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.
It is shown that the quantized Hall current may always be expressed as the difference between diamagnetic currents flowing at the two edges. It is argued that the high precision of the quantization may be aided by the establishment of a local equilibrium in each edge region. The basic ideas are illustrated by the discussion of a free two-dimensional electron gas in an infinite confining potential. Our derivation establishes the connection between quantum-mechanical and classical thermodynamic explanations for the quantum Hall effect.
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