Conductance plateaus and shot noise in fractional quantum Hall point contacts

Spånslätt, Christian; Park, Jin‐Hong; Gefen, Yuval; Mirlin, A. D.

doi:10.1103/physrevb.101.075308

Cited by 26 publications

(11 citation statements)

References 64 publications

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“…[21] for the ν = 1 phase. A biased neutral mode may also lead to generation of shot noise, despite the absence of a net charge current, due to the formation of quasiparticle-quasihole pairs [59][60][61]. Such observations were reported in Refs.…”

Section: B Emergent Non-topological Neutral Modesmentioning

confidence: 54%

Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases

Khanna,

Goldstein,

Gefen

2022

Preprint

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This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the ν = 2/5 phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream, and may support either charge or charge-neutral excitations. From topological considerations, particle-like QH states are expected to support only downstream charge modes. However the interplay between the electronic repulsion and the boundary confining potential may drive certain quantum phase transitions (called reconstructions) at the edge, which are associated to the nucleation of additional pairs of counter-propagating modes. Employing variational methods, here we study edge reconstruction in the prototypical particle-like phases at ν = 1, 1/3 and 2/5 as a function of the slope of the confining potential. Our analysis shows that subsequent renormalization of the edge modes, driven by disorder-induced tunnelling and intermode interactions, may lead to the emergence of upstream neutral modes. These predictions may be tested in suitably designed transport experiments. Our results are also consistent with previous observations of upstream neutral modes in these QH phases, and could explain the absence of anyonic interference in electronic Mach-Zehnder setups.Mark Azbel was a physicist in his heart and soul. Beside his major contributions to the quantum theory of electrons in metals, he left his footprints everywhere through talks, arguments and discussions on a broad spectrum of issues (including non-physics themes). He would take an issue that appears all but benign, and expose the intricacy, deep significance, and a scale of insight needed to really penetrate the problem at hand. Among his many notable works was the prediction of the anomalous skin effect in metals [1,2]. It is only natural to devote our manuscript in this commemorative volume to a study of another "skin" effect related to the boundary of a twodimensional electron gas in the presence of a strong perpendicular magnetic field. This concerns the gapless chiral edge modes which emerge at the boundary of quantum Hall phases.

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Section: B Emergent Non-topological Neutral Modesmentioning

confidence: 54%

Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases

Khanna,

Goldstein,

Gefen

2022

Preprint

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“…The charge is read off as q = 1 from Eq. (37). In other words, the operator ψ e describes a non-interacting, chiral fermion.…”

Section: B Examples Of the Relation Between Statistics And Scaling Di...mentioning

confidence: 99%

“…Then, application of Eqs. (37), (38), and (43) shows that the corresponding particle charges are q R = (K + 1)/2 − (K − 1)/2 = 1 (B30) q L = (K − 1)/2 − (K + 1)/2 = −1, (B31)…”

Section: Energy-dependent Transmission Probabilitymentioning

confidence: 99%

“…In recent decades, partition noise has successfully been used as a sensitive tool [2] to probe collective properties in systems of strongly correlated electrons. Examples include shot-noise measurements of fractional charges and nontrivial scaling dimensions in the fractional quantum Hall (FQH) [3][4][5][6][7][8][9][10] and Kondo [11][12][13][14][15][16][17][18] effects, observation of anyonic statistics via noise correlations [19][20][21][22][23][24][25][26][27][28][29][30][31], and detecting neutral modes in complex FQH states [32][33][34][35][36][37][38][39][40].…”

Section: Introduction a Background And Motivationmentioning

confidence: 99%

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Does delta-$T$ noise probe quantum statistics?

Z¹,

Gornyi²,

Spånslätt³

2022

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We study delta-T noise-excess charge noise at zero voltage but finite temperature bias-for weak tunneling in one-dimensional interacting systems. We show that the sign of the delta-T noise is generically determined by the nature of the dominating tunneling process. More specifically, the sign is governed by the leading charge-tunneling operator's scaling dimension. We clarify the relation between the sign of delta-T noise and the quantum exchange statistics of tunneling quasiparticles. We find that, for infinite systems hosting chiral channels with local interactions (e.g., quantum Hall or quantum spin Hall edges), when the delta-T noise is negative, the tunneling particles are boson-like, revealing their tendency towards bunching. However, the opposite is not true: Bosonlike particles do not necessarily produce negative delta-T noise. Importantly, the bosonic nature of particles generating the negative delta-T is not necessarily intrinsic, but can be induced by the interactions. This, in particular, implies that negative delta-T noise for tunneling between the edge states cannot serve as a smoking gun for detecting "intrinsic anyons". We also establish a connection between the delta-T noise and the temperature derivative of the Nyquist-Johnson (thermal) noise in interacting systems, both governed by the same scaling dimensions. As a demonstration of the above statements, we study tunneling between two interacting quantum spin Hall edges. With bosonization and renormalization-group techniques, we find that many-body interactions can generate negative delta-T noise for both direct tunneling through a point contact and in Kondo exchange tunneling via a localized spin. In both these setups, we show that the noise can become negative at sufficiently low temperatures, when interactions renormalize the tunneling to favor boson-like pair-tunneling of electrons rather than single-electron tunneling. Our findings show that delta-T noise can be used to probe the nature of collective excitations in interacting one-dimensional systems.

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“…[12,17]. Although there is no average charge flow in the upstream direction, the production the neutral modes lead to generation of shot noise [18,[60][61][62][63]. Additionally, neutral modes may suppress the visibility of anyonic interference in electronic Mach-Zehnder setups [21].…”

mentioning

confidence: 99%

Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases

Khanna¹,

Goldstein²,

Gefen³

2021

Preprint

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Chiral gapless boundary modes are characteristic of quantum Hall (QH) states. For hole-conjugate fractional QH phases counter-propagating edge modes (upstream and downstream) are expected. In the presence of electrostatic interactions and disorder these modes may renormalize into charge and upstream neutral modes. Orthodox models of Laughlin phases anticipate only a downstream charge mode. Here we show that in the latter case, in the presence of a smooth confining potential, edge reconstruction leads to the emergence of pairs of counter-propagating modes, which, by way of mode renormalization, may give rise to non-topological upstream neutral modes, possessing nontrivial statistics. This may explain the experimental observation of ubiquitous neutral modes, and the overwhelming suppression of anyonic interference in Mach-Zehnder interferometry platforms. We also point out other signatures of such edge reconstruction.

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Conductance plateaus and shot noise in fractional quantum Hall point contacts

Cited by 26 publications

References 64 publications

Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases

Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases

Does delta-$T$ noise probe quantum statistics?

Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases

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