David F. Mross

Position exchange of non-Abelian anyons affects the quantum state of their system in a topologically protected way1. Their expected manifestations in even-denominator fractional quantum Hall (FQH) systems offer the opportunity to directly study their unique statistical properties in interference experiments2. Here we present the observation of coherent AharonovBohm interference at two even-denominator states in high-mobility bilayer-graphene-based van der Waals (vdW) heterostructures by using the FabryPérot interferometry 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 $${e}^{* }=\frac{1}{2}e$$or that interference of $${e}^{* }=\frac{1}{4}e$$quasiparticles is thermally smeared. Notably, at two hole-conjugate states, we also observe oscillation periods of half the expected value, indicating interference of $${e}^{* }=\frac{2}{3}e$$quasiparticles instead of $${e}^{* }=\frac{1}{3}e$$. To investigate statistical phase contributions, we operated the FabryPérot interferometer (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 extra bulk quasiparticles carry the fundamental charge $${e}^{* }=\frac{1}{4}e$$, as expected for non-Abelian anyons.

The effective interaction between composite fermions, set entirely by the Coulomb potential and the underlying electronic Landau level orbitals, can stabilize exotic fractional quantum Hall states. In particular, half-filled Landau levels with different orbital character can host either metallic or paired phases of composite fermions. Here, we leverage experimental control over the orbital composition to realize a composite-fermion pairing transition in the first excited Landau level of bilayer graphene. Transport measurements at filling factors v = 9/2 and 11/2 reveal conductive states giving way to well-developed plateaus with increasing displacement fields. These states are insensitive to an in-plane magnetic field, indicating single-component ground states and thus pointing at non-Abelian orders. Our numerical study, based on displacement-field-dependent Landau-level wavefunctions, supports the orbital origin of the pairing transition and suggests Moore-Read or anti-Pfaffian ground states.

Chiral spin liquids (CSLs) are exotic phases of interacting spins in two dimensions, characterized by long-range entanglement and fractional excitations. We construct a local Hamiltonian on the triangular lattice that stabilizes the Kalmeyer-Laughlin CSL without requiring fine-tuning. Our approach employs coupled-wire constructions and introduces a lattice duality to construct a solvable chiral sliding Luttinger liquid, which is driven toward the CSL phase by generic perturbations. By combining symmetry analysis and bosonization, we make sharp predictions for the ground states on quasi-one-dimensional cylinders and tori, which exhibit a fourfold periodicity in the circumference. Extensive tensor network simulations demonstrating ground-state degeneracies, fractional quasiparticles, nonvanishing long-range order parameters, and entanglement signatures confirm the emergence of the CSL in the lattice Hamiltonian.