Figure 1

(a) Schematic diagram of the measurement setup with the scanning electron microscope image of the sample fabricated on the GaAs/AlGaAs 2DEG. Two gates electrodes, namely, the main gate $\left(V_m\right)$ and the side gate $\left(V_g\right)$, are used to define QPC. The conductance measurement was performed by a standard lock-in technique with an excitation voltage of $10\mu \text{V}$. For the shot-noise measurement, the cross-correlation technique was used with the two cryogenic amplifiers. (b) Typical examples of the QPC conductance are shown as a function of $V_g$ for several $V_m$ values. For $V_m=-1.80$, $-1.95$, and $-2.50\text{V}$, the conductance anomaly appears as indicated by the arrows. (c) When $V_m=-1.55\text{V}$ four conductance plateaus are clearly observed without any signature of the anomaly. (d) The obtained Fano factor for $V_m=-1.55\text{V}$ presented in points with error bars behaves just as the standard theory predicts (shown in the solid curve).Reuse & Permissions

Figure 2

(Color online) (a) The conductance $\left(G\right)$, the differential conductance, and the Fano factor $\left(F\right)$ are plotted as a function of $V_g$, $V_{\text{sd}}$, and $G$ in the upper, middle, and lower panels, respectively. These are obtained when there is no anomaly in the QPC profile. Each curve in the differential conductance plot is obtained for several different $V_g$’s. We set the bias range $e\left|V_{\text{sd}}\right|\le 150\mu \text{eV}$ for obtaining the Fano factor to minimize the effect of the nonlinearity of the conductance while we have confirmed that a slight variation in the bias window $\left(100–250\mu \text{eV}\right)$ does not affect the result. (b)–(d) the corresponding plots for the cases when the conductance has an anomaly around 0.9, 0.8, and $0.5G_0$. In the inset of the bottom panel in (b), the close-up of the Fano factor behavior around the anomaly region is shown. In the inset of the bottom panel in (d), the shot noise observed at $G=0.5G_0$ is shown as a function of $V_{\text{sd}}$. The solid circles represent the experimental data with the fitted curve by Eq. (1) in a solid curve with the dashed curve for the predicted shot noise for the noninteracting case.Reuse & Permissions

Figure 3

In the lower panel the decomposed spin-dependent transmissions of the last channel (${\tau }_{\uparrow }$ and ${\tau }_{\downarrow }$) for the $G_a\sim 0.5G_0$ case is shown as a function of the side gate voltage $V_g$ with the conductance profile superposed. In the middle and the top panels, the obtained asymmetry $A$ and the spin gap energy $\Delta ϵ$ are shown, respectively.Reuse & Permissions