Finite shot noise and electron heating at quantized conductance in high-mobility quantum point contacts

We report a precise experimental study on the shot noise of a quantum point contact (QPC) fabricated in a GaAs/AlGaAs based high-mobility two-dimensional electron gas (2DEG). The combination of unprecedented cleanliness and very high measurement accuracy has enabled us to discuss the Fano factor to characterize the shot noise with a precision of 0.01. We observed that the shot noise at zero magnetic field exhibits a slight enhancement exceeding the single particle theoretical prediction, and that it gradually decreases as a perpendicular magnetic field is applied. We also confirmed that this additional noise completely vanishes in the quantum Hall regime. These phenomena can be explained by the electron heating effect near the QPC, which is suppressed with increasing magnetic field.

Figure 1

(a) Schematic diagram of the current noise measurement setup. The QPC is formed by negative voltage $V_g$ applied on two opposing electrostatic gates. (b) and (c) Conductance of QPC 1 and 2 measured at 30 mK as a function of gate voltage.

Figure 2

$V_{\text{sd}}$ dependence of current noise (open circle) and conductance (solid line) of QPC 2 for different gate voltage and magnetic field. The dashed line shows fitting result. (a) In the region between plateaus, $G\sim 1.7\times (2e^2/h)$ for zero magnetic field. (b) At the second plateau for zero magnetic field. (c) At the second plateau for $B=0.80$ T. The fitted Fano factor is $F=0.12$, 0.029, and $1.7\times {10}^{-3}$, respectively.

Figure 3

(a) Conductance dependence of the Fano factor for $B=0$ T (open circle) and 0.80 T (filled square). The black dashed line shows theoretical value without Zeeman splitting. The current noise at $G\sim 1.7\times (2e^2/h)$ and $G=2\times (2e^2/h)$ is shown in Figs. 2 and 2, respectively. (b) $V_g$ dependence of Fano factor. The solid and dashed line curves conductance at $B=0$ and 0.80 T, respectively. (c) Detailed plot of Fano factor and conductance against $V_g$ near the region of first plateau (left figure) and second plateau (right figure). The upper and middle panels show the Fano factors at $B=0$ and 0.80 T, respectively. The bottom panels show the conductance. The solid and dashed curves represent conductance for $B=0$ and 0.80 T, respectively. Note that the horizontal axis for 0.80 T data is rescaled to superpose the 0 T data.

Figure 4

(a) $V_g$ dependence of Fano factor (triangle) and conductance (solid line) for the quantum Hall regime. The dashed curve shows the theoretical Fano factor deduced from the measured conductance. (b) Current noise (triangle) and conductance (solid line) as a function of $V_{\text{sd}}$ at the conductance plateau ($V_g=-1.35$ V).

Figure 5

(a) The Fano factor versus conductance of QPC 1 at zero magnetic field. The dashed curve shows the theoretical Fano factor deduced from the measured conductance. (b) and (c) The average value of the Fano factor at each conductance plateau for QPC 1 and QPC 2, respectively.

Figure 6

(a) Current noise at second plateau versus $V_{\text{sd}}$ for $B=0$ T (open circle) and $0.80$ T (open square). The solid curves show the fit of the data assuming $S_I\left(V_{\text{sd}}\right)=4k_B{T}_e^{JH}G$. $1/G_m$ is $2.78$ and $0.14\mathrm{\Omega }$ for $B=0$ and $0.80$ T, respectively. (b) and (c) The variation of the nominal Fano factor (red circle) and $1/G_m$ (blue square) with perpendicular magnetic field for the first and the second plateau region, respectively. These values are derived by fitting the measured current noise for QPC 2.

Figure 7

The conductance dependence of parameter $G_m$ of QPC 1 for $T_e=500$ mK (circle), 300 mK (triangle), and 100 mK (square). $G_m$'s are obtained at first, second,…, ninth plateau, respectively.