  We study theoretically the spin and orbital angular momentum (OAM) Hall
effect in a high mobility two-dimensional electron system with Rashba and
Dresselhuas spin-orbit coupling by introducing both the spin and OAM torque
corrections, respectively, to the spin and OAM currents. We find that when both
bands are occupied, the spin Hall conductivity is still a constant (i.e.,
independent of the carrier density) which, however, has an opposite sign to the
previous value. The spin Hall conductivity in general would not be cancelled by
the OAM Hall conductivity. The OAM Hall conductivity is also independent of the
carrier density but depends on the strength ratio of the Rashba to Dresselhaus
spin-orbit coupling, suggesting that one can manipulate the total Hall current
through tuning the Rashba coupling by a gate voltage. We note that in a pure
Rashba system, though the spin Hall conductivity is exactly cancelled by the
OAM Hall conductivity due to the angular momentum conservation, the spin Hall
effect could still manifest itself as nonzero magnetization Hall current and
finite magnetization at the sample edges because the magnetic dipole moment
associated with the spin of an electron is twice as large as that of the OAM.
We also evaluate the electric field-induced OAM and discuss the origin of the
OAM Hall current. Finally, we find that the spin and OAM Hall conductivities
are closely related to the Berry vector (or gauge) potential.
