Kondo Effect in a Few-Electron Quantum Ring

A small quantum ring with less than ten electrons was studied by transport spectroscopy. For strong coupling to the leads a Kondo effect is observed and used to characterize the spin structure of the system in a wide range of magnetic fields. At small magnetic fields Aharonov-Bohm oscillations influenced by Coulomb interaction appear. They exhibit phase jumps by $\pi$ at the Coulomb-blockade resonances. Inside Coulomb-blockade valleys the Aharonov-Bohm oscillations can also be studied due to the finite conductance caused by the Kondo effect. Astonishingly, the maxima of the oscillations show linear shifts with increasing magnetic field and gate voltage.

Figure 1

(a) AFM image of the quantum ring with an inner diameter of 190 nm and an outer of 450 nm. (b) Scheme of our measurement setup. (c) Aharonov-Bohm oscillations in the open regime of the quantum ring ($V_A,V_B>0\mathrm{m}\mathrm{V}$). (d) Coulomb-blockade oscillations as a function of the backgate voltage ($V_A=-250\mathrm{m}\mathrm{V}$, $V_B=-100\mathrm{m}\mathrm{V}$, $B=0$).

Figure 2

Linear conductance $G$ in function of the perpendicular magnetic field $B$ and the gate voltage $V_B$.

Figure 3

(a) Gray scale plot of the differential conductance as a function of $V_B$ and source-drain voltage $V_{\mathrm{S}\mathrm{D}}$ at $V_A=-80\mathrm{m}\mathrm{V}$ and $B=0$ with black (white) high (low) $G$. (b) Temperature dependence of the zero-bias peak in the center of the $N=5$-diamond [marked by the short bar in (a)], $T=30$, 50, 70, 100, 140, 200, 350, 500 mK. (c) $T$-dependent full width at half maximum (FWHM). (d) Peak conductance scaled with respective $T_K$ and $G_0$ (see text) for data in (b) (full circles) and for a stronger tunnel coupling (open symbols). (e) Split Kondo resonance at $B=3$ T. (f) $B$-dependent positions of the split Kondo peaks.

Figure 4

(a) $N=5$-Kondo valley at $V_A=-150\mathrm{m}\mathrm{V}$ (solid) and $V_A=-80\mathrm{m}\mathrm{V}$ (dashed line) at $B=0$. ■, ▲, ●, and ○ mark the gate voltages for the Aharonov-Bohm measurements in (b). (b) Upper part: Normalized conductance $G/G_0$ as a function of $B$ at $V_A=-150\mathrm{m}\mathrm{V}$. The curves are offset for clarity. Lower part: $G/G_0$ at $V_A=-80\mathrm{m}\mathrm{V}$ after subtraction of an increasing background. (c) $G/G_0(B,V_B)$ as gray scale plot at $V_A=-150\mathrm{m}\mathrm{V}$ with peaks marked by white dots. (d) Positions of the Aharonov-Bohm maxima extracted from (c).