Proliferation of neutral modes in fractional quantum Hall states

Inoue, Hiroyuki; Grivnin, Anna; Ronen, Yuval; Heiblum, Moty; Umansky, V.; Mahalu, D.

doi:10.1038/ncomms5067

Cited by 102 publications

(117 citation statements)

References 40 publications

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“…The propagation length diverges at T → 0 for topologically protected modes [32,33]. The observed propagation length of the neutral mode at ν = 5/2 is comparable with the propagation lengths at ν = 2/3 and 3/5 and much longer [34] than at ν = 1/3 and 2/5 in similar samples. Thus, the 5/2 upstream mode is topologically protected.…”

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confidence: 78%

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

2016

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Numerical results suggest that the quantum Hall effect at ν = 5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the particle-hole symmetry at ν = 5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.One of the most interesting features of topological insulators and superconductors is their surface behavior. A great variety of gapless and topologically-ordered gapped surface states have been proposed [1]. Such states are anomalous, that is, they can only exist on the surface of a 3D bulk system and not in a stand-alone film. Finding experimental realizations of exotic surface states proved difficult and most of them have remained theoretical proposals. Thus, it came as a surprise when Son [2] argued that one such exotic state [3], made of Dirac composite fermions with the particle-hole symmetry (PHS), has long been observed experimentally in a two-dimensional system: the electron gas in the quantum Hall effect (QHE) with the filling factor ν = 1/2.At first sight, Son's idea violates the fermion doubling theorem [4]. However, the theorem does not apply to interacting systems such as the one Son considered. Besides, in contrast to the conditions of the doubling theorem, the action of PHS is nonlocal in QHE since it involves filling a Landau level. Interestingly, the picture of composite Dirac fermions sheds light on the geometrical resonance experiments [5] which the classic theory [6] of the 1/2 state could not explain. In this paper we show that a closely related idea [2] provides a natural explanation of the observed phenomenology on the enigmatic QHE plateau at ν = 5/2 in GaAs.Cooper pairing of Dirac composite fermions in the s channel results in a fractional QHE state dubbed PHPfaffian [2,7], where "PH" stands for "particle-hole". We argue that the PH-Pfaffian topological order is present on the QHE plateau at ν = 5/2. This might seem unlikely because the particle-hole symmetry is violated by the Landau level mixing (LLM) in the observed states of the second Landau level in GaAs. Besides, numerics [11][12][13][14][15][16] supports the Pfaffian [8] and anti-Pfaffian [9,10] states at ν = 5/2 even in the presence of PHS. At the same time, the existing numerical work, which always neglects strong disorder and typically neglects strong LLM, is not yet in the position to explain the physics of the 5/2 state, as is evidenced by a large discrepancy between numerical and experimental energy gaps [17]. Note that a recent attempt to incorporate LLM [16] into simulations led to the manifestly wrong conclusion that the 5/2 state does not exist at realistic LLM. Indeed, as discussed in Ref. [16], the existing perturbative methods are justifi...

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confidence: 78%

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

2016

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“…Overall, none of the above-mentioned models seems to fit in the constraints set by the experiments, assuming the effect of edge reconstruction is less important. Edge reconstruction is likely in a pure ν = 5/2 liquid, 21,22 but is expected to be suppressed in real samples with disorder, as is evidenced by the recent experiment 23 showing relatively weak signals associated with edge reconstruction and that such signals disappear at long distances 20 .…”

Section: Introductionmentioning

confidence: 89%

Probing theν=52quantum Hall state with electronic Mach-Zehnder interferometry

Yang

2015

Phys. Rev. B

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It was recently pointed out that Halperin's 113 topological order explains the transport experiments in the quantum Hall liquid at filling factor ν = 5/2. The 113 order, however, cannot be easily distinguished from other likely topological orders at ν = 5/2 such as the non-Abelian Pfaffian and anti-Pfaffian states and the Abelian Halperin 331 state in Fabry-Perot interferometry. In this paper, we show that an electronic Mach-Zehnder interferometer provides a clear identification of these candidate ν = 5/2 states. Specifically, the I-V curve for the tunneling current through the interferometer is more asymmetric in the 113 state than in other ν = 5/2 states. Moreover, the Fano factor for the shot noise in the interferometer can reach 13.6 in the 113 state, much greater than the maximum Fano factors 3.2 in the Pfaffian and anti-Pfaffian states and 2.3 in the 331 state.

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“…In that model, depicted in Fig. 1a III, the inner three edge channels were expected to renormalize to a single downstream charge mode with conductance 1 On the experimental front, recent observations of upstream neutral modes [6,7,14,15,16] supported the KFP model of the = 2 3 state [5]. However, Bid et al [17], while studying partitioning of the downstream charge channel for = 2 3 in a quantum point contact (QPC), ) with strong noise.…”

Section: Introductionmentioning

confidence: 99%