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Spin accumulation caused by confining potential in a two dimensional electron system

We investigate spin accumulation caused by spin-orbit interactions (SOIs) in a two dimensional electron system confined in one direction. We calculate spin density caused by three kinds of SOIs; arising from edge potential, Rashba and Dresselhaus mechanisms. All SOIs are shown to generate out-of-plane spin accumulations at the lateral edges of the system. We also find that the Rashba and the Dresselhaus mechanisms are competitive. Especially, when the strength of both interactions are equal, their effects cancel out each other. In that case, only the edge potential mechanism becomes relevant, and analytical expression is obtained for the spin density. The edge potential mechanism is shown to induce spin accumulation similar to and consistent with the experiment [Sih {\it et al}., Nature Phys {\bf 1}, 31 (2005)]. We discuss the mechanism of the spin accumulation for each SOIs in some detail.