Giant edge spin accumulation in a symmetric quantum well with two subbands

We have studied the edge spin accumulation in a high mobility two-dimensional electron gas formed in a symmetric well with two subbands. This study is strongly motivated by the recent experiment of Hernandez et al. [Phys. Rev. B {\bf 88}, 161305(R) (2013)] who demonstrated the spin accumulation near the edges of a bilayer symmetric GaAs structure in contrast to no effect in a single-layer configuration. The intrinsic mechanism of the spin-orbit interaction we consider arises from the coupling between two subband states of opposite parities. We obtain a parametrically large magnitude of the edge spin density for the two-subband sample as compared to the usual single-subband structure. We show that the presence of a gap in the system, i.e., the energy separation $\Delta$ between the two subband bottoms, changes drastically the picture of the edge spin accumulation. Thus one can easily proceed from the regime of weak spin accumulation to the regime of strong one by varying the Fermi energy (electron density) and/or $\Delta$. We estimate that by changing the gap $\Delta$ from zero up to $1\div 2$ K, the magnitude of the effect changes by three orders of magnitude. This opens up the possibility for the design of new spintronic devices.