While microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is this irreversibility that leads to intrinsic dissipations in electronic devices and limits the possibility of quantum computation. We theoreticallypredict that the electric field can induce a substantial amount of dissipationless quantum spin current at room temperature, in hole doped semiconductors such as Si, Ge and GaAs. Based on a generalization of the quantum Hall effect, the predicted effect leads to efficient spin injection without the need for metallic ferromagnets. Principles found in this work could enable quantum spintronic devices with integrated information processing and storage units, operating with low power consumption and performing reversible quantum computation.Comment: 18 pages, 3 figures, Submitted to Science on May 22, and published by Science within the Science Express web site (see http://www.sciencemag.org/sciencexpress/recent.shtml) on August 7, 2003 (10.1126/science.1087128). Movie file available at http://appi.t.u-tokyo.ac.jp/~murakami/spintronics.htm and http://so5.stanford.edu/Research/Projects/spintronics.htm . For related work on spin current, please see cond-mat/030766

We derive the semiclassical equation of motion for the wave-packet of light taking into account the Berry curvature in momentum space. This equation naturally describes the interplay between orbital and spin angular-momenta, i.e., the conservation of total angular-momentum of light. This leads to the shift of wave-packet motion perpendicular to the gradient of dielectric constant, i.e., the polarization-dependent Hall effect of light. An enhancement of this effect in photonic crystals is also proposed.PACS numbers: 42.15. Eq, 03.65.Sq, 03.65.Vf, The similarity between geometrical optics and particle dynamics has been the guiding principle to develop the quantum mechanics in its early stage. One can consider a trajectory or ray of light at the length scale much larger than the wavelength λ. By setting = c = 1, the equation for the eikonal ψ in the geometrical optics reads [∂ µ ψ(x)] 2 = [∇φ(r)] 2 − n(r) 2 = 0, where x µ = (r, t) is the four-dimensional coordinates, ψ(x) = φ(r) − n(r)t, and n(r) is the refractive index slowly varying within the wavelength [1]. This equation is identical to the Hamilton-Jacobi equation for the particle motion by replacing ψ by the action S. The equation for the ray of light can be derived from the eikonal equation in parallel to the Hamiltonian equation of motion. Deviation from this geometrical optics is usually treated in terms of the diffraction theory. However, most of the analyses have been done in terms of the scalar diffraction theory, neglecting its vector nature. However, the light has the degree of freedom of the polarization, which is represented by the spin S = 1 parallel or anti-parallel to the wavevector k. It is known that this spin produces the Berry phase when the light is guided by the optical fiber with torsion [2]. Also the adiabatic change of the polarization even without the change of k produces the phase change called Pancharatnam phase [3]. In this Letter, we will show that the trajectory or ray of light itself is affected by the Berry phase [4], which leads to various nontrivial effects including the Hall effect.For simplicity, we focus on an isotropic, nonmagnetic medium; the refractive index n(r) is real and scalar, but is not spatially uniform. Let us consider the wavefunction for the wave-packet with the wavevector centered at k c and position centered at r c . Because of the conjugate relation of the position and wavevector, both of them inevitably have finite width of distribution. Therefore, the relative phase of the wavefunctions at k and k + dk matters, which is the Berry connection or gauge field Λ k defined by [Λ k , where e λk is the polarization vector of λ-polarized photon, and λ = ± correspond to the right-and left-circular polarization. Here, it is noted that the SU(2) gauge field Λ k is 2 × 2 matrix. The corresponding Berry curvature (BC) or field strength is given byDue to the masslessness of a photon, it is diagonal in the basis of the right and left circular polarization as given by Ω k = σ 3 k/k 3 [a massive case will be discussed late...