Fractional edge reconstruction in integer quantum Hall phases

Khanna, Udit; Goldstein, Moshe; Gefen, Yuval

doi:10.1103/physrevb.103.l121302

Cited by 26 publications

(14 citation statements)

References 46 publications

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“…Note that the states with a fractional edge are found to have a lower energy than the states with an integer edge whenever reconstruction is favored. We have verified that our results do not depend on the detailed form of the confining potential [33]. The fractionally reconstructed edge [Fig.…”

Section: Variational Resultssupporting

confidence: 76%

“…For Slater determinants, the energy ( H ) of the variational states may be evaluated trivially given the matrix elements of the Coulomb interaction and the confining potential [33]. On the other hand, for Laughlin states these may be evaluated using standard classical Monte-Carlo techniques [45,[52][53][54][55].…”

Section: B Variational Analysismentioning

confidence: 99%

“…In the early 90s, it was realized that in the presence of a smooth confining potential at the boundary, electronic interactions may induce quantum phase transitions at the edge (which leave the bulk unperturbed). Such edge transitions (or edge reconstructions) may occur in both integer [24][25][26][27][28][29][30][31][32][33] and fractional [34][35][36][37][38][39][40][41][42][43][44][45][46] QH phases, as well as in time-reversal-invariant topological insulators [47,48]. The reconstructed edge structure may differ in terms of the number, order, or even the nature of the edge modes.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we describe our recent attempts [33,45] to theoretically account for the experimental surprises described above, in terms of reconstruction and the subsequent renormalization of the edge for ν = 1 and 1/3 QH phases. Additionally, we present new analysis of edge reconstruction of the ν = 2/5 QH phase.…”

Section: Introductionmentioning

confidence: 99%

“…Figures 1, 2 depict some of the a priori possible configurations of the reconstructed edge at ν = 1, 1/3 and 2/5. Here, we find the lowest energy state among these structures as a function of the slope of the confining potential through a variational analysis [33,34,45], which allows us to include a large number of electrons while accounting for quantum correlations inherently present in QH states. Specifically, we treat the strip-size (N S ) and separation (L S ) as variational parameters.…”

Section: Introductionmentioning

confidence: 99%

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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: Variational Resultssupporting

confidence: 76%

Section: B Variational Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Khanna,

Goldstein,

Gefen

2022

Preprint

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Determination of topological edge quantum numbers of fractional quantum Hall phases by thermal conductance measurements

et al. 2022

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To determine the topological quantum numbers of fractional quantum Hall (FQH) states hosting counter-propagating (CP) downstream (Nd) and upstream (Nu) edge modes, it is pivotal to study quantized transport both in the presence and absence of edge mode equilibration. While reaching the non-equilibrated regime is challenging for charge transport, we target here the thermal Hall conductance GQ, which is purely governed by edge quantum numbers Nd and Nu. Our experimental setup is realized with a hexagonal boron nitride (hBN) encapsulated graphite gated single layer graphene device. For temperatures up to 35 mK, our measured GQ at ν = 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime (Nd + Nu)κ0T, where κ0T is a quanta of GQ. With increasing temperature, GQ decreases and eventually takes the value of the equilibrated regime ∣Nd − Nu∣κ0T. By contrast, at ν = 1/3 and 2/5 (without CP modes), GQ remains robustly quantized at Ndκ0T independent of the temperature. Thus, measuring the quantized values of GQ in two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.

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Shot noise does not always provide the quasiparticle charge

et al. 2022

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The fractional charge of quasiparticles is a fundamental feature of quantum Hall effect (QHE) States. The charge, important in characterizing the state and in interference experiments, has long been measured via shot-noise at moderate temperatures (T>30mK), with the Fano factor F=e * /e revealing the charge e * of the quasiparticles 1-3 . However, at sufficiently low temperatures (T≈10mK), we consistently find F being equal to the bulk filling factor, 𝝂𝝂 𝐛𝐛 4 . Surprisingly, noise with 𝑭𝑭 = 𝝂𝝂 𝐛𝐛 is also observed on intermediate conductance plateaus in the transmission of the quantum point contact (QPC), where shot noise is not expected 5,6 . We attribute the unexpected Fano factor to upstream neutral modes, which proliferate at the lowest spinless Landau level 6,7 . The universality of the Fano factor is also confirmed when the edge modes do not conform to the bulk (breaking bulk-edge correspondence). For this, the ubiquitous edge modes at the periphery of the sample are replaced by artificially constructed 'interface modes', propagating at the interface between two adjoined QHE states: the tested state and a different state. We present a new theoretical paradigm based on an interplay between charge and neutral modes, explaining the origin of the universal Fano factor.13 , which carry current and energy. 'Bulk-Edge' correspondence dictates that both the Hall conductance 𝜎𝜎 xy and the thermal Hall conductance 𝐾𝐾 xy are determined by the topological order of the bulk 14 . The quasiparticle charge, e * , being the most fundamental quantity of a fractional state, is crucial in determining the quasiparticle statistics (in interference experiment) 15 .According to the orthodox paradigm, weak partitioning of edge modes, done in a quantum point contact (QPC) constriction, leads to shot noise with a Fano factor F=e*/e (F=1 for integers) [16][17][18] . Moreover, shot noise (at zero temperature) should be zero on an intermediate conductance plateau of the QPC, as modes are either fully transmitted or fully reflected, i.e., no intra-mode partitioning. Indeed, early on, experimental results performed at moderate temperatures, T>30mK adhered to this expectation 2,3,19,20 .However, in more recent shot noise measurements, performed at T≈10mK, we found 4-6 : i.Non-zero noise on intermediate conductance plateaus with the partitioning QPC; ii. The Fano factor is equal to the filling factor in the bulk (away from the QPC), on and off the intermediate conductance plateaus within a QPC. These observations necessitate further investigation and a new understanding beyond the orthodox paradigm.

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Fractional edge reconstruction in integer quantum Hall phases

Cited by 26 publications

References 46 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

Determination of topological edge quantum numbers of fractional quantum Hall phases by thermal conductance measurements

Shot noise does not always provide the quasiparticle charge

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