Filtering and analyzing mobile qubit information via Rashba–Dresselhaus–Aharonov–Bohm interferometers

Spin-1/2 electrons are scattered through one or two diamond-like loops, made of quantum dots connected by one-dimensional wires, and subject to both an Aharonov–Bohm flux and (Rashba and Dresselhaus) spin-orbit interactions. With some symmetry between the two branches of each diamond, and with appropriate tuning of the electric and magnetic fields (or of the diamond shapes), this device completely blocks electrons with one polarization and allows only electrons with the opposite polarization to be transmitted. The directions of these polarizations are tunable by these fields, and do not depend on the energy of the scattered electrons. For each range of fields one can tune the site and bond energies of the device so that the transmission of the fully polarized electrons is close to unity. Thus, these devices perform as ideal spin filters, and these electrons can be viewed as mobile qubits; the device writes definite quantum information on the spinors of the outgoing electrons. The device can also read the information written on incoming polarized electrons: The charge transmission through the device contains full information on this polarization. The double-diamond device can also act as a realization of the Datta–Das spin field-effect transistor.

Figure 1

The single diamond and the leads. The diamond is penetrated by a magnetic flux $\Phi$, and the bonds around it (of length $L$) are subject to SOIs.

Figure 2

Schematic diagrams of the two-diamond filters.

Figure 3

Schematic diagram of the rotated diamond, in the presence of the Dresselhaus SOI. The $x$ and $y$ axes are set at the crystal axes of the material.

Figure 4

The transmission of the polarized electrons, $T_{+}^{}\left(\epsilon \right)$. LHS: in the band center ($\epsilon =0$) versus the AB flux $\phi$ (in units of $\pi$); RHS: versus $ka$ [the electron energy is $\epsilon =-2j\cos \left(ka\right)$], for hopping strengths around the diamond $J_{uv}^{}=J=4j$ and site energies ${\epsilon }_0^{}={\epsilon }_1^{}=-j/\sin {\phi }_0^{},{\epsilon }_b^{}={\epsilon }_c^{}=-2J^2\sin {\phi }_0^{}/j$. These site energies are chosen so that $T_{+}^{}$ is maximal at $\phi ={\phi }_0^{}$. Small (large) dashes correspond to maxima of $T_{+}^{}\left(0\right)$ at ${\phi }_0^{}=0.1\pi \left(0.2\pi \right)$.

Figure 5

The relation between the AB flux $\phi$ and the Rashba SOI strength $\alpha$ at full filtering [Eq. (46)]. The full line and the dashed lines with decreasing sized dashes correspond to the rhombus’s opening angle $\beta /\pi =0.25,0.15$ and $0.05$. Results are the same under $(\pi /4-\beta )\leftrightarrow (\beta -\pi /4)$.

Figure 6

The outgoing spin components for rhombus angles $\beta =0.25\pi ,0.23\pi$ and $0.27\pi$ (full line, small dashes and large dashes, respectively) as a function of the Rashba SOI strength $\alpha$ when the AB flux is given by Eq. (46). Changing $\phi$ to $-\phi$ switches the direction of the polarized spins. The lower panel shows the actual spin directions in the xz plane for $\beta =\pi /4$, as $\alpha$ increases from zero to $\pi$ (left to right).

Figure 7

Top: The relation between the strength of the Rashba SOI ${\alpha }_1^{}=k_R^{}{L}_0$ and the diamond angle $\beta$ for full filtering, Eq. (47). Bottom: the two components of the outgoing polarized spins versus $\beta$. Full line and increasing dashes correspond to ${\phi }_1^{}=0.05,0.1,0.15$, and $0.2$.

Figure 8

Same as Fig. 5, with $\beta =\pi /4$, $\nu =0$ (as defined in Fig. 3) and with the Dresselhaus SOI strength ${\alpha }_D^{}=0,\pi /4$, and $\pi /2$ (full line, medium, and long dashes respectively), Eq. (54). The line with the smallest dashes shows the filtering condition for $\beta =\nu =\pi /4$ and ${\alpha }_D^{}=\pi /4$, Eq. (55).