The nonuniform spin polarization in the square-shaped 1D wire induced by spin-orbit coupling

It is shown that the Rashba spin-orbit coupling induces the spatially nonuniform spin state in the square-shaped 1D wire. The electron states of this type are characterized with spin orientation changing according to the harmonic motion along the square side. The period of the oscillation is determined only by the spin-orbital coupling and the hopping parameters ratio. The modulation of spin orientation is caused by step-like changing of Rashba field direction. The obtained results were generalized on the case of polygon-shaped wire.