The purpose of this thesis is to explain the origin of the spin accumulation. The non-equilibrium transportation of the
two-dimensional electron gas through a narrow channel is
investigated under the influence of the Rashba spin-orbit
interaction. We discuss the effect with modeling impurities by randomly distributed isotropic short-range potentials. To analyze numerically, we will construct the system in lattice points in the y direction. We firstly derive the correction due to the existence of the impurities and then show the spin distribution under the electron-impurity scattering. By introducing suitable lifetime in the Green's function, the spin distribution can be calculated from the ballistic regime to the diffusive regime. We will derive the continuity equation of spin to clarify the origin of the spin accumulation. It is shown that the spin accumulation is a combined effect of the spin current and disorders. Furthermore, we will consider other interactions which may be important to the system. We will discuss the effect of spin-spin interaction, screened Coulomb potential, and on-site u. Because those interactions are too hard to be exactly solved, we will consider these interactions by way of mean-field theory. It indicates that the inclusion of ferromagnetic spin-spin interaction increases the spin accumulation.

1.D. Grundler, ibid. 84 6074 (2000)
2.M. I. Dyakonov and V. I. Perel, Phys. Lett. 35A 459(1971)
3.Y. K. Kato et al., Science 306, 1910(2004)
4.J. Sinova et al., Phys. Rev. Lett. 94, 047204(2005)
5.S. Datta and B. Das, Appl. Phy. Lett. 56, 665(1990)
6.M. Onoda and N. Nagaosa, Phys. Rev. B 72, 081301(2005)
7.V. K. Dugaev et al., Superlatt. Microstr. 16, 413(1994)
8.H.U. Jalabert et al., Chaos 3, 665(1993)
9.R. Blumel, U. Smilansky, Phys. Rev. Lett. 60, 477(1988)
10.Yu. L. Bychkov and E. I. Rashba, J.Phys. C 17 6093(1984)
11.Iunren Shi et al., Phys. Rev. Lett. 96 076604(2006)