Affiliation
Princeton University
Title
Even-denominator fractional quantum Hall states in ultra-high-mobility GaAs two-dimensional hole systems
Abstract
The discovery of the fractional quantum Hall state (FQHS) in 1982 opened a new era of research in many-body condensed matter physics. Among the numerous FQHSs, those observed at even-denominator Landau level filling factors, e.g. at ν = 5/2 when an excited electron Landau level is half filled, are of particular interest as they may host quasiparticles obeying non-Abelian statistics. The dominant candidate for the ν = 5/2 FQHS is a BCS-type, p-wave paired state of flux-particle composite fermions (CFs), described by the Moore-Read Pfaffian wave function. The even-denominator FQHSs, however, are very rare and fragile, and have been observed predominantly in high-quality two-dimensional electron systems when an N = 1 electron Landau level is half filled.
In our recent studies, we observe numerous, even-denominator FQHSs at ν = 3/4, 3/8, and 3/10, evinced by deep minima in longitudinal resistance and developing quantized Hall plateaux, in the lowest Landau level of ultrahigh-mobility GaAs two-dimensional hole systems (2DHSs) [1, 2]. We interpret these states as even-denominator FQHSs of CFs, arising from pairing of CFs when a CF Landau level, rather than a hole Landau level, is half-filled. We also observe another even-denominator FQHS at a lower filling factor ν = 1/4. Specifically, we observe a distinct minimum in longitudinal resistance at ν = 1/4, superimposed on a highly insulating background, indicating a close competition between the ν = 1/4 FQHS and the magnetic-field-induced Wigner solid states. The observation of a FQHS at ν = 1/4 is consistent with the very recent theoretical calculations which suggest that substantial Landau level mixing can induce CF pairing and lead to a non-Abelian FQHS at ν = 1/4 [3]. Our results affirm enhanced interaction between CFs in a system with significant Landau level mixing thanks to the larger effective mass of 2D holes, and further support the pairing of CFs as a valid mechanism for even-denominator FQHSs.
[1] C. Wang et al., Phys. Rev. Lett. 129, 156801 (2022).
[2] C. Wang, A. Gupta, et al., unpublished.
[3] T. Zhao et al., Phys. Rev. Lett. 130, 186302 (2023).