Topological phase transition between composite fermion and Pfaffian daughter states near ν = 1/2 fractional quantum Hall state

The even-denominator fractional quantum Hall state (FQHS) at filling-factor ν = 1/2 is among the most enigmatic many-body phases in two-dimensional electron systems as it appears in the ground-state rather than an excited Landau level. It is observed in wide quantum wells where the electrons have a bilayer charge distribution with finite tunneling. Whether this 1/2 FQHS is two-component (Abelian) or one-component (non-Abelian) has been debated since its experimental discovery over 30 years ago. Here, we report strong 1/2 FQHSs in ultrahigh-quality, wide, GaAs quantum wells, with transport energy gaps up to ≈ 4 K, among the largest gaps reported for any even-denominator FQHS. The 1/2 FQHS is flanked by numerous, Jain-sequence FQHSs at ν = p/(2p±1) up to 8/17 and 9/17. Remarkably, as we raise the density while keeping the charge distribution in the quantum well symmetric, and strengthen the 1/2 FQHS, the 8/17 and 7/13 FQHSs suddenly become strong, much stronger than their neighboring high-order FQHSs. Insofar as FQHSs at ν = 8/17 and 7/13 are precisely the theoretically-predicted, simplest, daughter states of the one-component Pfaffian 1/2 FQHS, our data suggest a topological phase-transition of 8/17 and 7/13 FQHSs from the Jain- states to the daughter states of the Pfaffian, and that the parent 1/2 FQHS we observe is the Pfaffian state.