Half-metal phases in a quantum wire with modulated spin-orbit interaction

We propose a spin filter device based on the interplay of a modulated spin-orbit interaction and a uniform external magnetic field acting on a quantum wire. Half-metal phases, where electrons with only a selected spin polarization exhibit ballistic conductance, can be tuned by varying the magnetic field. These half-metal phases are proven to be robust against electron-electron repulsive interactions. Our results arise from a combination of explicit band diagonalization, bosonization techniques, and extensive density matrix renormalization group computations.

Figure 1

A qualitative sketch of the quantum device discussed in this paper. A quantum wire supporting Rashba SOI is gated by a periodic sequence of equally charged top gates. A transverse uniform magnetic field is applied in the direction perpendicular to the current (wire) and the external electric field.

Figure 2

Single-particle dispersion relation for $Q=\pi ,\nu =3/4,m=1/4$, with Fermi level ${\epsilon }_F=0$. The lower band with spin “+” is completely filled, but the lower band with spin “$-$” is partially filled. There is a gap to charge excitations with spin +, but no gap to charge excitations with spin $-$. Rashba coefficients are taken as ${\gamma }_0/t=tan(\pi /6)$ and ${\gamma }_1/t=0.2$, filling and magnetization correspond to magnetic field $h_y/t=1.78$ and chemical potential $\mu /t=-0.89$.

Figure 3

DMRG results for one-particle gaps as function of $U$ in the half-metal phase depicted in Fig. 2.

Figure 4

DMRG results for two-particle gaps as function of $U$ in the half-metal phase depicted in Fig. 2.