Composite fermion picture for the second generation of fractional quantum Hall liquids

A flux attachment transformation is derived for correlated composite fermions in their partially filled second Landau level. The transformation generates a hierarchy of “second generation” incompressible quantum liquids at electron filling factors 1/3<νe<2/5. The hierarchy stems from a zero‐energy ground state of an appropriate model pseudopotential and it includes the entire family of quantum Hall states observed in experiment.