High-order two-component fractional quantum Hall states around filling factor $ν= 1$

Abstract

Two-component fractional quantum Hall (2C-FQH) states in electron bilayers have been known for decades, yet their experimental realization remained limited to low-order fractions. Here we report on several families of high-order 2C-FQH states that emerge when an in-plane magnetic field drives a controlled monolayer-to-bilayer transition in an ultra-high-mobility GaAs quantum well. These families of states proliferate symmetrically toward the filling factor $ν= 1$, from both $ν= 2/3$ and $ν= 4/3$, thereby respecting particle-hole symmetry. Surprisingly, many unbalanced states (with unequal layer fillings) are more robust than their parent balanced states, defying the expected hierarchy of Jain sequences. Our findings substantially expand the known landscape of 2C-FQH states, highlighting the unexpected richness of the bilayer quantum Hall regime and opening new routes for probing the interplay of symmetry, topology, and interactions in quantum Hall systems.

Figures (4)

• Figure 1: Longitudinal resistance $R_L$ in (a) perpendicular magnetic field $(\theta = 0^\circ)$ and (b) in tilted magnetic fields $(\theta = 76.6^\circ, \nu > 1)$, $(\theta = 72.5^\circ, \nu < 1)$ as a function of filling factor $\nu$. Insets illustrate electron distribution within our quantum well at (a) $B_\parallel = 0$ and (b) $B_\parallel = 15$ T, a representative value, as illustrated in panel (c), showing $B_\parallel$, corresponding to panel (b), versus $\nu$.
• Figure 2: Longitudinal resistance $R_L$ (left axis, in k$\Omega$) and Hall resistance $R_H$ (right axis, in units of von Klitzing constant, $R_K = h/e^2$) as a function of $\nu$ measured at $\theta = 76.6^\circ$. Thick vertical lines mark balanced (parent) 2C-FQH states and thin vertical lines are drawn at $\nu$ corresponding to the unbalanced (daughter) states. Near the top axis we also mark the CF filling factors in each layer, $n_\alpha$ and $n_\beta$.
• Figure 3: (a) Longitudinal resistance $R_L$ as a function of $\nu$, measured at $\theta = 74.4^\circ$, showing the $\nu^-_{3n_\beta}$ family of states, $\nu^-_{33} =6/5$, $\nu^-_{34} = 41/35$, and $\nu^-_{35} = 52/45$. The CF filling factors in each layer, $n_\alpha$ and $n_\beta$, are marked near the top axis. (b) $\Lambda$-levels in layers $\alpha$ and $\beta$ at $\nu^-_{35} = 52/45$ ($\nu^-_\alpha = 3/5, \nu^-_\beta = 5/9)$. Levels below (above) the Fermi level $E_F$ (dotted line) are full (empty).
• Figure 4: Longitudinal resistance $R_L$ as a function of filling factor $\nu$ (bottom axis) and partial filling factor $\tilde{\nu} = \nu - 1$ (top axis), measured at (a) $\theta = 76.6^\circ$ and (b) $\theta = 73.4^\circ$. As in Fig. \ref{['fig2']}, thick vertical lines mark balanced (parent) 2C-FQH states and thin lines mark unbalanced (daughter) states. The CF filling factors, $n_\alpha$ and $n_\beta$ and partial fillings of parent states are shown near the top and bottom axes, respectively.