Resistance fluctuations in the integral- and fractional-quantum-Hall-effect regimes

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).