Magnetoconductance properties of rectangular arrays of spintronic quantum rings

Electron transport through multi-terminal rectangular arrays of quantum rings is studied in the presence of Rashba-type spin-orbit interaction (SOI) and of a perpendicular magnetic field. Using the analytic expressions for the transmission and reflection coefficients for single rings we obtain the conductance through such arrays as a function of the SOI strength, the magnetic flux, and of the wave vector $k$ of the incident electron. Due to destructive or constructive spin interferences caused by the SOI, the array can be totally opaque for certain ranges of $k$, while there are parameter values where it is completely transparent. Spin resolved transmission probabilities show nontrivial spin transformations at the outputs of the arrays. When point-like random scattering centers are placed between the rings, the Aharonov-Bohm peaks split, and an oscillatory behavior of the conductance emerges as a function of the SOI strength.