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Register a new userDirect observation of anyonic braiding statistics at the $ u$=1/3 fractional quantum Hall state
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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.
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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.
Resonant inelastic light scattering experiments at $ u=1/3$ reveal a novel splitting of the long wavelength modes in the low energy spectrum of quasiparticle excitations in the charge degree of freedom. We find a single peak at small wavevectors that splits into two distinct modes at larger wavevectors. The evidence of well-defined dispersive behavior at small wavevectors indicates a coherence of the quantum fluid in the micron length scale. We evaluate interpretations of long wavelength modes of the electron liquid.
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.
Strong resonant enhancements of inelastic light scattering from the long wavelength inter-Landau level magnetoplasmon and the intra-Landau level spin wave excitations are seen for the fractional quantum Hall state at $ u = 1/3$. The energies of the sharp peaks (FWHM $lesssim 0.2meV$) in the profiles of resonant enhancement of inelastic light scattering intensities coincide with the energies of photoluminescence bands assigned to negatively charged exciton recombination. To interpret the observed enhancement profiles, we propose three-step light scattering mechanisms in which the intermediate resonant transitions are to states with charged excitonic excitations.
New low-lying excitations are observed by inelastic light scattering at filling factors $ u=p/(phi p pm 1)$ of the fractional quantum Hall regime with $phi=4$. Coexisting with these modes throughout the range $ u leq 1/3$ are $phi=2$ excitations seen at 1/3. Both $phi=2$ and $phi=4$ excitations have distinct behaviors with temperature and filling factor. The abrupt first appearance of the new modes in the low energy excitation spectrum at $ u lesssim 1/3$ suggests a marked change in the quantum ground state on crossing the $phi=2 to phi=4$ boundary at $ u = 1/3$.
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