The aim of this paper is to show that a two-dimensional Schrödinger operator with the potential in the form of a 'ditch' of a fixed profile can have a geometrically induced discrete spectrum; this happens if such a potential channel has a single or multiple bends being straight outside a compact. Moreover, under stronger geometric restrictions the claim remains true in the presence of a potential bias at one of the channel 'banks'.

No abstract

We theoretically analyze the possibility to use a ferromagnetic gate as a spin-polarization filter for one-dimensional electron systems formed in semiconductor heterostructures showing strong Rashba spin-orbit interaction. The proposed device is based on the effect of the breaking time-reversal symmetry due to the presence of weak magnetic fields. For a proper strength and magnetic field orientation there appears an energy interval in the electron energy spectrum at which the orientation of spin states is controlled by the direction of the electron velocity. It leads to the natural spin polarization of the electron current if the Fermi energy falls into this energy interval.