Competing interplay between Rashba and cubic- k Dresselhaus spin-orbit interactions in spin-Hall effect

Focusing on the interplay between the Rashba and cubic- k Dresselhaus spin-orbit interactions (SOI), we calculate the spin accumulation Sz and the spin polarizations SiB at, respectively, the lateral edges and in the bulk of the two-dimensional electron gas. Their dependences on both the ratio between the Rashba and the Dresselhaus SOI coupling constants and the electron densities are studied systematically. Strong competition features in Sz are found. In the Dresselhaus-dominated regime Sz changes sign when the electron density is large enough. In the Rashba-dominated regime Sz is essentially suppressed. Most surprising is our finding that the Rashba-dominated regime occurs when α≈2 β, where α and β are the Rashba and the effective linear- k Dresselhaus SOI coupling constants, respectively. For the spin polarizations SiB, the Rashba-dominated regime occurs when α≥ β. Our results point out that decreasing |α| leads to the restoration of the spin accumulation Sz.