The fractional quantum Hall effect at even-denominator fillings has long attracted attention because its quasiparticles may possess non-Abelian statistics, making such states candidates for topological quantum computation. In the lowest Landau level, the 1/2 and 3/2 states are usually compressible, but in wide quantum wells under certain conditions they become incompressible. This work stands apart: the nearest neighbors in the archive explore fractional quantum crystals, magnetic nodes, quantum barriers, topological states, magnetic resonance, the parton ocean of black holes, orbit geometry, and a quantum critical point, but none consider a tilt-induced transition at filling 3/2 in medium-width wells. This work fills that gap by showing how a parallel magnetic field splits the Fermi contour and gives rise to two sequential quantum states.
The sample is a GaAs/AlGaAs quantum well of width 40.5 nm with a two-dimensional electron gas of density 1.4×10¹¹ cm⁻² and ultra-high mobility 5.0×10⁶ cm²/V·s after brief illumination with a red LED. Measurements were performed in a dilution refrigerator at a base temperature of about 25 mK in magnetic fields up to 18 T. The sample was mounted on a rotating holder, allowing the tilt angle θ to be changed directly in the cryostat. The parallel field component B∥ = $B_{tota}$l·sinθ continuously tuned the topological phase, while the perpendicular component B⊥ = $B_{tota}$l·cosθ determined the Landau level filling factor. Resistance was measured using the van der Pauw method, and energy gaps were determined in two ways: for the soft state, the ratio of the resistance minimum to the average peak was used; for the robust state, an Arrhenius plot of resistance versus inverse temperature.
At zero tilt, the state at filling 3/2 is a compressible composite-fermion liquid, as expected for the lowest Landau level. As the parallel field increases, at B∥ ≈ 12.2 T (angle about 72°), a soft fractional quantum Hall state emerges with a finite resistance minimum and an almost quantized Hall plateau. Its energy gap is about 30 mK. Upon further increasing the field to B∥ ≈ 14.7 T (angle about 75.3°), a topological phase transition occurs: the gap closes, and then a robust state appears with a gap that grows and saturates for B∥ > 15.5 T. Simultaneously with the robust state, a daughter state appears at filling 19/13. The resistance at the minimum first rises from nearly zero to about 300 Ω, then drops to about 130 Ω, indicating gap closure and reopening. The 19/13 daughter state survives at a somewhat larger parallel field because its effective B∥ is higher.
The work shows that in medium-width quantum wells, where only the symmetric subband is occupied at zero tilt, a strong parallel magnetic field splits the Fermi contour into two disconnected parts in momentum space. This induces a transition from a one-component to a two-component system and gives rise to two sequential fractional quantum Hall states at filling 3/2. Unlike neighboring works that study either wide wells with two occupied subbands or states in higher Landau levels, here a transition fully controlled by field tilt in the lowest Landau level is demonstrated for the first time. The observation of the 19/13 daughter state provides an indirect way to determine the topological order of the parent state, which was previously proposed theoretically but not realized experimentally in such a configuration.
The topic may develop toward precise determination of the topological order of the soft and robust 3/2 states. Theoretical models, such as anti-Pfaffian or anti-(331), predict different sets of daughter states, and searching for a second daughter state at filling 26/17 or 29/19 would help distinguish among candidates. In addition, numerical calculations that account for Landau level mixing and Zeeman energy are needed to explain the observed sharp growth of the gap with field. Other materials, such as ZnO or graphene, might be explored, where similar transitions could be more pronounced.
The results will impact the physics of the fractional quantum Hall effect, especially the understanding of even denominators in the lowest Landau level. They are also important for the development of topological qubits, where non-Abelian states such as anti-Pfaffian are candidates.
The next step will be to search for a second daughter state at higher fields or in samples with different well widths, to unambiguously determine the topological order. Interference measurements are also planned to test the non-Abelian statistics of the quasiparticles.
The work directly relates to the unresolved problem of determining the topological order of even denominators in the lowest Landau level. It also touches on the mechanism of composite-fermion pairing and the role of Fermi contour anisotropy in stabilizing states.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The study explores the state with filling factor 3/2 in a GaAs quantum well of width 40.5 nm. When the magnetic field is tilted, a soft state with a small gap emerges, and at a larger tilt, a hard state with a growing gap appears; the transition between them occurs through gap closure. A daughter state at filling 19/13 is observed, which helps determine the topological order.
Where its strength is
This demonstrates the tuning of topological order through the splitting of the Fermi contour by a parallel field in wells of intermediate width. It fills the gap between narrow and wide wells and offers a new way to manipulate states with non-Abelian statistics.
Where it could go next
Worth trying
Why this may matter
If the hard state at 3/2 indeed possesses non-Abelian statistics, it opens a path to topological qubits controlled by tilting the magnetic field, which may be simpler to implement than other methods.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.54, against a usual 0.64. It looks like few have drilled nearby.
The energy gap of the robust state at filling 3/2 grows so sharply with field that it saturates within just 0.8 T, which is comparable to the field change when tilting the sample by a couple of degrees.