Spin-dependent transmission in waveguides with periodically modulated strength of the spin-orbit interaction

The electron transmission $T$ is evaluated through waveguides, in which the strength of the spin-orbit interaction(SOI) $\alpha$ is varied periodically, using the transfer-matrix technique. It is shown that $T$ exhibits a {\it spin-transistor} action, as a function of $\alpha$ or of the length of one of the two subunits of the unit cell, provided only one mode is allowed to propagate in the waveguide. A similar but not periodic behavior occurs as a function of the incident electron energy. A transparent formula for $T$ through one unit is obtained and helps explain its periodic behavior. The structure considered is a good candidate for the establishment of a realistic spin transistor.