Spin-current generation from Coulomb-Rashba interaction in semiconductor bilayers

Electrons in double-layer semiconductor heterostructures experience a special type of spin-orbit interaction that arises in each layer from the perpendicular component of the Coulomb electric field created by electron-density fluctuations in the other layer. We show that this interaction, acting in combination with the usual spin-orbit interaction, can generate a spin current in one layer when a charge current is driven in the other. This effect is distinct symmetrywise from the spin-Hall drag. The spin current is not, in general, perpendicular to the drive current.

Figure 1

Scheme of the device under study: An electric field $\mathit{E}$ is applied to the active layer (2), and a spin current is generated in the passive layer (1). Blue circles depict electrons, and the wavy line shows the interlayer Coulomb interaction. Arrows marked ${\mathit{k}}_1,{\mathit{k}}_2$ and ${\mathit{p}}_1,{\mathit{p}}_2$ are the wave vectors in the initial and final states. The vertical arrow emphasizes the relevant component of the interlayer Coulomb field.

Figure 2

Schematic of the spin-current generation in the passive layer.[10] The circle is the Fermi surface, and the arrows are the electron spins. Panel (a) shows the scattering stage of the process: The top part shows electrons with spin parallel to the $y$ axis, and the bottom part shows electrons with spin antiparallel to the $y$ axis. The arrows show the spin-dependent scattering process: Solid arrows indicate the stronger transitions, having $k_x+p_x>0$ for $s_y>0$ and $k_x+p_x<0$ for $s_y<0$, while dashed arrows indicate the weaker transitions. Scattering processes that increase the $x$ component of the wave vector (i.e., with $q_x>0$) dominate due to the current flowing in the active layer. (b) Precession stage of the process. The resulting spin distribution after the scattering contains second angular harmonics. Green arrows demonstrate the spin precession caused by the Dresselhaus field ${\mathit{\Omega }}_{\mathit{k}}$, Eq. (4). Electron spins with opposite wave vectors precess in opposite directions. The resulting dipolar distribution of electron spins is presented in panel (c).