Edge reconstruction and emergent neutral modes in integer and fractional quantum Hall phases

Udit Khanna, Moshe Goldstein, Yuval Gefen

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)471-479
Number of pages9
JournalFizika Nizkikh Temperatur
Volume48
Issue number5
StatePublished - May 2022

Bibliographical note

Publisher Copyright:
© Udit Khanna, Moshe Goldstein, and Yuval Gefen, 2022

Funding

Grants No. 2016224 and 2020072. Y.G. was supported by CRC 183 (project C01), the Minerva Foundation, DFG Grant No. RO 2247/11-1, MI 658/10-2, the German Israeli Foundation (Grant No. I-118-303.1-2018), the National Science Foundation through award DMR-2037654 and the US-Israel Binational Science Foundation (BSF), and the Helmholtz International Fellow Award. U.K. was supported by the Raymond and Beverly Sackler Faculty of Exact Sciences at Tel Aviv University and by the Raymond and Beverly Sackler Center for Computational Molecular and Material Science. _______ We acknowledge illuminating discussions with Jinhong Park and Moty Heiblum. M.G. was supported by the Israel Science Foundation (ISF) and the Directorate for Defense Research and Development (DDR&D) grant No. 3427/21 and by the US-Israel Binational Science Foundation (BSF)

FundersFunder number
Directorate for Defense Research and Development3427/21
German Israeli FoundationI-118-303.1-2018
National Science FoundationDMR-2037654
Minerva Foundation
Deutsche ForschungsgemeinschaftMI 658/10-2, RO 2247/11-1
United States-Israel Binational Science FoundationCRC 183
Israel Science Foundation
Tel Aviv University

    Keywords

    • chiral modes
    • integer and fractional quantum Hall phases
    • quantum phase transition

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