Robustness of a persistent spin helix against a cubic Dresselhaus field in (001) and (110) oriented two-dimensional electron gases

The persistent spin helix (PSH) state in III--V semiconductor quantum wells (QWs) is a promising candidate for spin-based applications because the PSH state realizes controllable spin orientation with long spin lifetime. Although the cubic Dresselhaus spin-orbit (SO) interaction is known for breaking the PSH state in both (001)-oriented and (110)-oriented QWs, it is not well understood how the distinct symmetry of cubic Dresselhaus terms ${\ensuremath{\beta}}_{3}$ between (001) and (110) QWs affects the robustness of the PSH state. Here we investigate robustness of the PSH state between (001) and (110) QWs under various strengths of cubic Dresselhaus SO interaction based on numerical Monte Carlo approach and magnetoconductance simulation, respectively, representing optical spin excitation/detection and weak localization/weak antilocalization in magnetotransport. For electron spins initialized along $z\ensuremath{\parallel}[001]$ in a (001) QW and $x\ensuremath{\parallel}[001]\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}y\ensuremath{\parallel}[1\overline{1}0]$ in a (110) QW, where the spin distribution is developed with the helical spin mode, a (001) QW shows a more robust PSH state against the increase of ${\ensuremath{\beta}}_{3}$ than does a (110) QW. This phenomenon is contrary to numerically computed magnetoconductance, where weak localization is maintained on the variation of ${\ensuremath{\beta}}_{3}$ in a (110) QW, whereas weak antilocalization appears in a (001) QW. By deriving the spin lifetime of the PSH state in a (110) QW from a diffusion equation using a random-walk approach, we demonstrate that such a difference arises directly from the magnitude and orientation of third angular harmonics in cubic Dresselhaus fields for (001) and (110) QWs.