Non-Abelian to Abelian transition of the 1/2 fractional quantum Hall state

The nature of the 1/2 fractional quantum Hall state (FQHS) observed in wide GaAs quantum wells (QWs) has been a subject of debate because the 2D electron system (2DES) has a bilayer charge distribution with significant interlayer tunneling. We report the evolution of the 1/2 FQHS in a 72.5 nm wide quantum well as a function of density (n, in units of 10¹¹ cm^-2), from 1.0 to 1.59, keeping the charge distribution symmetric. The transport energy gap of the 1/2 FQHS shows an upward cusp with a maximum value of about 6 K at n = 1.37 and monotonically decreases to zero as the density is changed in either direction. We find qualitative agreement with theoretical calculations of the energy gap of the 1/2 FQHS where the upward cusp in the energy gap is identified to stem from a transition between the Pfaffian (non-Abelian) and the Halperin-331 (Abelian) states as n is increased from a small to high value. In a finite density range where the 1/2 FQHS is strongest, we also observe its daughter states at 8/17 and 7/13, consistent with the daughter states of the Pfaffian state. At the highest densities, the 2DES becomes 2-component, signaled by the emergence of the bilayer Wigner crystal and the destruction of odd-numerator FQHSs. The transition of the 1/2 FQHS from the non-Abelian state to the Abelian state is unique to 2DESs in wide GaAs QWs, and potentially opens avenues for experiments in topological quantum computing and quantum criticality.

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