Spin-dependent transmission through a chain of rings: influence of a   periodically modulated spin-orbit interaction strength or ring radius
  We study ballistic electron transport through a finite chain of quantum circular rings in the presence of spin-orbit interaction of strength \alpha. For a single ring the transmission and reflection coefficients are obtained analytically and from them the conductance for a chain of rings as a function of \alpha and of the wave vector k of the incident electron. We show that due to destructive spin interferences the chain can be totaly opaque for certain ranges of k the width of which depends on the value of \alpha. A periodic modulation of the strength \alpha or of the ring radius widens up the gaps considerably and produces a nearly binary conductance output. 
B. Molnar, P. Vasilopoulos, and F. M. Peeters