A general spin symmetry argument is proposed for spin currents in semiconductors. In particular, due to the symmetry with respect to spin polarization of the helicity eigenstates of the Luttinger Hamiltonian for a hole-doped semiconductor, the spin polarized flux from a single helicity eigenstate induced by an external electric field, is canceled exactly when all such contributions from eigenstates that are degenerate in energy are summed. Thus, the net spin current predicted by Murakami et al, Science 301, 1348 (2003), cannot be produced by such a Hamiltonian. Possible symmetry breaking mechanisms which may generate a spin current are discussed.
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