Second generation of composite fermions in the Hamiltonian theory

In the framework of a recently developed model of interacting composite fermions restricted to a single level, we calculate the activation gaps of a second generation of spin-polarized composite fermions. These composite particles each consist of a composite fermion of the first generation and a vortexlike excitation and may be responsible for the recently observed fractional quantum Hall states at unusual filling factors such as ν=4/11, 5/13, 5/17, and 6/17. Because the gaps of composite fermions of the second generation are found to be more than one order of magnitude smaller than those of the first generation, these states are less visible than the usual states observed at filling factors ν=p/(2ps+1). Their stability is discussed in the context of a pseudopotential expansion of the composite-fermion interaction potential.