Spin-orbit induced interference of ballistic electrons in polygon structures

We investigate the spin-orbit induced spin-interference pattern of ballistic electrons traveling along any regular polygon. It is found that the spin interference depends strongly on the Rashba and Dresselhaus spin-orbit constants as well as on the sidelength and alignment of the polygon. We derive the analytical formulas for the limiting cases of either zero Dresselhaus or zero Rashba spin-orbit coupling, including the result obtained for a circle. We calculate the nonzero Dresselhaus and Rashba case numerically for the square, triangle, hexagon, and circle and discuss the observability of the spin interference which can potentially be used to measure the Rashba and Dresselhaus coefficients.