Spin Filtering by Field-Dependent Resonant Tunneling

We consider theoretically transport in a spinful one-channel interacting quantum wire placed in an external magnetic field. For the case of two pointlike impurities embedded in the wire, under a small voltage bias the spin-polarized current occurs at special points in the parameter space, tunable by a single parameter. At sufficiently low temperatures complete spin polarization may be achieved, provided repulsive interaction between electrons is not too strong.

Figure 1

Ground state energy configurations of the charging $E_C(n_{\uparrow },n_{\downarrow })$ for repulsive interaction $U_{\sigma }<U_{\rho }$. Points at boundaries between different ground state configurations correspond to the resonance points, special points where the ground state degeneracy is present. Boundaries with solid lines describe resonances for either up or down spins, while the dotted line is the Kondo resonance for spin exchange process at the island which exists without magnetic field, when $k_{F\uparrow }=k_{F\downarrow }$.

Figure 2

The renormalization group flow diagram for $V_{\downarrow }$ as a function of interaction for parameters when the resonance is achieved for strong but not for weak impurities (a) and for weak but not for strong impurities (b). The middle region contains a line of fixed points in case (a), and a phase transition line in case (b), precise form of which is unknown. The noninteracting point is $K_{\rho }=K_{\sigma }=K_{\mathrm{eff}}=1$.