Universal Intrinsic Spin Hall Effect

We describe a new effect in semiconductor spintronics that leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. We argue that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening.

Figure 1

(a) The 2D electronic eigenstates in a Rashba spin-orbit coupled system are labeled by momentum (green or light gray arrows). For each momentum the two eigenspinors point in the azimuthal direction (red or dark gray arrows). (b) In the presence of an electric field the Fermi surface (circle) is displaced an amount $|e{E}_x{t}_0/\hslash |$ at time $t_0$ (shorter than typical scattering times). While moving in momentum space, electrons experience an effective torque which tilts the spins up for $p_y>0$ and down for $p_y<0$, creating a spin current in the $y$ direction.

Figure 2

Plot of ${\sigma }_{\mathrm{sH}}$ vs the two-dimensional electron density $n_{2\mathrm{D}}$ and the Rashba coupling constant $\lambda$. The scale is $\mathrm{\text{yellow/light gray}}=e/8\pi$ and $\mathrm{\text{dark red/dark gray}}=0$. The dashed line indicates the boundary between the universal region (constant ${\sigma }_{\mathrm{sH}}$) and the linear density dependence region. Most of the current experimental samples are deep in the universal value region. We expect the intrinsic spin Hall contribution to be present only when the Rashba splitting is larger than the disorder broadening of the quasiparticle energy levels, i.e., when $\lambda p_F\tau /{\hslash }^2>1$.