Emergent and reentrant fractional quantum Hall effect in trilayer systems in a tilted magnetic field

Magnetotransport measurements in triple-layer electron systems with high carrier density reveal fractional quantum Hall effect at total filling factors $\nu >2$. With an in-plane magnetic field we are able to control the suppression of interlayer tunneling which causes a collapse of the integer quantum Hall plateaus at $\nu =2$ and $\nu =4$, and an emergence of fractional quantum Hall states with increasing tilt angles. The $\nu =4$ state is replaced by three fractional quantum Hall states with denominator 3. The state $\nu =7/3$ demonstrates reentrant behavior and the emergent state at $\nu =12/5$ has a nonmonotonic behavior with increasing in-plane field. We attribute the observed fractional quantum Hall plateaus to correlated states in a trilayer system.

Figure 1

(Color online) Longitudinal (red/gray) and Hall resistances as functions of the perpendicular magnetic field for a TQW with a barrier thickness $d_b=20\text{Å}$. Filling factors determined from the Hall resistance are labeled. FQH states are marked with arrows. The inset shows the electron energy levels.

Figure 2

(Color online) (a) Resistance in the tilt angle—magnetic field plane for a TQW with $d_b=20\text{Å}$. The minimum at filling factor $\nu =4$ is suppressed and three minima with denominator three are developed. (b) Longitudinal and Hall resistances as functions of the perpendicular magnetic field for two angles: 0 (red dashed) and $49°$ (blue/dark gray) at $T=50\text{mK}$.

Figure 3

(Color online) Longitudinal resistance as a function of the perpendicular magnetic field for TQWs with a barrier width of (a) $20\text{Å}$ for different tilt angles $\Theta =0$ (black), 29.5 (red/gray), 34.4 (blue/dark gray), $39°$ (pink/light gray) and (b) $14\text{Å}$ for $\Theta =0$ (black), 35 (red/gray), 49 (blue/dark gray), $55°$ (pink/light gray) at $T=100\text{mK}$.

Figure 4

(Color online) Hall resistance as a function of $B_{\perp }$ for different tilt angles of a TQW with $d_b=20\text{Å}$ at $T\simeq 100\text{mK}$. As $\Theta$ increases, the plateau $R_{xy}=3h/7e^2$ disappears and is replaced by the plateau $R_{xy}=5h/12e^2$ (a), then the plateau $R_{xy}=3h/7e^2$ reappears and becomes wide while the width of the plateau $R_{xy}=5h/12e^2$ decreases (b).