Edge-induced spin polarization in two-dimensional electron gas P. Bokes 1,2, ∗ and F. Horv´ath 1 $^{1}$Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkoviˇcova 3, 812 19 Brat islava, Slovak Republic $^{2}$European Theoretical Spectroscopical Facility (ETSF, www.etsf.eu ) (Dated: November 9, 2018) We characterize the role of the spin-orbit coupling between electrons and the confining potential of the edge in nonequilibrium 2D homogeneous electronic gas. We derive a simple analytical result for the magnitude of the current induced spin polarization at the edge and prove that it is independent of the details of the confinement edge potential and the electronic density within realistic values of the parameters of the considered models. While the amplitude of the spin accumulation is comparable to the experimental values of extrinsic spin Hall effect in similar samples, the spatial extent of edge induced effect is restricted to the distances of the order of Fermi wavelength ( ∼ 10nm). PACS numbers: 72.25.-b; 85.75.-d; 73.63.Hs One of the exciting new discoveries in solid state physics in the last few years has been the experimental observation of the extrinsic spin Hall effect$^{1–4}$in GaAs heterostructures. The mechanism of this effect relies on the spin-orbit cou- pling between the spin of electrons with the perturbing po- tential of impurities. Another example of similar coupling is the Rashba-Bytchkov interaction in asymmetrically doped GaAs quantum wells containing two-dimensional electron gas (2DEG) where the coupled potential comes from the internal electrostatic electric field induced by the structural asym metry of the well. In modeling both of these situations, the atomic potential of the ideal bulk semiconductor enters only through the renormalization of the effective mass and the spin-orbit interaction strength. Interestingly, the Rashba-Bytchkov interaction has been also suggested as a source of spin Hall-like phenomenology 5 for a clean 2DEG. While the effect has been shown to disap- pear in extended 2D systems with arbitrarily weak disorder$^{6,7}$, it is now known that finite size of the sample in combina- tion with Rashba-Bytchkov coupling results in the transverse spin current and accumulation of opposite spin densities at the edges of the sample$^{8,9}$. Furthermore, it has been found that boundaries might directly influence the spin polarization d ue to the Rashba-Bytchov coupling either in very wide 2D elec- tronic systems with an edge$^{10–14}$or narrow Rashba strips$^{15,16}$. However, the physical origin of the latter is quite different from the former: whereas the bulk Rashba-Bytchkov effect arises from accelerations of electrons in the external electric field, the latter result from the reflection of electrons from the sample’s boundary. Motivated by this development, it is natural to explore fur- ther alterations of the perfectly periodic bulk potential and its consequences on the spin polarization in the presence of the current. Several authors have considered such a situation in quantum wires with a parabolic confining potential 17–20 , wider strips with parabolic 21 or abrupt 22 confinement edge. These alterations in the potential landscape can be also viewed as the “impurity” which leads to nonzero spin polarization i n- where j is the electrical current density in the 2DEG, E is the parameter giving the strength of the spin-orbit coupling$^{26}$, and m$_{e}$ and q$_{e}$ are the effective mass and the charge of elec- tron respectively. Noticeably, this result is independent of the density of the 2DEG and the details of the edge potential as long as the electrons are confined within the sample. In this paper we consider the edge of the 2DEG in Si doped GaAs quantum well, a system for which the spin Hall effect has been experimentally observed. This allows us to estimate the values of all the parameters entering and we can compare the importance of this edge-effect to the contribution of other mechanisms leading to current-induced spin polarization. The models considered here are reasonably realistic yet simple enough to be solved almost analytically. We derive a gen- erally valid simple analytical formula for the induced number of electrons with un-compensated spin per unit length of the edge, In our previous work 22 we have compared the magnitude of the spin polarization induced by the latter mechanism with the one induced by the Rashba-Bytchkov coupling and scat- tering of the edge$^{10}$. It turns out that for a typical 2DEG with an edge, it is about three orders of magnitude larger than the one caused by the edge and the Rashba-Bytchkov interaction. This substantial difference is mostly due to the fact that the pa- rameter characterizing spin-orbit coupling appears in second order in the case of the Rashba-Bytchov-based mechanism 10 whereas for the edge-induced spin-orbit coupling it comes al- ready in the first order. duced by the flow of the electric current. Recently, exper- imental evidence of this effect of the in-plane field on spin polarization has been reported$^{23}$. Further enhancement of this kind of spin-polarization has been suggested using a transport through chaotic quantum dot 24 or resonant tunable scattering center$^{25}$. I. INTRODUCTION arXiv:1001.0720v1[cond-mat.mes-hall]5 Jan 2010 m$_{z}$ = − m$_{e}$ ¯ hq$_{e}$$^{α}$ E j , (1)