Observation of finite excess noise in the voltage-biased quantum Hall regime as a precursor for breakdown

We performed noise measurements in a two-dimensional electron gas to investigate the nonequilibrium quantum Hall effect (QHE) state. While excess noise is perfectly suppressed around the zero-biased QHE state reflecting the dissipationless electron transport of the QHE state, considerable finite excess noise is observed in the breakdown regime of the QHE. The noise temperature deduced from the excess noise is found to be of the same order as the energy gap between the highest occupied Landau level and the lowest empty one. Moreover, unexpected finite excess noise is observed at a finite source-drain bias voltage smaller than the onset voltage of the QHE breakdown, which indicates finite dissipation in the QHE state and may be related to the prebreakdown of the QHE.

Figure 1

(a) Equilibrium conductance of the device as a function of $B$ and schematic illustration of the present two-terminal device. (b) Differential conductance of the device as a function of $V_{\mathrm{sd}}$. $V_{\mathrm{BD}}$ is defined as $V_{\mathrm{sd}}$ at which $\Delta G=G\left(V_{\mathrm{sd}}\right)-G\left(0\right)=0.01$$e^2/h$.

Figure 2

(a) Schematic illustration of the two-terminal device and setup for the high-frequency noise measurements. (b) Noise spectra with a resonant peak at 2.55 MHz obtained at $V_{\mathrm{sd}}=0$ and 15 mV. The solid curves are the result of the fitting by Eq. (1).

Figure 3

(a) Schematic illustration of the setup for the low-frequency noise measurement utilizing the cross-correlation technique. (b) Noise spectra in the kilohertz range obtained at $V_{\mathrm{sd}}$ $=$ 0 and 12 mV. The solid curves are the result of the fitting by Eq. (3).

Figure 4

(a) $G$ as a function of $V_{\mathrm{sd}}$. (b) $S$ as a function of $V_{\mathrm{sd}}$. Measurements are performed at $B=4.2$, 5.6, and 8.0 T ($\nu =2.1$, 1.6, and 1.1, respectively) and $T=100$ mK.

Figure 5

(a) Color plot of $\Delta G=G\left(V_{\mathrm{sd}}\right)-G\left(0\right)$ as a function of $B$ and $V_{\mathrm{sd}}$. (b) Color plot of $T_{\mathrm{N}}$ as a function of $B$ and $V_{\mathrm{sd}}$. (c) Equilibrium conductance as a function of $B$. The open circles in (a) and (b) indicate $V_{\mathrm{BD}}$ at each field.

Figure 6

(a) Equilibrium conductance as a function of $B$ at $T=4.4$ K. (b) Plot of $a\left(V_{\mathrm{sd}}\right)$ as a function of $V_{\mathrm{sd}}$ and $B$.

Figure 7

$G\left(V_{\mathrm{sd}}\right)$ and $S\left(V_{\mathrm{sd}}\right)$ as a function of $V_{\mathrm{sd}}$ obtained at (a) $\nu \sim 2$ and (b) $\nu \sim 1$. The range of $V_{\mathrm{sd}}$ is divided into a QHE regime, a precursor regime, and a breakdown regime.

Figure 8

Schematic illustration of the edge states and the localized bulk states in (a) the QHE regime and (b) the precursor regime. (left) Energy-position plot; the vertical axis is the energy, and the horizontal axis is the position across the counterflowing edge channels. (right) Real space image of the edge and the bulk states. The dashed curve and the solid curve represent unoccupied states and occupied states, respectively. The dotted line denotes electron tunneling between the edge state and the bulk states.