Our group's research focuses on exotic phases of quantum condensed matter. Microscopically, they are comprised of electrons but exhibit properties that belie these humble ingredients. Their excitations may carry fractional quantum numbers or obey exchange statistics that are neither bosonic nor fermionic. An essential question is how to 'get fractions by combining integers' and what conditions may prompt a microscopic system to do so. We address this challenge by deriving and applying duality relations. The best-known experimental system exhibiting such phenomena is the fractional quantum Hall effect, which is a central part of our work. Additionally, we use insights and techniques developed there to predict new phases of matter in other topological systems and quantum magnets.
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.
Kim J., Dev H., Shaer A., Kumar R., Ilin A., Haug A., Iskoz S., Watanabe K., Taniguchi T., Mross D. F., Stern A. & Ronen Y.
(2024)
arXiv.org.
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.
We introduce a spin ladder with discrete symmetries designed to emulate a two-dimensional spin-1/2 boson system at half-filling. Using global properties, such as the structure of topological defects, we establish a correspondence between the two systems and construct a dictionary of symmetries and operators. In particular, translation invariance leads to Lieb-Schultz-Mattis constraints for both systems, resulting in exotic deconfined quantum critical points. Subsequently, we study the spin ladder in detail. An exact duality transformation maps it onto a Z2 gauge theory of three partons, analogous to the U(1) gauge theory of chargons and spinons in two-dimensional spin-1/2 boson systems. With the mapping between spins and partons, we construct exactly solvable models for all pertinent symmetry-breaking phases and analyze their transitions. We further make connections between our exact analysis and conventional parton gauge theories.
