Boebinger, GS; Stormer, HL; Tsui, DC; Chang, AM; Hwang, JCM; Cho, AY; Tu, CW; Weimann, G, *Activation energies and localization in the fractional quantum Hall effect*,
Physical Review. B, Condensed Matter, vol. 36 no. 15
(1987),
pp. 7919-7929 [doi] .
**Abstract:**

*This paper summarizes an extensive study of the temperature dependence of magnetotransport in the fractional quantum Hall effect in GaAs-AlxGa1-xAs heterostructure devices of varying mobility and density. For devices with electron mobility 400 000 1 000 000 cm2/V s, we find a single activation energy, /23, in the longitudinal transport coefficients, xx and xx, for Landau-level filling factors=(1/3, (2/3, (4/3, and (5/3, with a magnetic field dependence which is vanishingly small for B 5.5 T and increases to 63.8 K at B=30 T. The observed 3 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 0 300 000 cm2/V s yield even smaller 3. 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, 0150 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 =(2/5 and (3/5 also yield a single activation energy, /25, with a weak magnetic field dependence. Experimentally, we find 35 0.4, compared with an expected ratio of 0.28 from simple theoretical considerations. © 1987 The American Physical Society.*