH}}$ at zero temperature for impurities producing a local electrostatic potential $V_0$. (b),(c) ${\theta }_{\text{sH}}$ at different temperatures and considering a random $V_0$ potential with uniform distribution $V_0\in [0,\mathrm{\Delta }V]$. In all panels we have taken ${\mathrm{\Delta }}_I=25\mathrm{meV}$.