A most interesting feature of certain fractional quantum Hall states is that their quasiparticles obey non-Abelian fractional statistics. So far, candidate non-Abelian wave functions have been constructed from conformal blocks in cleverly chosen conformal field theories. In this work we present a hierarchy scheme by which we can construct daughter states by condensing non-Abelian quasiparticles (as opposed to quasiholes) in a parent state, and show that the daughters have a non-Abelian statistics that differs from the parent. In particular, we discuss the daughter of the bosonic, spin-polarized Moore-Read state at nu=4/3 as an explicit example.
The even-denominator fractional quantum Hall (FQH) states, understood as topological superconductors of composite fermions, are predicted to support elementary quasiparticles (QPs) or quasiholes (QHs) obeying non-Abelian braid statistics. Using the microscopic framework of parton theory, we investigate many experimentally observed paired composite-fermion states and find that their elementary QPs and QHs in general bind to form Abelian molecules, thus obscuring non-Abelian braid statistics. An exception is the
ν=1/2 state in wide quantum wells, where our calculations show free QPs or QHs; we thus identify this state as an especially promising candidate for realizing and studying non-Abelian braid statistics. We also indicate how the study of such bound states can help reveal the topological structure of the state.