Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state

Abstract

The fractional quantum Hall state (FQHS) observed in the lowest Landau level at filling factor $\nu =1/2$ in wide quantum wells has been enigmatic for decades because the two-dimensional electron system (2DES) has a bilayer charge distribution but with significant interlayer tunneling. Of particular interest is whether the 1/2 FQHS in this system has a one-component (1C) or two-component (2C) origin; these are typically identified as the Pfaffian (non-Abelian) or the ${\Psi }_{331}$ (Abelian) FQHSs, respectively. We report here our experimental study of the evolution of the correlated states of an ultrahigh-quality 2DES confined to a 72.5-nm-wide GaAs quantum well. At the lowest densities, the 2DES displays only odd-denominator FQHSs, and the ground state at $\nu =1/2$ is a composite fermion Fermi sea. As the density is increased, a FQHS emerges at $\nu =1/2$, and becomes very strong. In a finite density range where the 1/2 FQHS is strongest, we also observe its daughter FQHSs at $\nu =8/17$ and 7/13, consistent with the theoretically expected daughter states of a Pfaffian 1/2 FQHS. At the highest densities, the 2DES becomes 2C, signaled by the emergence of a bilayer Wigner crystal state and the transitions of FQHSs flanking $\nu =1/2$. The 1/2 FQHS remains robust near this transition and, notably, its charge transport energy gap exhibits an \textit{upward} cusp with a maximum value of about 6 K on the 1C side of the transition; this is the largest gap reported for any even-denominator FQHS. Our observation of the transition of the 2DES ground states near $\nu =1/2$ to 2C states at high densities, and our measurements of the robustness of the 1/2 FQHS against charge distribution asymmetry, suggest that the 1/2 FQHS also makes a transition from 1C to 2C. Such a transition from a non-Abelian to Abelian state can open avenues for topological quantum information and quantum criticality.

arXiv commentAccepted for publication in Phys. Rev. Lett., 8+13 pages, 3+7 figures

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• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
• Interlayer-correlated fractional quantum Hall state in a trilayer electron system