Quantum Well Width Dependence of the Fractional Quantum Hall Energy Gaps

The fractional quantum Hall effect (FQHE) stems from the strong short-range Coulomb interaction in a two-dimensional (2D) electron system at high magnetic fields. However, the Coulomb interaction is softened in realistic samples which contain quasi-2D systems with a finite (non-zero) electron layer thickness. This softening leads to a weakening of the FQHE states, as manifested in a lowering of their energy gaps in both experiments [1] and calculations [2,3]. Here we present measurements of the energy gaps, from the temperature dependence of the magnetoresistance minima, of several fractional states in the lowest Landau level as a function of the width of the confining square quantum well. Our samples have a fixed density (n ≈ 1x10¹¹ cm^-2) while the width of the confining GaAs well varies between 20 and 80 nm. This is in contrast to measurements reported in [1] where the electrons were confined to parabolic Al_xGa_1-xAs quantum wells. The gaps in our measurements change in magnitude when plotted versus the GaAs well width. We contrast our results with numerical calculations that include the role of finite layer thickness [2,3].

[1] M. Shayegan et al., PRL 65, 2916 (1990).
[2] S. He et al., PRB 42, 11376 (1990).
[3] K. Park et al., J. Phys.: Condens. Matter 11, 7283 (1999).