Kondo Effect in a Semiconductor Quantum Dot with a Spin-Accumulated Lead

We study the Kondo effect in a semiconductor quantum dot in contact with a spin-accumulated lead. The spin accmulation in a nonmagnetic semiconductor is realized by spin injection from a spin-polarized quantum point contact in combination with magnetic focusing, thus creating spin-unbalanced chemical potentials. We demonstrate that the spin splitting of the Kondo densities of states (DOS) for spin-up and spin-down electrons can be controlled by selectively shifting only the spin-up DOS using spin accumulation. We also show the possibility to recover the Kondo effect in a high magnetic field, by compensating for Zeeman splitting by spin accumulation.

Figure 1

(a) Spin splitting of the Kondo DOS peaks by spin accumulation at $B=0$. The peak separation equals ${\mu }_{\uparrow }-{\mu }_{\downarrow }$. (b) Expected Kondo conductance peak positions probed by a spin-unaccumulated reference lead when only ${\mu }_{\uparrow }$ is changed. $V_D=-({\mu }_{\uparrow }-{\mu }_{\downarrow })/e$ (red line) corresponds to ${\rho }_{\uparrow }$ and $V_D=0$ (blue line) corresponds to ${\rho }_{\downarrow }$. (c) Scanning electron micrograph of the device and measurement scheme. The gate electrodes form a QD (left) and a QPC (right). With the spin-polarization measurement, the QD is used as another QPC by positively biasing two lower-left gate electrodes.

Figure 2

(a),(b) Conductance plateaus of drain (a) and emitter (b) QPCs. Both QPCs exhibit a half conductance plateau in a high magnetic field. (c) Magnetic focusing measurement of the device. Both QPCs are tuned in the middle of the first conductance plateau. The focusing signal $(2e^2/h)V_D/I_E$ represents the possibility that $I_E$ is focused on the drain lead. (d) Spin-polarization measurement of the QPCs at $B=5.1\mathrm{T}$. $(2e^2/h)V_D/I_E$ increases as $I_E$ is spin polarized. The conductance of the drain QPC ($g_D$) is fixed at $e^2/h$, $1.5e^2/h$, $1.8e^2/h$, or $2e^2/h$ (from top to bottom). The conductance of the emitter QPC ($g_E$) is also shown (broken line).

Figure 3

(a)–(c) Schematic energy diagrams of the Kondo DOS peaks at $g_E=0$, $e^2/h$, and $2e^2/h$, for $V_D=0$ and finite $V_E$ and $B$. (d)–(f) $g_D(V_D,V_E)$ measured at $g_E=0$ (d), $e^2/h$ (e), and $2e^2/h$ (f). All measurements are performed in the middle of the Kondo valley at $B=5.1\mathrm{T}$. (g)–(i) $g_D$ vs $V_D$ curves from (d)–(f) for $V_E$ between $-100\mu \mathrm{V}$ (bottom) and $150\mu \mathrm{V}$ (top) in steps of $50\mu \mathrm{V}$. The curves are vertically offset by $0.2e^2/h$. The broken lines are guides for the eye.

Figure 4

Kondo peak parameters extracted from $g_D$ in Fig. 3. (a) The background is subtracted from the raw conductance curve (red dots) by a double-Lorentzian function, $g_{\mathrm{dL}}(V)=g_1/(1+[(V-V_1)/(w_1/2){]}^2)+g_2/(1+[(V-V_2)/(w_2/2){]}^2)$, (broken line) and the residual (black triangles) is further fitted by another double-Lorentzian function (blue line). (b)–(d) Extracted peak parameters at $g_E=e^2/h$ and $g_E=2e^2/h$. $P_1$ and $P_2$ correspond to the Kondo peaks at negative and positive $V_D$. The peaks at $|V_E|>100\mu \mathrm{eV}$ are difficult to resolve except for $P2$ at $g_E=e^2/h$. The broken lines in (b) are $V_D=V_E\pm 130\mu \mathrm{V}$ and $V_D=130\mu \mathrm{V}$. See text and Ref. 28 for detail.