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Register a new userImpact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers
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Quantum Hall interferometers have been used to probe fractional charge, and more recently, fractional statistics of quasiparticles. Theoretical predictions have been made regarding the effect of electrostatic coupling on interferometer behavior and observation of anyonic phases. Here we present measurements of a small Fabry-Perot interferometer in which these electrostatic coupling constants can be determined experimentally, facilitating quantitative comparison with theory. At the $ u = 1/3$ fractional quantum Hall state, this device exhibits Aharonov-Bohm interference near the center of the conductance plateau interrupted by a few discrete phase jumps, and $Phi_0$ oscillations at higher and lower magnetic fields, consistent with theoretical predictions for detection of anyonic statistics. We estimate the electrostatic parameters $K_I$ and $K_{IL}$ by two methods: by the ratio of oscillation periods in compressible versus incompressible regions, and from finite-bias conductance measurements, and these two methods yield consistent results. We find that the extracted $K_I$ and $K_{IL}$ can account for the deviation of the values of the discrete phase jumps from the theoretically predicted anyonic phase $theta _a = 2pi /3$. In the integer quantum Hall regime, we find that the experimental values of $K_I$ and $K_{IL}$ can account for the the observed Aharonov-Bohm and Coulomb dominated behavior of different edge states.
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Utilizing an electronic Fabry-Perot interferometer in which Coulomb charging effects are suppressed, we report experimental observation of anyonic braiding statistics for the $ u=1/3$ fractional quantum Hall state. Strong Aharonov-Bohm interference of the $ u=1/3$ edge mode is punctuated by discrete phase slips consistent with an anyonic phase of $theta_{anyon}=frac{2pi}{3}$. Our results are consistent with a recent theory of a Fabry-Perot interferometer operated in a regime in which device charging energy is small compared to the energy of formation of charged quasiparticles. Close correspondence between device operation and theoretical predictions substantiates our claim of observation of anyonic braiding.
We study theoretically resonant tunneling of composite fermions through their quasi-bound states around a fractional quantum Hall island, and find a rich set of possible transitions of the island state as a function of the magnetic field or the backgate voltage. These considerations have possible relevance to a recent experimental study, and bring out many subtleties involved in deducing fractional braiding statistics.
Recent schemes for experimentally probing non-abelian statistics in the quantum Hall effect are based on geometries where current-carrying quasiparticles flow along edges that encircle bulk quasiparticles, which are localized. Here we consider one such scheme, the Fabry-Perot interferometer, and analyze how its interference patterns are affected by a coupling that allows tunneling of neutral Majorana fermions between the bulk and edge. While at weak coupling this tunneling degrades the interference signal, we find that at strong coupling, the bulk quasiparticle becomes essentially absorbed by the edge and the intereference signal is fully restored.
We point out some major technical and conceptual mistakes which invalidate the conclusion drawn in Anyonic braiding in optical lattices by C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma published in PNAS 104, 18415 (2007).
Many intriguing phenomena occur for electrons under strong magnetic fields. Recently, it was proposed that an appropriate strain texture in graphene can induce a synthetic gauge field, in which the electrons behave like in a real magnetic field. This opened the door to control quantum transport by mechanical means and to explore unprecedented physics in high-field regime. Such studies have been achieved in molecular and photonic lattices. Here we report the first experimental realization of giant uniform pseudomagnetic field in acoustics by introducing a simple uniaxial deformation to acoustic graphene. Benefited from the controllability of our macroscopic platform, we observe the acoustic Landau levels in frequency-resolved spectroscopy and their spatial localization in pressure-field distributions. We further visualize the quantum-Hall-like edge states (connected to the zeroth Landau level), which have been elusive before owing to the challenge in creating large-area uniform pseudomagnetic fields. These results, highly consistent with our full-wave simulations, establish a complete framework for artificial structures under constant pseudomagnetic fields. Our findings, conceptually novel in acoustics, may offer new opportunities to manipulate sound.
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