Effects of Impurities on the Spin Hall Effect
Bertrand I. Halperin
In the presence of "spin-orbit coupling," an electric field Ex in the plane of a two-dimensional electron gas (2DEG) can lead to a "spin current" j Z/y where electrons have a velocity in the y direction with opposite sign for spins in the +z and -z directions. Sinova et al. predicted that in the absence of impurity scattering, the "spin Hall conductivity" -j Zy /Ex should take on a universal value e/8p. We have shown that in the simplest case, an arbitrarily small concentration of impurities will cause the spin Hall conductivity to vanish far from the boundaries of the 2DEG. However, an electrical current can induce spin currents close to the contacts, and produce spin polarization, as illustrated in the figure.