We report on our measurements of resistance fluctuations as a function of magnetic field B in an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs heterostructure of etched width w=2.5 μm in the integral- and fractional-quantum-Hall-effect regimes. High-frequency fluctuations are observed near the longitudinal resistance (${\mathit{R}}_{\mathit{x}\mathit{x}}$) minima for ν=1, 2, 3, 4, and 1/3. The quasiperiods ΔB(ν = integer) of the fluctuations for integer ν are all ∼0.016 T, while for ν=1/3, the quasiperiod ΔB(ν = 1/3) is ∼0.05 T, or a factor of 3 larger. The fluctuations at integer ν are consistent with inter-edge-state tunneling via magnetically bound states encircling a potential hill of a diameter roughly equal to the conducting width of the channel. A similar model, with the difference that the tunneling is by quasiparticles of fractional charge ${\mathit{e}}^{\mathrm{*}}$=e/q, predicts a scaling of the quasiperiod as ΔB(ν=1/q)=q ΔB(ν = integer).

Interpreted in terms of this model, the data provide direct evidence of the existence of quasiparticles of charge ${\mathit{e}}^{\mathrm{*}}$=e/3 in the ν=1/3 fractional quantum Hall effect. For both ν=1/3 and ν= integer, the individual fluctuation patterns for different pairs of voltage probes are strongly correlated only if the pairs share a length of the channel, indicating that the source of the fluctuations is local, as predicted by the model. A Coulomb blockade as the origin of the fluctuations is ruled out by the fact that for ν=1 and 2 the fluctuation amplitudes saturate at temperatures ${\mathit{T}}_{\mathit{c}}$(ν=1)≃66 mK and ${\mathit{T}}_{\mathit{c}}$(ν=2)≃121 mK, and also saturate at currents ${\mathit{I}}_{\mathit{c}}$(ν=1)≃0.5 nA and ${\mathit{I}}_{\mathit{c}}$(ν=2)≃1.7–3.0 nA. These results indicate that for integer ν, the bound-state-energy spacing Δɛ(ν) scales as ν or ${\mathit{B}}^{\mathrm{-}1}$, inconsistent with a Coulomb blockade.

• Received 22 April 1991

DOI:https://doi.org/10.1103/PhysRevB.44.12933