Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States

Via the application of a parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors $\nu =1$ and $1/2$. Near $\nu =1$, the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to $\nu =1/2$, CFs appear single-layer-like (single component) as their resonance features correspond to the total density.

Figure 1

Self-consistently calculated charge distribution of a 2DES confined to a 50-nm-wide QW with density $n=1.7\times 10^{11}{\mathrm{cm}}^{-2}$ for (a) $B_{||}=0$ and (b) 15 T. In both cases, we assume that $B_{\perp }=0\mathrm{T}$. (c) Schematics of the $L$-shaped Hall bar used in our study. The blue lines represent the surface superlattice. The sample is tilted in the field at angle $\theta$ to introduce an in-plane field component ($B_{||}$). The sample’s geometry allows the measurement of the magnetoresistance along ($R_{xx}$) and perpendicular ($R_{yy}$) to $B_{||}$.

Figure 2

(a) $R_{xx,\mathrm{ref}}$ (black) and $R_{xx,\mathrm{pat}}$ (red) traces, measured at $\theta =0°$, i.e., $B_{||}=0$. There are clear signatures of geometric resonance of CFs near $\nu =1/2$ and $1/4$ in the $R_{xx,\mathrm{pat}}$ trace. Inset: Magnified $R_{xx,\mathrm{pat}}$ trace near $\nu =1/2$. The green lines mark the expected positions of the $i=1$ and 2 CF geometric resonance features (see the text).

Figure 3

(a)–(d) Magnetoresistance traces near $\nu =1$ at different $\theta$. The $R_{xx,\mathrm{ref}}$ and $R_{xy,\mathrm{ref}}$ traces are shown in black and blue, respectively. The $R_{xx,\mathrm{pat}}$ (red) and $R_{yy,\mathrm{pat}}$ (green) traces correspond to a current passing along and perpendicular to $B_{||}$ [Fig. 1]. For clarity, the traces are offset vertically. We also include the self-consistently calculated (assuming $B_{\perp }=0\mathrm{T}$) charge distributions for $B_{||}=0$ and 15 T in the insets in (a) and (d).

Figure 4

Magnetoresistance data near $\nu =1/2$ at $\theta =0°$ (lower two traces) and 46° (upper four traces). The black and blue traces correspond to the reference region, while the red and green traces are for the patterned regions. On the right, we also show the self-consistently calculated (assuming $B_{\perp }=0$) charge distributions for $B_{||}=0$ and 15 T. Traces are shifted vertically for clarity.