  We study the quantum interference effects induced by the Aharonov-Casher
phase in asymmetrically confined two-dimensional electron and heavy-hole ring
structures systems taking into account the electrically tunable spin-orbit (SO)
interaction. We have calculated the non-adiabatic transport properties of
charges (heavy-holes and electrons) in two-probe thin ring structures and
compare how the form of the SO coupling of the carries affects it. We show that
both the SO splitting of the bands and the carrier density can be used to
modulate the conductance through the ring. We show that the dependence on
carrier density is due to the backscattering from the leads which shows
pronounce resonances when the Fermi energy is close to the eigenenergy of the
ring. We also calculate the spin Hall conductivity and longitudinal
conductivity in four-probe rings as a function of the carrier density and SO
interaction, demonstrating that for heavy-hole carriers both conductivities are
larger than for electrons. Finally, we investigate the transport properties of
mesoscopic rings with spatially inhomogeneous SO coupling. We show that devices
with inhomogeneous SO interaction exhibit an electrically controlled
spin-flipping mechanism.
