We present studies of edge states induced by the Aharonov-Casher vector potential or Rashba-type spin-orbit interaction using quantum transport in InGaAs/InAlAs herterostructures. The Aharonov-Casher effect is electromagnetically dual to the Aharonov-Bohm effect and is predicted to lead to edge states in a parabolic confinement at two-dimensional sample edges. As a narrow gap material, InGaAs has a low effective mass, high mobility, and strong spin-orbit interaction, which indicate that it can be used as a good material to detect the Aharonov-Casher effect or SOI interaction. Using InGaAs, we measured the magnetoresistance in a quantum antidot in narrow short channels in a tilted magnetic field. The fine structure (mT spacing) observed in the magnetoresistance indicate a probable energy spacing between AC edge states. We also fabricated side-gate channel structures in InGaAs/InAlAs quantum wells and investigated the values of the Rashba spin-orbit coupling constant α using the weak antilocalization analysis as a function of the side-gate voltage. We take the effect of the finite width into account and find the corrected values. With the simulation of electric fields in the wide channel and narrow channel, we found that the electric field components can be changed using side-gate voltages. While our results do not indicate which electric field component is responsible, the data indicate that the deduced spin-orbit strength values in a narrow channel are tunable by the side-gate voltage. / Ph. D.