Quantized acoustoelectric current in the presence of large tunneling counterflow

A surface acoustic wave drives an electrical current through a short quantum wire. A second tunneling current is injected by biasing one side of the quantum wire. These two contributions to the total current, which flow in opposite directions, are controlled almost independently by the gate and the bias voltage, respectively. We have observed the quantization of the acoustoelectric current at up to ten times larger counterflowing tunneling currents. At large tunneling currents the acoustoelectric current can be strongly suppressed. However, this does not seem to be due to an electrostatic interaction between the two currents, but is probably caused by the complex potential landscape in the narrow channel of the quantum wire.

Figure 1

(Color online) (a) Scanning-electron micrograph of the shallow etched constriction of sample 2B. (b) Section of the interdigital transducer (IDT). (c) Schematic sample layout: 2DEG mesa with the QPC, four Ohmic contacts (1–4) to the 2DEG, two side gates (G), and the active IDT. In the experiments, the SAW is incident from the left, contact 3 is biased, and the current detected at contact 1, defining the virtual ground. (d) Schematic potential landscape through the center of the positively biased QPC along the propagation direction of the superposed SAW (thick solid line). The electrical component of the SAW is reduced outside the QPC due to screening by the 2DEG. Also shown is the potential of the unbiased constriction (dotted line) and of the positively biased QPC (thin solid line), both without SAW. In all cases, the right-hand side of the QPC is kept at virtual ground.

Figure 2

(Color online) Typical characteristics of the three devices with respect to the gate voltage $V_g$ at $T=1.8\mathrm{K}$. The upper traces (SAW off) show the conductance $G$ normalized to the quantum conductance $G_0=2e^2∕h$. The data are corrected for a series resistance of $0.6\mathrm{k}\Omega$. Lower traces (SAW on) are the AE current $I$ in units of $ef$. Also shown are the same current traces blown up along the $V_g$ axis by a factor of 10 to visualize the first few quantized current steps. The rf generator was set at the indicated power and frequencies of 2472.085 (2B), 2464.780 (2C), and $2466.565\mathrm{MHz}$ (2E).

Figure 3

(Color online) (a) AE current $I$ and (b) conductance $dI∕d{V}_{\mathit{sd}}$ vs gate voltage $V_g$. The curves were recorded at fixed bias voltages from $-300\text{to}+100\mathrm{mV}$ in steps of $50\mathrm{mV}$ (from left to right). The bias voltage was applied to contact 3 on the same side as the active IDT.

Figure 4

(Color online) (a) AE current $I$ and (b) transconductance $dI∕d{V}_g$ vs bias voltage $V_{\mathit{sd}}$. The $I\left(V_{\mathit{sd}}\right)$ curves were recorded at fixed gate voltages from $+90\text{to}+160\mathrm{mV}$ in steps of $10\mathrm{mV}$ as indicated. At $160\mathrm{mV}$ anomalies due to the quantized AE current can no longer be resolved. The bias voltage was applied to contact 3 on the same side as the active IDT, as in Fig. 3. This explains why the AE current is negative. The positive tunneling counterflow starts at sufficiently positive bias voltages.

Figure 5

(Color online) Transconductance $dI∕d{V}_g$ vs bias voltage $V_{\mathit{sd}}$. The eight curves from Fig. 4b at fixed gate voltages from $90\text{to}160\mathrm{mV}$ in steps of $10\mathrm{mV}$ have been displaced along the bias voltage axis to match (a) at low voltages where the tunneling contribution is small and (b) at large voltages where the AE current is negligible. The required shifts $\delta V_{\mathit{sd}}$ for matching, in the AE (ae) and in the tunneling (tunnel) regime, are shown in the inset. Solid lines guide the eye. The bias voltage was applied to contact 3 near the active IDT.

Figure 6

(Color online) (a) AE current $I$ and (b) transconductance $dI∕d{V}_g$ vs bias voltage $V_{\mathit{sd}}$. The $I\left(V_{\mathit{sd}}\right)$ curves were recorded at fixed gate voltages from $0\text{to}-120\mathrm{mV}$ in steps of $10\mathrm{mV}$ as indicated. The bias voltage was applied to contact 1 opposite the active IDT. Therefore, the AE current is positive and the negative tunneling counterflow starts at sufficiently negative bias voltages.

Figure 7

(Color online) (a) AE current $I$ and (b) transconductance $dI∕d{V}_g$ vs bias voltage $V_{\mathit{sd}}$. The 13 curves from Figs. 6a, 6b at fixed gate voltages from $0\text{to}-120\mathrm{mV}$ in steps of $10\mathrm{mV}$ have been displaced along the bias voltage axis to match at high voltages where the tunneling contribution is small. The corresponding shift $\delta V_{\mathit{sd}}$ is shown in the inset (ae) along with the shift that would be required to match the traces in the tunneling regime (tunnel). Solid lines guide the eye. The bias voltage was applied to contact 1 opposite the active IDT.

Figure 8

(Color online) (a) Position of the onset of the AE current (closed symbols) and the first four plateaus at $1–4ef$ (open symbols, from top to bottom), defined by the transconductance minima in Fig. 4b. The solid lines through the data points have a slope of 0.60. (b) The actual current at these positions together with the ideal AE current (dashed lines). The bias voltage was applied to contact 3 near the active IDT.

Figure 9

(Color online) (a) Conductance $dI∕d{V}_{\mathit{sd}}$ vs bias voltage $V_{\mathit{sd}}$ at $V_g=135\mathrm{mV}$ (upper solid line) and the part of the conductance due to tunneling through the QPC (dotted line). The AE conductance contributes then just the difference between the two curves (lower solid line). (b) Thick solid line is the AE current $I_{\mathit{AE}}$ vs bias voltage $V_{\mathit{sd}}$ calculated by integrating the lower solid line in (a). The other curves obtained similarly for gate voltages $V_g=145$, $140\mathrm{mV}$ and $V_g=130$, 125, $120\mathrm{mV}$ are displaced horizontally in steps of $10\mathrm{mV}$ to the left and the right, respectively. Open symbols mark the position of the measured conductance minima. The bias voltage was applied to contact 3 near the active IDT.

Figure 10

(Color online) AE current $I_{\mathit{AE}}=I-I_T$ at the plateaus vs tunneling counterflow $I_T$ for the three investigated samples. For samples 2B and 2C, the solid lines indicate a possible convergence of the first four acoustoelectric current plateaus at a common fixed point in tunneling current. The dotted lines represent the asymptotic behavior at large tunneling currents. The bias voltage was applied to contact 3 near the active IDT.