David F. Mross

Even-denominator fractional quantum Hall states are promising candidates for fault-tolerant quantum computing due to their underlying non-Abelian topological order. However, the topological order of these states remains hotly debated. Here, we report transport measurements on ultra-clean bilayer graphene heterostructures, where we observed four quarter-filled states and their corresponding Levin-Halperin daughter states, constraining their topological order. Moreover, we complete the sequence of half-filled plateaus by detecting states at ν=−32 and ν=12 whose daughters suggest an alternating sequence of non-Abelian orders. This pattern suggests a universal origin supporting their use in identifying topological order at even-denominator fillings, though further confirmation is needed via direct measurements. The observed quarter- and half-filled states appear in N = 0 and N = 1 Landau levels, respectively, and thus highlight a competition between interactions favoring paired states of either four- or two-flux composite fermions. Additionally, we observe several next-generation quantum Hall states that require strong interactions between composite fermions.

The observed fractional quantum Hall (FQH) plateaus follow a recurring hierarchical structure that allows an understanding of complex states based on simpler ones. Condensing the elementary quasiparticles of an Abelian FQH state results in a new Abelian phase at a different filling factor, and this process can be iterated ad infinitum. We show that condensing clusters of the same quasiparticles into an Abelian state can instead realize non-Abelian FQH states. In particular, condensing quasiparticle pairs in the ν=23 Laughlin state yields the anti-Pfaffian phase at half filling. We moreover show that the successive condensation of Laughlin quasiparticles produces quantum Hall states whose fillings coincide with the most prominent plateaus in the first excited Landau level of GaAs. More generally, such condensation can realize any non-Abelian FQH state that admits a parton representation. This surprising result is supported by an exact analysis of explicit wave functions, field theory arguments, conformal-field theory constructions of trial states, and numerical simulations.

Fractional quantum statistics are the defining characteristic of anyons. Measuring the phase generated by an exchange of anyons is challenging, as standard interferometry set-upssuch as the FabryPérot interferometersuffer from charging effects that obscure the interference signal. Here we present the observation of anyonic interference and exchange phases in an optical-like MachZehnder interferometer based on co-propagating interface modes. By avoiding backscattering and deleterious charging effects, this set-up enables pristine and robust AharonovBohm interference without any phase slips. At various fractional filling factors, the observed flux periodicities agree with the fundamental fractionally charged excitations that correspond to Jain states and depend only on the bulk topological order. To probe the anyonic statistics, we used a small, charged top gate in the interferometer bulk to induce localized quasiparticles without modifying the AharonovBohm phase. The added quasiparticles introduce periodic phase slips. The sign and magnitude of the observed phase slips align with the expected value at filling 1/3, but their direction shows systematic deviations at fillings 2/5 and 3/7. Control over added individual quasiparticles in this design is essential for measuring the coveted non-abelian statistics in the future.