Spin filtering and scaling of spin-dependent potentials in quasi-one-dimensional electron liquids with Rashba spin-orbit interaction

We investigate theoretically the spin-filtering effect in a quasi-one-dimensional (Q1D) electron liquid with spin-orbit interaction. The Q1D system considered is formed from a two-dimensional electron-gas (2DEG) subject to both a lateral confining potential and an interface potential perpendicular to the 2DEG. Spin and charge degrees of freedom in the system are mixed by the interface potential through the Rashba mechanism of spin-orbit interaction [A. V. Moroz and C. H. W. Barnes, Phys. Rev. B 60, 14272 (1999)] and we show that when a spin-dependent delta potential is further introduced into the system, for example, via implantation of magnetic/ferromagnetic impurities, the mixing leads to the spin-filtering effect which favors electrons with a certain spin orientation to transport through the delta potential. In particular, we calculate the scaling dimension of electron scattering both by spin-flip and by spin-independent delta potentials when the temperature is varied and show that, in the spin-flip case, the scaling of electron scattering with temperature varies with spin orientation. Conductance is calculated for both spin and charge transport, and the spin-filtering effect is discussed quantitatively in terms of the conductance.