Spin-orbit interactions cause many remarkable phenomena in many fields of physics. In this talk I will discuss a new state of matter that it can bring about. In the presence of electric current, the electron spin polarization normal to the plane of the two-dimensional (2D) semiconductor can reach its maximal possible value, making all electrons polarized spin up or spin down. I will show that this happens at the edges of the 2D sample if spin relaxation is weak. In the spin-electric state, two stripes near the edges emerge with induced electric fields directed perpendicular to flowing electric current caused by applied external field.
The directions of the induced fields at two edges are opposite to each other. These electric fields and corresponding voltages represent true Hall voltage and electric signal caused by spin current. In the central stripe between the two edge stripes, the spin polarization and electric fields change their sign in the middle, where their magnitude vanishes. The spin-electric structure can be detected by measuring the potential drop between the edge and the middle of the sample. I will describe microscopic theory of the spin-electric state, and discuss self-consistent solution of the two-dimensional electrostatic problem in the presence of spin currents. I will show how to make spin-orbit interactions for electrons and holes being large enough to generate the spin electric state but small enough to give weak spin relaxation.