  The generation of spin current and spin polarization in a 2DEG structure is
studied in the presence of Dresselhaus and Rashba spin-orbit couplings (SOC),
the strength of the latter being modulated in time by an ac gate voltage. By
means of the non-Abelian gauge field approach, we established the relation
between the Lorentz spin force and the spin current in the SOC system, and
showed that the longitudinal component of the spin force induces a transverse
spin current. For a constant (time-invariant) Rashba system, we recover the
universal spin Hall conductivity of $\frac e{8\pi}$, derived previously via the
Berry phase and semiclassical methods. In the case of a time-dependent SOC
system, the spin current is sustained even under strong impurity scattering. We
evaluated the ac spin current generated by a time-modulated Rashba SOC in the
absence of any dc electric field. The magnitude of the spin current reaches a
maximum when the modulation frequency matches the Larmor frequency of the
electrons.
