Relaxation mechanisms of the persistent spin helix

We study the lifetime of the persistent spin helix in semiconductor quantum wells with equal Rashba and linear Dresselhaus spin-orbit coupling strengths. In order to address the temperature dependence of the relevant spin relaxation mechanisms we derive and solve a semiclassical spin diffusion equation taking into account the effects of spin-dependent impurity scattering, cubic Dresselhaus spin-orbit coupling and electron-electron interactions. For the experimentally relevant regime we find that the lifetime of the persistent spin helix is mainly determined by the interplay of cubic Dresselhaus spin-orbit interaction and electron-electron interactions. We propose that even longer lifetimes can be achieved by generating a spatially damped spin profile instead of the persistent spin helix state.

Figure 1

(a) Temperature-dependent relaxation rates due to electron-electron interactions, ${\tau }_{\mathrm{e}-\mathrm{e},1}^{-1}$ (solid curve), ${\tilde{\tau }}_{\mathrm{e}-\mathrm{e},1}^{-1}$ (dot-dashed curve) and ${\tau }_{\mathrm{e}-\mathrm{e},3}^{-1}$ (dashed curve), as numerically computed from Eq. (49) using the experimental parameters of Ref. 7. For comparison: the inverse transport time at $T=100$ K is ${\tau }^{-1}=1{\mathrm{ps}}^{-1}$. We use this value of the inverse transport time as an input for the calculation of the PSH lifetimes over the whole temperature range depicted in Fig. 2. (b) The resulting effective relaxation rates: ${\tau }_1^{-1}$ (solid), ${\tau }_3^{-1}$ (dashed), and ${\tilde{\tau }}_1^{-1}$ (dot-dashed); cf. Eqs. (47), (48), and (54).

Figure 2

(a) Temperature-dependent lifetimes of the enhanced (red/gray) and reduced (blue/black) modes. The points are experimental data from Ref. 7. Solid lines are the respective theoretical curves including extrinsic and cubic Dresselhaus spin-orbit interactions as well as electron-electron interactions; the thin dashed line is the simplified result from Eq. (83). In panel (b) we zoom in on the theoretical curve of panel (a) close to the maximum of ${\tau }_E$. The dashed line is the theoretical curve without extrinsic spin-orbit interaction. Panel (c) depicts the results of a calculation, where we include extrinsic and cubic Dresselhaus spin-orbit interaction but exclude electron-electron interactions. [Also here, a comparison as in (b) would show that the influence of the extrinsic spin-orbit interactions is marginal.]