Ballistic transport in one-dimensional loops with Rashba and Dresselhaus coupling

We discuss the combined effect of Rashba and Dresselhaus spin-orbit interactions in polygonal loops formed by quantum wires, when the electron are injected in a node and collected at the opposite one. The conditions that allow perfect localization zero transmission coefficient are found. Furthermore, we investigate the suppression of the transmission coefficient oscillations that appear, in the presence of a magnetic flux, when the electron is injected and collected at the same node. The transmission suppression appears also in the Aharonov- Bohm configuration where the input and the output node are at opposite sides of the loop. Finally, we point out that a recent experimental realization of a ballistic spin interferometer can be used to obtain a reliable estimate of the magnitude ratio of the two spin-orbit interactions.