Contacts, equilibration, and interactions in fractional quantum Hall edge transport

Spånslätt, Christian; Gefen, Yuval; Gornyi, I. V.; Polyakov, D. G.

doi:10.1103/physrevb.104.115416

Cited by 22 publications

(7 citation statements)

References 97 publications

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“…As a final remark, we note that in LL systems with attached electrical contacts, it is known that the mismatch in interactions between the system and the contacts induces backscattering of the eigenmodes (see, e.g., Refs. [96] and [122] for the case of complex FQH edges). This is not an issue for fully chiral single channels such as those on Laughlin FQH edges.…”

Section: Discussionmentioning

confidence: 99%

Does delta-$T$ noise probe quantum statistics?

Z¹,

Gornyi²,

Spånslätt³

2022

Preprint

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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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Section: Discussionmentioning

confidence: 99%

Does delta-$T$ noise probe quantum statistics?

Z¹,

Gornyi²,

Spånslätt³

2022

Preprint

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show abstract

“…Indeed, the transport properties (e.g., conductance) of the Luttinger liquid depend crucially on the nature of its interface with external leads (see, e.g., [78,79]). Quantum Hall edges may also experience such non-universal effects [80][81][82], implying the need to employ other methods for probing the noise generated at a QPC, e.g., that of Ref. [83].…”

Section: Discussionmentioning

confidence: 99%

Extracting the scaling dimension of quantum Hall quasiparticles from current correlations

Schiller,

Oreg,

Snizhko

2021

Preprint

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Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge Q and scaling dimension ∆. For the simplest states (such as the Laughlin series) the scaling dimension determines the quasiparticle's anyonic statistics (the statistical phase θ = 2π∆). For more complicated states (featuring counterpropagating modes or non-Abelian statistics) knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases knowing the scaling dimension facilitates distinguishing different candidate theories for describing the quantum Hall state at a particular filling (such as PH-Pfaffian and anti-Pfaffian at ν = 5/2). Here we propose a scheme for extracting the scaling dimension of quantum Hall quasiparticles from thermal tunneling noise produced at a quantum point contact. Our scheme features the level of robustness and simplicity comparable to extracting the quasiparticle charge from tunneling shot noise.

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“…In a two-terminal setup, in the absence of edge equilibration, the chiral channels exiting the source contact are biased with respect to the modes entering it. The presence of impurities and potential disorder generates random tunneling between the chiral modes at the edge, which may facilitate intermode equilibration over a characteristic length eq [56,57]. Therefore, we may expect that g 2-ter varies as a function of L over the equilibration length scale eq .…”

Section: A Two-terminal Conductancementioning

confidence: 99%

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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Contacts, equilibration, and interactions in fractional quantum Hall edge transport

Cited by 22 publications

References 97 publications

Does delta-$T$ noise probe quantum statistics?

Does delta-$T$ noise probe quantum statistics?

Extracting the scaling dimension of quantum Hall quasiparticles from current correlations

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

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