Dependence of the fractional quantum Hall effect energy gap on electron layer thickness

Low-disorder, two-dimensional electron systems (2DESs) at large perpendicular magnetic fields provide an ideal platform for studies of exotic, correlated phenomena such as the fractional quantum Hall effect (FQHE). While the simplest theoretical models assume zero electron layer thickness, 2DESs confined to semiconductor heterostructures have finite layer thickness which results in weakened Coulomb interactions and reduced FQHE energy gaps (Δ) [1]. We systematically address the changes in Δ, for the FQHE at filling factor 1/3, as a function of electron layer thickness by studying 2DESs confined to GaAs quantum wells of varying width, ranging from 20 to 80 nm. All the 2DESs have a density of 1x10¹¹cm^-2. Experimentally, we obtain Δ from fitting the temperature dependence of the longitudinal resistance minimum in an Arrhenius plot. We present a Δ vs. layer thickness plot and contrast it to different theoretical calculations [2,3]. Even allowing for the reduction of the energy gaps by disorder, we find that the experimentally deduced gaps are smaller than the calculated values by over 10%, especially in the limit of very small layer thickness.
[1] M. Shayegan et al., PRL 65, 2916 (1990).
[2] Melik-Alaverdian et al., PRB 52, R17032 (1995).
[3] Morf et al., PRB 66, 075408 (2002).