Activation energies and localization in the fractional quantum Hall effect

This paper summarizes an extensive study of the temperature dependence of magnetotransport in the fractional quantum Hall effect in GaAs-Alₓ{Ga}_{1{{-}}x}As heterostructure devices of varying mobility and density. For devices with electron mobility 400 000μ1 000 000{cm}²$/V s, we find a single activation energy, $³/2$, in the longitudinal transport coefficients, ${{σ}}ₓₓ$ and ${{ρ}}ₓₓ, for Landau-level filling factors ν=(1/3, (2/3, (4/3, and (5/3, with a magnetic field dependence which is vanishingly small for B5.5 T and increases to³6$.8 K at B=30 T. The observed $³{{Δ}}$ is smaller by more than a factor of 3 than either the unbound quasiparticle-quasihole pair-creation energy gap or the magneto-roton energy gap, calculated for an ideal two-dimensional electron system. Observations for devices of mobility μ₀{}300 000 cm²/V s yield even smaller ³Δ. Adequate fitting of all our results requires inclusion of finite electron layer thickness and disorder, with the effect of decreasing the energy gaps and providing a finite magnetic field threshold. At low temperatures and high magnetic fields, deviations from activated conduction are observed. These deviations are attributed to two-dimensional hopping conduction in a magnetic field. Samples of sufficiently low mobility, μ₀{}150 000 cm²/V s exhibit no evidence of activated conduction. Rather, the transport is qualitatively consistent with two-dimensional hopping alone. Studies at Landau-level filling factors {ν}=(2/5 and (3/5 also yield a single activation energy, ⁵/2, with a weak magnetic field dependence. Experimentally, we find ⁵³{Δ}{~}0.4, compared with an expected ratio of 0.28 from simple theoretical considerations.