Voltage-controlled group velocity of edge magnetoplasmon in the quantum Hall regime

We investigate the group velocity of edge magnetoplasmons (EMPs) in the quantum Hall regime by means of time-of-flight measurement. The EMPs are injected from an Ohmic contact by applying a voltage pulse, and detected at a quantum point contact by applying another voltage pulse to its gate. We find that the group velocity of the EMPs traveling along the edge channel defined by a metallic gate electrode strongly depends on the voltage applied to the gate. The observed variation of the velocity can be understood to reflect the degree of screening caused by the metallic gate, which damps the in-plane electric field and, hence, reduces the velocity. The degree of screening can be controlled by changing the distance between the gate and the edge channel with the gate voltage.

Figure 1

(Color online) (a) Schematic device structure and experimental setup for time-of-flight measurement. A short voltage pulse $V_{\text{PS}}\left(t\right)$ of 1.0 mV in amplitude is applied to the source to inject a pulse of EMPs. Another voltage pulse $V_{\text{PG}}\left(t\right)$ of 20 mV in amplitude is applied to the QPC to probe the local potential. The time interval between the two voltage pulses is changed by the mechanical delay line. Four delay gates between the source and the QPC can be used to add extra path length. (b) A scanning electron micrograph of the device. The white lines are metallic gates for the delay gates. The QPC is shown in an enlarged view inside the white circle. Disabled gates are biased at $\sim +0.2\text{V}$ to minimize backscattering. The complicated gate patterns are designed for another purpose, but their different perimeters are useful for this work.

Figure 2

(Color online) (a) Schematic potential diagram of the EMP pulse and the QPC. If the timing of the voltage pulse applied to the QPC coincides with the arrival of the EMP pulse at the QPC, the EMP pulse passes through the QPC (solid line); otherwise, the EMP pulse is reflected at the QPC and returns to the source contact (dashed line). (b) Schematic pulse patterns of the two voltage pulses. (c) $I_{\text{DS}}\left(t_{\text{d}}\right)$ curves observed at $B=6.5\text{T}$ for various pulse widths. The solid line is an exponential fit.

Figure 3

(Color online) (a) and (b) $I_{\text{DS}}\left(t_{\text{d}}\right)$ curves observed at (a) $B=6.5\text{T}$ $\left(\nu =2\right)$ and (b) $B=0\text{T}$. The origin of the time interval is chosen at the peak position of the reference data in (b). Active delay gates are biased at $V_{\text{G}}=-1.1\text{V}$. These curves are offset for clarity. (c) Time interval for various extra path length $\Delta L$ with a straight-line fit.

Figure 4

(Color online) (a) $I_{\text{DS}}\left(t_{\text{d}}\right)$ curves observed for various $V_{\text{G}}$. These curves are offset for clarity. (b) Group velocity $v_{\text{g}}$ as a function of $V_{\text{G}}$. (c) Schematic cross-section of the heterostructure. The location of the edge channel is shifted away from the gate as the 2DEG is depleted.

Figure 5

(Color online) (a) Schematic cross-section of a heterostructure covered with a metal. (b) Schematic illustration of the group velocity depending on the depth.

Figure 6

(Color online) (a) Normalized electron density profiles at the distance $x$ from the gate for various $V_{\text{G}}$. The pinch-off voltage of $-0.2\text{V}$ and the 2DEG depth of 110 nm are used for the calculation. (b) Characteristic width $a^{\ast }$ as a function of $V_{\text{G}}$. (c) Depletion length $l$ as a function of $V_{\text{G}}$. The inset shows a schematic cross-section around the edge channel.