Hall Voltage with the Spin Hall Effect

The spin Hall effect does not generally result in a charge Hall voltage. We predict that in systems with inhomogeneous electron density in the direction perpendicular to main current flow, the spin Hall effect is instead accompanied by a Hall voltage. Unlike the ordinary Hall effect, we find that this Hall voltage is quadratic in the longitudinal electric field for a wide range of parameters accessible experimentally. We also predict spin accumulation in the bulk and sharp peaks of spin-Hall induced charge accumulation near the edges. Our results can be readily tested experimentally, and would allow the electrical measurement of the spin Hall effect in non-magnetic systems and without injection of spin-polarized electrons

Relativistic Hall Effect

We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, and mechanical flywheels, and also discuss various fundamental aspects of this phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let

Spin Hall Effect

The intrinsic spin Hall effect in semiconductors has developed to a remarkably lively and rapidly growing branch of research in the field of semiconductor spintronics. In this article we give a pedagogical overview on both theoretical and experimental accomplishments and challenges. Emphasis is put on the the description of the intrinsic mechanisms of spin Hall transport in III-V zinc-blende semiconductors, and on the effects of dissipation.Comment: 22 pages, minor adjustments, version as publishe