Kondo Effect from a Tunable Bound State within a Quantum Wire

We investigate the conductance of quantum wires with a variable open quantum dot geometry, displaying an exceptionally strong Kondo effect and most of the 0.7 structure characteristics. Our results indicate that the 0.7 structure is not a manifestation of the singlet Kondo effect. However, specific similarities between our devices and many of the clean quantum wires reported in the literature suggest a weakly bound state is often present in real quantum wires.

Figure 1

(a) A classic 0.7 structure can be observed with $\Delta V_g=+1.2\mathrm{V}$ (traces offset laterally), defined as $\Delta V_g=V_{\mathrm{left}}-V_{\mathrm{right}}$, and $V_{\mathrm{average}}=[V_{\mathrm{left}}+V_{\mathrm{right}}]/2$. The inset shows a SEM image of our device; (b) the resonant peak disappears as $\Delta V_g$ is varied from 0 to $+1.2\mathrm{V}$ in 0.4 V steps from right to left traces. The inset shows a schematic diagram of the geometry of the narrow entrance and exit.

Figure 2

(a) Temperature is decreased from 1.1 K to 42 mK (in $\sim 0.1\mathrm{K}$ increments; $\Delta V_g=0$; traces offset laterally). (b) The increase of $G$ as $T$ decreases is a hallmark of Kondo interactions ($\Delta V_g=0$). (c) The CB peak smears out for $T\ge 1.0\mathrm{K}$ while a shoulder at $0.7(2e^2/h)$ strengthens ($\Delta V_g=0$; traces offset laterally).

Figure 3

(a) Plot of $f_A=(1-G_A)/C_A$ versus $T_A/T$ for $-22\mathrm{mV}\le V_{\mathrm{gate}}\le -16\mathrm{mV}$. The inset shows a detailed view of the range $0<T_A/T<2$ for $-14\mathrm{mV}\le V_{\mathrm{gate}}\le -8\mathrm{mV}$. (b) Plot of $f_K=\sqrt{(G_K^{-1/s}-1)/(2^{1/s}-1)}$ versus $T/T_K$ ($s=0.11$). The inset shows the extracted $T_A$ and $T_K$ ($\pm 5\%$), consistent with values found in previous studies [4, 24]. In both (a) and (b), the black solid line shows the theoretical universal curve.

Figure 4

Low-temperature conductance with a source-drain bias when: (a), (c) $\Delta V_g=0\mathrm{V}$, and (b), (d) $\Delta V_g=-1.4\mathrm{V}$. $|V_{\mathrm{sd}}|$ is increased from 0 to $100\mu \mathrm{V}$ in (a)–(b), and from 0.1 to 0.3 mV in (c)–(d). High source-drain bias conductance for $\Delta V_g=0$ at: (e) $T=0.03\mathrm{K}$ and (f) $T=1\mathrm{K}$. From left to right (traces offset laterally), $V_{\mathrm{sd}}$ is increased from $-2$ to $+2\mathrm{mV}$ in $40\mu \mathrm{V}$ steps (orange traces show $V_{\mathrm{sd}}=0$).

Figure 5

(a) “Map” of the $V_{\mathrm{gate}}$ ranges defining zones I, II, and III ($\Delta V_g=0$, $V_{\mathrm{sd}}=+100\mu \mathrm{V}$). Nonlinear differential conductance traces taken at fixed $V_{\mathrm{gate}}$ at $T=0.03\mathrm{K}$ are shown for (b) zone I (green), (c) zone II (orange), and (d) zone III (purple). $V_{\mathrm{gate}}$ is stepped by 0.3 mV between traces. The black trace in (c) was taken at $T=0.04\mathrm{K}$ (see main text). The inset in (c) shows data at larger source-drain bias. $\Delta h_{\mathrm{ZBA}}$ (defined in main text) is shown: (e) after and (f) before illumination. Note how $\Delta h_{\mathrm{ZBA}}$ have a local minimum at the CB peak.

Figure 6

(a) A classic 0.7 structure in a clean quantum wire. (b) Nonlinear differential conductance traces of the device shown in (a) taken for fixed $V_{\mathrm{gate}}$ at $T=0.03\mathrm{K}$. Plots of $\Delta h_{\mathrm{ZBA}}$ are shown for: (c) data from panel (b), (d) data from Fig. 2(b) in Ref. 28, and (e) data from Fig. 1(d) in Ref. 4. Note how all $\Delta h_{\mathrm{ZBA}}$ plots have a local minimum.

Figure 7

(a) Magnetic field is increased from 0 to 11.8 T in 0.2 T steps from left to right (traces offset laterally, $T=0.04\mathrm{K}$, $V_{\mathrm{sd}}=0$, and $\Delta V_g=0$). (b) Splitting of the ZBA for five decreasing values of $V_{\mathrm{gate}}$ from zone III (purple, traces offset vertically) and zone II (orange, no offset).