Spin-dependent transmission through a chain of rings: Influenceof 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 $α$⁠. 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 $α$ and of the wave vector $k$ of the incident electron. We show that due to destructive spin interferences, the chain can be totally opaque for certain ranges of $k$⁠, the width of which depends on the value of $α$⁠. A periodic modulation of the strength $α$ or of the ring radius widens the gaps considerably and produces a nearly binary conductance output.