Exploring the daughter states of the 1/2 fractional quantum Hall state in GaAs two-dimensional hole systems

The nature of the fractional quantum Hall state (FQHS) in the lowest (N = 0) Landau level of two-dimensional electron systems confined to wide GaAs quantum wells has been debated since its discovery [1]. Recently, the observation of daughter states of the 1/2 FQHS (at ν=7/13 and 8/17) has provided evidence that the 1/2 FQHS in wide quantum wells with appropriate parameters is likely a Pfaffian state with non-Abelian statistics [2]. Here, we examine the origin of the 1/2 FQHS in 2D hole systems (2DHSs) in wide GaAs quantum wells. In 2DHSs, the strong spin-orbit coupling complicates the Landau level (LL) energy structure, giving rise to another type of 1/2 FQHS stemming from a LL crossing [3]. In our ultrahigh-quality 2DHSs [4], we observe a strong 1/2 FQHS at a LL crossing induced by an in-plane magnetic field. At ν=7/13, the R_xx minimum is deeper than those at the neighboring Jain-sequence fillings and is accompanied by a developing plateau in R_xy. This suggests the observation of the daughter state of a 1/2 FQHS which is stabilized by a LL crossing.



[1] Suen et al., Correlated states of an electron system in a wide quantum well, PRL. 69, 3551 (1992)

[2] Singh et al., Topological phase transition between Jain states and daughter states of the n = 1/2 fractional quantum Hall state, Nat. Phys. 20, 1247 (2024)

[3] Liu et al., Even-denominator fractional quantum Hall effect at a Landau level crossing, PRB 89, 165313 (2014)

[4] Gupta et al., Ultraclean two-dimensional hole systems with mobilities exceeding 10⁷ cm²/Vs, PRM 8, 014004 (2024)