All-electric single-electron spin-to-charge conversion

We examine spin-dependent displacement of a single electron, resulting in separation and relocation of the electron wave-function components, and thus charge parts, corresponding to opposite spins. This separation is induced by a pulse of an electric field which generates varying Rashba type spin-orbit coupling. This mechanism is next implemented in a nanodevice based on a gated quantum dot defined within a quantum nanowire. The electric-field pulse is generated by ultrafast changes of voltages, of the order of several hundred mV, applied to nearby gates. The device is modeled realistically with appropriate material parameters and voltages applied to the gates, yielding an accurate confinement potential and Rashba coupling. At the end, we propose a spin-to-charge conversion device, which with an additional charge detector will allow for electron-spin state measurement.

Figure 1

The modeled nanodevice consists of an InSb nanowire and a layout of nearby gates. The bottom gates are used to create a confinement potential in the $x$ direction and, in the second stage of conversion, to generate a potential barrier separating previously split opposite spin densities. The lateral gates serve to generate a spin-orbit pulse within the wire, splitting spin densities spatially.

Figure 2

The confinement potential landscapes in the center of the wire during the first stage of conversion along the all three directions: (left) along the wire axis $x$, (middle) perpendicular to the wire along the $y$ direction connecting the lateral gates, and (right) along the $z$ direction, perpendicular to the substrate.

Figure 3

The expectation value of position of the spin-up component $x_{\uparrow }\left(t\right)$ (solid lines) for a single driving pulse $F[1-cos(\omega t\left)\right]$ of different durations $T=2\pi /\omega$ (dashed lines). We set $F=1$ and $\omega =\{0.7,0.9,1.0,1.1,1.3\}$ for red, orange, green, blue, and magenta curves respectively.

Figure 4

(a) The Rashba coupling pulse generates oscillations of the spin densities for spin up (blue convex density) and spin down (red convex density). They are in antiphase to each other. (b) Pulses of voltages on lateral gates induce an RSOI pulse. (c) At the second stage of conversion we set up a barrier in the middle of the wire to separate and stabilize spatially both spin densities. (d) Simulations with an additional barrier rise shown. Changes to the confinement potential are shown as a color map beneath the densities.

Figure 5

Conversion for various initial spin setups: (a) spin-up orientation, (b) orientation between spin up and spin down, (c) and spin down. After conversion the sides contain charge $Q_R$ and $Q_L=1-Q_R$ proportional to the initial spin contributions.

Figure 6

Spin-to-charge conversion: (a) time course of the charge amount in the right half of the wire $Q_R\left(t\right)$ depending on the initial spin orientation. The spin is parametrized by angles $(\vartheta ,\phi )$ on the Bloch sphere. (b) Final charge in the right half depends on the spin $z$ projection, thus on the angle $\vartheta$, yet is independent of $\phi$. (c) Error of conversion depending on the initial spin orientation.

Figure 7

Error of conversion for different durations $T$ of the pulse and different times of separating barrier rise $t_2=t_1+T/2+\mathrm{\Delta }{t}_2$. A black square denotes optimal parameters used in a previously described simulation shown in Figs. 4–6.