Session E50: Unconventional States and Excitations in the Fractional Quantum Hall Effect

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In the partially filled second Landau level (SLL) emergent exotic quantum fluids overlap and interplay with fractional quantum Hall (FQH) liquids. Collective modes of the exotic quantum fluids uncover underlying physical mechanisms responsible for emerging new ground states [1-3]. Resonant inelastic light scattering (RILS) spectra access unprecedented collective modes in the FQH regime of the SLL: intra-Landau-level plasmons[3]. The plasmons herald rotational-symmetry-breaking (nematic) phases in the SLL and reveal the nature of long-range translational invariance in these phases. The intricate dependence of plasmon features on filling factor provides new insights on complex interplay between topological quantum Hall order and nematic electronic liquid crystal phases. A marked intensity minimum in the plasmon spectrum at Landau level filling factor v = 5/2 strongly suggests that the paired state, which may support non-Abelian excitations, overwhelms competing phases, revealing the robustness of the 5/2 superfluid state for small tilt angles. In contrast, a sharp and intense plasmon peak in the state at v=7/3 reveals that the macroscopic coherence of the FQH liquid coexists with nematic order, supporting the proposed model of a FQH nematic at 7/3. Other interpretations of the new collective mode, such as chiral graviton [4], will be discussed.

[1]. U. Wurstbauer, et al, Phys. Rev. B 92, 241407 (2015).
[2]. A. L. Levy, et al, Phys. Rev. Lett. 116, 016801 (2016).
[3]. L. J. Du, et al, Science Advances 5, eaav3407 (2019).
[4]. S. F. Liou, et al, Phys. Rev. Lett. 123, 146801 (2019).   

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We present our latest experimental results on composite fermions and other interaction-induced phases, such as
Wigner crystal, in very dilute 2D electron and hole systems.
Work done in collaboration with Md. Shafayat Hossain, Meng K. Ma, Kevin A. Villegas Rosales, Yoon Jang
(Edwin) Chung, Pranav Thekke Madathil, Siddharth, Singh, Chengyu Wang, Insun Jo, Hao Deng, Roland
Winkler, Yang Liu, Ken West, Kirk Baldwin, and Loren Pfeiffer.   

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It has long been known (at least since 1997) empirically that
quantum Hall plateau transitions enjoy an apparent self-dualty symmetry. The
emaning of this statement is that the current-voltage (I-V) curves are nonlinear
and are symmetric around their liner behavior at the quantum phase
transition. This behavior was first observed in dirtier samples and is now
know to occur in the compressible sattes at filling fractions 1/2 and 1/4. This
empirical result was interpreted by Shimshoni, Sondhi and Shahar (PRB 55,
13730 (1997)) as a manifestation of a particle-vortex duality.Yet, the origin of
this symmetry has been misterious and has remained unexplained until quite
recently. In a recent paper (Hart Goldman and Eduardo Fradkin, PRB
98, 165137 (2018)) we used the recently developed
dualities of Dirac fermions (D. T. Son Phys. Rev X. 5, 031027 (2015); N.
Seiberg, T. Senthil, C. Wang and E. Witten, Ann. Phys. 374, 3095 (2016)) to
show that the mirror symmetry of the Jain sequences converging on 1/2n
compressible states explain the observed self-duality as a property of the
compressible states. I will also discuss the role of duality in nonabelian fractional quantum Hall states.   

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In the parton construction of the FQHE [1], one divides each electron into fictitious particles called partons, places each species of partons into an IQH state, and then fuses the partons back into physical electrons. This produces candidate FQHE states that are products of IQH states. Some of the states so produced are predicted to have non-Abelian excitations. I will review recent work on the applicability of such wave functions to physically observed states at ν=5/2 [2], ν=2+6/13 [4], and ν=1/4 in wide quantum wells [4], and ν=7/3 [5]. Theory suggests that a non-Abelian "221" state may appear at ν=1/2 in bilayer and trilayer graphene [6].
[1] J. K. Jain, Phys. Rev. B 40, 8079 (1989);
[2] A. C. Balram, S. M. Barkeshli, M.S. Rudner, Phys. Rev. B 98, 035127 (2018); Phys. Rev. B 99, 241108 (2019);
[3] A. C. Balram, S. Mukherjee, K. Park, M. Barkeshli, M. S. Rudner, J.K. Jain, Phys. Rev. Lett. 121, 186601 (2018);
[4] W. Faugno, A. C. Balram, M. Barkeshli, J. K. Jain, Phys. Rev. Lett. 123, 016802 (2019);
[5] A. C. Balram, J.K. Jain, and M. Barkeshli, Phys. Rev. Res. 2, 013349 (2020); William N. Faugno, Tongzhou Zhao, Ajit C. Balram, Thierry Jolicoeur, and Jainendra K. Jain, preprint;
[6] Y. Wu, T. Shi, J.K. Jain, Nano Letters 17, 8643 (2017).   

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Bilayer 2D electron systems at high magnetic field exhibit an interlayer coherent excitonic phase when the layer separation is sufficiently small, the temperature sufficiently low, and the total 2D electron density equals the degeneracy of a single Landau level. This phase displays exotic transport phenomena, notably Josephson-like interlayer tunneling and essentially dissipationless transport of excitons across the bulk of the 2D system. While first detected GaAs-based double quantum wells, this and related interlayer phases have recently been observed in graphene-based multilayer systems.

The nature of the transition between the incoherent phase at large layer separation and the coherent excitonic phase at small separations remains poorly understood. In this talk I will report on recent experiments which shed new light on the transition. In particular, I will discuss tunneling spectroscopy measurements which reveal evidence for interlayer electron-hole correlations at layer separations near, but above, the transition to the exciton condensate at total Landau level filling ν_T=1. These correlations are manifested by a nonlinear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly coupled bilayers and an anomalous dependence of the pseudogap on an added in-plane magnetic field . The pseudogap suppression is strongest at ν_T=1 and grows rapidly as the critical layer separation for exciton condensation is approached from above. These and other observations suggest that electron-hole pairing fluctuations exist in the incoherent phase well above the critical layer separation, in a manner reminiscent of Cooper pair fluctuations above the superconducting critical temperature.