Abstract
Most states of the fractional quantum Hall effect may be interpreted in terms of an integral quantum Hall effect of weakly-interacting quasiparticles (composite fermions). The recently discovered 4 11 state does not belong to these states because its formation is due to the residual interactions between composite fermions, which become relevant when the composite-fermion levels are only partially filled. We have derived a model of interacting composite fermions, which reveals the self-similarity of the fractional quantum Hall effect and which allows for a systematic study of higher generations of composite fermions. Here, we derive the form of the interaction potential between these hierarchical composite fermions and provide some stability criteria for such states.
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