Topological phase transition between Jain states and daughter states of the ν = 1/2 fractional quantum Hall state

The even-denominator fractional quantum Hall state at a filling factor of ν = 1/2 is an intriguing many-body phase 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 tunnelling between the layers. Whether this state takes an Abelian two-component form or a non-Abelian one-component form has been debated since its experimental discovery. Here we report the observation of the ν = 1/2 state that is flanked by numerous Jain-sequence composite fermion states at ν = p/(2p ± 1) up to ν = 8/17 and 9/17. As we raise the density, the ν = 1/2 state is strengthened, its energy gap increases up to 4 K and, at the same time, the 8/17 and 7/13 states abruptly become stronger than their neighbouring high-order fractions. The states at ν = 8/17 and 7/13 are the theoretically predicted, simplest daughter states of the one-component Pfaffian ν = 1/2 state. This means that our data suggest a topological phase transition of 8/17 and 7/13 states from the Jain-sequence states to the daughter states of the Pfaffian.