Spin relaxation in narrow wires of a two-dimensional electron gas

How does an initially homogeneous spin polarization in a confined two-dimensional electron gas with Rashba spin-orbit coupling evolve in time? How does the relaxation time depend on system size? We study these questions for systems of a size that is much larger than the Fermi wavelength, but comparable and even shorter than the spin relaxation length. Depending on the confinement spin relaxation may become faster or slower than in the bulk. An initially homogeneously polarized spin system evolves into a spiral pattern.

Figure 1

Time evolution of the spin polarization in a wide channel ($L=200l\approx 40L_s$, $\alpha p_F\tau =0.1$) with conserving boundary conditions. The curves from top to bottom correspond to different times, with $\Delta t=50\tau \approx {\tau }_s$. $s_z$ changes sign at various positions where a steep drop of $\mid s_z\mid$ is visible in the figure.

Figure 2

Lowest eigenvalues of the spin-diffusion operator for the Rashba model and conserving boundary conditions, Eqs. (23, 24, 25). Modes with $\gamma <7∕16{\tau }_s$ have a complex wave vector, and can therefore exist only at the edges of the wire. The dashed curve is $\gamma {\tau }_s={(L∕L_s)}^2∕12$ obtained in Ref. 5 for very narrow wires.

Figure 3

Time evolution of the spin polarization in the $x$ direction for a wire with adiabatic boundary condition for the same set of parameters as in Fig. 1.

Figure 4

Lowest eigenvalues of the spin-diffusion operator for adiabatic boundary conditions.