Figure 1

(a) AFM micrograph of the sample. The transport through the point contact channel is controlled by the application of voltages on two surrounding conducting areas G1 and G2, while all the other gates are grounded. (b) Temperature dependence of the conductance anomaly from 0.1 K (right) to 2 K (left). The conductance value of the anomaly decreases with increasing temperature. This measurement was performed at $\Delta V=0$ V (see text for details). Curves are shifted horizontally for clarity. (c) and (d) Nonlinear differential conductance $g=dI/d{V}_{sd}$ as a function of the bias voltage for different gate voltages at 600 mK and 100 mK. The first plateau has an upward slope with $V_{sd}$ in both cases. In (d) this upward slope is more extreme and linear and a peak at zero bias is also evident. The $dI/d{V}_{sd}$ curves show a clear accumulation, called bunching here, around two gate voltages shown with blue arrows. (e) Transconductance $d^{2}I/d{V}_{sd}d{V}_g$ (arbitrary units) as a function of source-drain bias and gate voltage obtained by numerical differentiation from the data presented in Fig. 1d over larger gate and source-drain voltage ranges. The nonlinear conductances are indicated in units of $2e^2/h$. The bunchings marked with blue arrows are also visible in this plot. (c) and (d) were measured at $V_G=V_{G1}=V_{G2}$ [$\Delta V$ was changed by 64 mV during this gate sweep, which is small compared to the $\Delta V$ variation of 0.8 V in Fig. 2a and 0.3 V in the rest of the paper].Reuse & Permissions

Figure 2

(a) Linear conductance $G$ as a function of $V_g$ for different gate asymmetries ranging from $\Delta V=-0.4$ V to $+0.4$ V at $T=100$ mK. The symmetric configuration ($\Delta V=0$) is marked with a thick line. Due to the breakdown across the oxide lines the gate voltage range is limited at extreme asymmetries. The conductance anomaly gets stronger for positive asymmetries (when the channel is shifted towards the gate $G2$), transforming to a plateau at $G\sim 0.75\times 2e^2/h$ for $\Delta V\sim 100$ mV, and disappears at negative asymmetries. (b) Temperature dependence of the linear conductance $G$ vs $V_g$ at $\Delta V=+113$ mV in the range of 100 mK (right) to 600 mK (left). The conductance of the anomalous plateau decreases with increasing temperature. The curves are shifted horizontally for clarity.Reuse & Permissions

Figure 3

(a) Linear conductance $G$ as a function of $V_g$ at different in-plane magnetic fields ranging from 0 T to 12 T at the gate asymmetry of $\Delta V=+113$ mV at $T=100$ mK. Note that the anomalous feature moves to lower conductances and even below $0.5\times 2e^2/h$ as the field is increased. A constant series resistance attributed to the leads was subtracted from the raw data. (b)–(d) The effect of a magnetic field perpendicular to the 2DHG plane on linear conductance $G$ vs $V_g$ at three different gate asymmetries of $\Delta V=+113$, 0, and $-186$ mV. Each plot shows the effect of perpendicular magnetic fields up to 5 T. The same trend in the anomalous feature as shown in (a) is observed for (b) and (c). In all three cases, a seemingly independent half plateau is formed at $0.5\times 2e^2/h$ for $B_{\perp }>3$ T. In the case of perpendicular magnetic fields a $B_{\perp }$-dependent but gate-independent series resistance is subtracted from the raw resistance data which was checked to be due to SdH oscillations in the leads. The curves are shifted horizontally for clarity.Reuse & Permissions

Figure 4

(a)–(c) Differential conductance $g$ vs $V_{sd}$ and $V_g$ exhibiting a ZBA at three different gate asymmetries $\Delta V$. At $\Delta V=-186$ mV the ZBA is single peaked and only slightly asymmetric. At zero and positive $\Delta V$ values the peak becomes more asymmetric and splits. The arrows point to the accumulation of the individual $dI/d{V}_{sd}$ curves at $\Delta V=+113$ mV. A zoom into the low bias regime at $\Delta V=-186$ mV [marked by the green vertical lines in (a)] is shown in (d)–(f) for different in-plane magnetic fields. The ZBA splits at $B_{\parallel }=2$ T and the splitting grows further at 4 T. All data are taken at $T=100$ mK.Reuse & Permissions

Figure 5

Characteristics of a model QPC with a resonance in the transmission. (a) Transmission vs energy is assumed to have a Lorentzian resonance at the Fermi energy superimposed on the transmission of a saddle-point potential. (b) Calculated linear conductance vs $V_g$ for equally spaced temperatures in steps of 20 mK. The resonance disappears quickly by increasing the temperature (shifted horizontally for clarity). (c) Nonlinear differential conductance calculated from the transmission shows that a peak appears at zero bias. (d) Effect of an in-plane magnetic field on the linear conductance. (e) Effect of an in-plane magnetic field on the differential conductance.Reuse & Permissions

Figure 6

Characteristics of a model QPC with a capacitive coupling to a nearby chargeable impurity. (a) Schematic of the model with an assumed potential profile along the dashed line. (b) Calculated linear conductance vs $V_g$ for equally spaced temperatures in steps of 20 mK. The anomaly in the conductance arises due to the charging of the impurity (shifted horizontally for clarity). (c) Nonlinear differential conductance calculated from the transmission. The red arrows point to the bunchings of several curves at the gate voltage corresponding to the charging of the impurity. (d) Effect of an in-plane magnetic field on the linear conductance (shifted horizontally for clarity).Reuse & Permissions

Figure 7

Evolution of the ZBA at $T=100$ mK with perpendicular magnetic field $B_{\perp }$ and gate asymmetry $\Delta V$. A field-dependent series resistance has been subtracted to keep the first plateau at $2e^2/h$.Reuse & Permissions

Figure 8

Visualization of the differential conductance integral for the three cases of (a) a saddle-point potential, (b) a saddle-point potential plus a resonance, and (c) a nonzero Zeeman splitting of the two subbands while the Fermi energy is at point $B$. The red curves represent the two Fermi-Dirac distribution derivatives in the integrand and the blue curve represents the transmission probability. The scales are adjusted for better visibility. (d)–(f) The qualitative $V_{sd}$ dependence of $dI/d{V}_{sd}$ at low biases as the Fermi energy equals to the energies labeled by $A$, $B$, and $C$ on the corresponding panels of (a)–(c), respectively.Reuse & Permissions