Origin of the hysteresis in bilayer two-dimensional systems in the quantum Hall regime

The hysteresis observed in the magnetoresistance of bilayer two-dimensional (2D) systems in the quantum Hall regime is generally attributed to the long-time constant for charge transfer between the 2D systems due to the very low conductivity of the quantum Hall bulk states. We report electrometry measurements of a bilayer 2D system that demonstrate that the hysteresis is instead due to nonequilibrium induced current. This finding is consistent with magnetometry and electrometry measurements of single 2D systems and has important ramifications for understanding hysteresis in bilayer 2D systems.

Figure 1

(Color online) (a) A schematic of the device and measurement circuit with (from bottom) the lower 2DES in gray, the upper 2DES in white, and the top gate in blue. The upper 2DES shares only one common contact with the lower 2DES, which is connected to ground, allowing the upper 2DES density to respond to changes in top-gate bias. The measured Hall voltage $V_{xy}$ can be used to obtain the upper 2DES chemical potential ${\mu }_T$. (b) The measured longitudinal resistance $R_{xx}$ (lower two traces) and Hall resistance $R_{xy}$ (upper two traces) in the lower 2DES versus magnetic field $B$ demonstrating similar hysteresis to that previously reported in bilayer 2D systems (Refs. 7, 9, 10). (c) and (d) are schematics illustrating the expected behavior of the measured electrostatic potential ${\varphi }_T$ in the upper 2DES as a function of top-gate bias $V_{TG}$ for the charge transfer and nonequilibrium induced current mechanisms, respectively. In (b)–(d) the blue solid/red dotted lines indicate data taken with increasing/decreasing $B$ or $V_{TG}$.

Figure 2

(Color online) (a) The measured lower 2DES Hall resistance $R_{xy}$ and (b) the corresponding upper 2DES electrostatic potential ${\varphi }_T$ versus top-gate voltage $V_{TG}$ for decreasing $V_{TG}$ (red dotted lines) and increasing $V_{TG}$ (blue solid lines). The dashed black line in (b) highlights the ideal behavior of ${\mu }_T$ in the absence of any hysteresis. In each case, five traces are presented, obtained at $V_{TG}$ sweep rates of 3, 1, 0.3, 0.1, and 0.05 mV/s with the largest deviation from ideal behavior occurring at highest sweep rate.

Figure 3

(Color online) The Hall resistance $R_{xy}$ vs $V_{TG}$ obtained at $B=1.55\text{T}$ for (a) a fixed sweep rate of 1 mV/s for temperatures $T$ of 100, 200, 300, and 500 mK, and (b) a fixed temperature $T=500\text{mK}$ for sweep rates of 0.05, 0.1, 0.3, 1, and 3 mV/s. In both panels, up-sweeps/down-sweeps are indicated with solid/dashed lines.