Competiting interplay between Rashba and cubic-k Dresselhaus spin-orbit interaction in spin Hall effect

We study the interplay between the Rashba and cubic-$k$ Dresselhaus spin-orbit interactions (SOI) in a diffusive two-dimensional electron gas (2DEG). Within the spin Hall configuration, we perform a systematic calculation of the spin accumulation $S_{z}$ and the spin polarizations $S_{i}^{B}$ at the lateral edges and in the bulk of the 2DEG, respectively. Both the relative coupling strength of the Rashba and the Dresselhaus SOI, and the electron densities are varied. The spin accumulation exhibits strong competiting features, including in the Dresselhaus-dominant regime the sign change in $S_{z}$ when electron density is large enough, and in the Rashba-dominant regime the complete suppression of $S_{z}$. Most surprisingly is our finding that the Rashba-dominant regime occurs as early as $\alpha\approx 2\tilde{\beta}$, where $\alpha$, $\tilde{\beta}$ are the Rashba and the effective linear-$k$ Dresselhaus SOI coupling constant, respectively. Similar Rashba-dominant regime is found in the spin polarizations, when $\alpha\geq \tilde{\beta} $. Our results point out that decreasing $|\alpha|$ leads to the restoration of the spin accumulation.