David F. Mross

Topological and crystalline orders of electrons both benefit from enhanced Coulomb interactions in partially filled Landau levels. In bilayer graphene (BLG), the competition between fractional quantum Hall liquids and electronic crystals can be tuned electrostatically. Applying a displacement field leads to Landau-level crossings, where the interaction potential is strongly modified due to changes in the orbital wave functions. Here, we leverage this control to investigate phase transitions between topological and crystalline orders at constant filling factors in the lowest Landau level of BLG. Using transport measurements in high-quality hBN-encapsulated devices, we study transitions as a function of displacement field near crossings of N=0 and N=1 orbitals. The enhanced Landau-level mixing near the crossing stabilizes electronic crystals at all fractional fillings, including a resistive state at ν=13 and a reentrant integer quantum Hall state at ν=73. On the N=0 side, the activation energies of the crystal and fractional quantum Hall liquid vanish smoothly and symmetrically at the transition, while the N=1 transitions out of the crystal appear discontinuous. Additionally, we observe quantized plateaus forming near the crystal transition at half filling of the N=0 levels, suggesting a paired composite fermion state stabilized by Landau level mixing.

Quantum Hall plateaus at quarter fillings occur in GaAs wide quantum wells, hole-doped GaAs, and bilayer graphene. However, the interactions favoring incompressible states over compressible composite-Fermi liquids at such fillings are not well understood. We devise a method for the computation of the trial energies for Haldane pseudopotentials via Monte Carlo sampling. Applying it to the quarter-filled lowest Landau level, we find that tuning the third and fifth pseudopotential values can stabilize the anti-Pfaffian, Moore-Read, and f-wave states. The smallest deviations from pure Coulomb interactions are required by anti-Pfaffian, whose presence is indicated by daughter states in recent experiments of bilayer graphene at ν=34.

Position exchange of non-Abelian anyons affects the quantum state of their system in a topologically-protected way. Their expected manifestations in even-denominator fractional quantum Hall (FQH) systems offer the opportunity to directly study their unique statistical properties in interference experiments. In this work, we present the observation of coherent Aharonov-Bohm interference at two even-denominator states in high-mobility bilayer graphene-based van der Waals heterostructures by employing the Fabry-Pérot interferometry (FPI) technique. Operating the interferometer at a constant filling factor, we observe an oscillation period corresponding to two flux quanta inside the interference loop, ΔΦ=2Φ0, at which the interference does not carry signatures of non-Abelian statistics. The absence of the expected periodicity of ΔΦ=4Φ0 may indicate that the interfering quasiparticles carry the charge e∗=12e or that interference of e∗=14e quasiparticles is thermally smeared. Interestingly, at two hole-conjugate states, we also observe oscillation periods of half the expected value, indicating interference of e∗=23e quasiparticles instead of e∗=13e. To probe statistical phase contributions, we operated the FPI with controlled deviations of the filling factor, thereby introducing fractional quasiparticles inside the interference loop. The resulting changes to the interference patterns at both half-filled states indicate that the additional bulk quasiparticles carry the fundamental charge e∗=14e, as expected for non-Abelian anyons.