We study systematically the effect of finite thickness of the quasi-two-dimensional layer on the fractional quantum Hall effect using small-system calculations. As the layer thickness increases, there is a crossover from the incompressible Laughlin-type liquid to a compressible state, which has almost vanishing overlap with the Laughlin wave function. We predict that the fractional quantum Hall state will eventually be destroyed with increasing layer thickness as a consequence of the weakening of the short-range component of the interaction. The relevance of our calculation to some recent experiments in thick parabolic wells is discussed.

• Received 2 August 1990

DOI:https://doi.org/10.1103/PhysRevB.42.11376