Theoretical study of the stability of the fractional quantum Hall effect in higher Landau levels

We have studied the fractional quantum Hall effect in higher Landau levels following Jain's composite-fermion theory. Our framework provides numerical calculations for the gaps in a range of electron densities typically used in experiments. As expected, the gaps diminish as the Landau level index increases. Surprisingly, however, they become negative in the third and higher Landau levels, indicating an absence of the fractional quantum Hall effect beyond the second Landau level.