We find that the total spectrum of electron states in a bounded 2D electron gas with spin-orbit interaction contains two types of evanescent states lying in different energy ranges. The first-type states fill in a gap, which opens in the band of propagating spin-splitted states if tangential momentum is nonzero. They are described by a pure imaginary wavevector. The states of second type lie in the forbidden band. They are described by a complex wavevector. These states give rise to unusual features of the electron transmission through a lateral potential barrier with spin-orbit interaction, such as an oscillatory dependence of the tunneling coefficient on the barrier width and electron energy. But of most interest is the spin polarization of an unpolarized incident electron flow. Particularly, the transmitted electron current acquires spin polarization even if the distribution function of incident electrons is symmetric with respect to the transverse momentum. The polarization efficiency is an oscillatory function of the barrier width. Spin filtering is most effective, if the Fermi energy is close to the barrier height.

We find a specific mechanism of background spin currents in two-dimensional electron systems with spatially nonuniform spin-orbit interaction ͑SOI͒ at thermodynamic equilibrium, in particular, in the systems consisting of regions with and without SOI. The spin density flows tangentially to the boundary in the normal and SOI regions within a layer of the width determined by the SOI strength. The density of these edge currents significantly exceeds the bulk spin current density. The spin current is polarized normally to the boundary. The spatial distribution of equilibrium spin currents is investigated in detail in the case of a steplike variation of the SOI strength and potential at the interface.The generation and manipulation of electron-spin polarization in semiconductor nanostructures solely by means of electric fields has attracted significant attention as an interesting manifestation of spin-orbit interaction ͑SOI͒ as well as a valuable capability for spintronic devices. 1,2 A key point in solving this problem is searching for mechanisms of effective generation of purely spin currents. In this connection a great deal of interest was paid recently to the dissipationless spin currents in semiconductors with SOI ͑Refs. 3 and 4͒ and particularly to the spin currents in two-dimensional ͑2D͒ electron systems under thermodynamic equilibrium. 5,6 The existence of equilibrium background spin currents was first pointed out by Rashba 5 for an infinite 2D electron gas ͑2DEG͒ with SOI. This phenomenon has arisen a wide discussion of the definition of spin currents 7-11 and the possibility to observe the equilibrium spin currents. 11,12 The definition of the spin currents is known to be somewhat arbitrary since the spin is not conserved in the presence of SOI. The discussion has led to the evident conclusion that observable effects do not depend on any definitions. One can use the standard definition of spin current to calculate correctly measurable values. Sonin 12 proposed to detect the equilibrium spin current by measuring the mechanical torques near the edges of the SOI medium. Sun et al. 11 argued that the equilibrium spin current can be interpreted as a persistent current and considered the possibility to determine this current in a ring device by measuring an electric field it generates.In this Brief Report we draw attention to another aspect of the spin current problem. We study equilibrium spin currents in a 2D electron system with nonuniform SOI. We were initially motivated by a question of whether the equilibrium spin currents penetrate from a 2DEG with SOI into a normal 2DEG. This problem is interesting for two reasons: ͑i͒ if the spin current could penetrate into a normal 2DEG, it could be a measure of the spin current in a SOI medium since in a normal 2DEG the spin current is unambiguously defined; 13 ͑ii͒ many realistic 2D structures usually contain regions in which Rashba SOI is induced by a normal electric field produced by gates forming mesoscopic structures or by built-in charges. In particular, the SO...

We study electronic transport in two-dimensional spin-orbit coupled electron gas subjected to an in-plane magnetic field. The interplay of the spin-orbit interaction and the magnetic field leads to the Van Hove singularity of the density of states and strong anisotropy of Fermi contours. We develop a method that allows one to exactly calculate the nonequilibrium distribution function for these conditions within the framework of the semiclassical Boltzmann equation without using the scattering time approximation. The method is applied to calculate the conductivity tensor and the tensor of spin polarization induced by the electric field (Aronov-Lyanda-Geller-Edelstein effect). It is found that both the conductivity and the spin polarization have a sharp singularity as functions of the Fermi level or magnetic field, which occurs when the Fermi level passes through the Van Hove singularity. In addition, the transport anisotropy dramatically changes near the singularity.

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