Semiconductor few-electron quantum dot operated as a bipolar spin filter

We study the spin states of a few-electron quantum dot defined in a two-dimensional electron gas, by applying a large in-plane magnetic field. We observe the Zeeman splitting of the two-electron spin triplet states. Also, the one-electron Zeeman splitting is clearly resolved at both the zero-to-one and the one-to-two electron transition. Since the spin of the electrons transmitted through the dot is opposite at these two transitions, this device can be employed as an electrically tunable, bipolar spin filter. Calculations and measurements show that higher-order tunnel processes and spin-orbit interaction have a negligible effect on the polarization.

Figure 1

(Color) (a)–(c) Energy diagrams showing (a) spin filtering at the $0\leftrightarrow 1$ electron transition, which can be lifted by either (b) changing the gate voltage, $V_G$, or (c) increasing the source-drain bias, $V_{\mathit{SD}}=({\mu }_S-{\mu }_D)∕e$. (d) $dI∕d{V}_{\mathit{SD}}$ as a function of $V_G$ and $V_{\mathit{SD}}$ around the $0\leftrightarrow 1$ electron transition at $B_{\Vert }=12\mathrm{T}$ (Ref. 16). In the entire region I the dot acts as a spin filter, allowing only spin-up electrons to flow through the dot. Letters “a”–“c” indicate the level positions depicted by the diagrams in (a)–(c).

Figure 2

(Color) (a) Energy diagram schematically showing the energy levels of the one- and two-electron states. The allowed transitions between these levels are indicated by arrows. (b) Electrochemical potential ladder corresponding to the transitions shown in (a), using the same color coding. Changing the gate voltage shifts the ladder as a whole. Note that the three triplet states appear at only two values of the electrochemical potential.

Figure 3

(Color) (a) Energetically allowed $1\leftrightarrow 2$ electron transitions as a function of $V_{\mathit{SD}}$ and $V_G$. The lines corresponding to $\uparrow \leftrightarrow S$ outline the region of transport; outside this region, where lines are dashed, the dot is in Coulomb blockade. (b) $dI∕d{V}_{\mathit{SD}}$ as a function of $V_G$ and $V_{\mathit{SD}}$ around the $1\leftrightarrow 2$ electron transition at $B_{\Vert }=12\mathrm{T}$. In the region labeled $A$ only spin-down electrons pass through the dot.