Chirality-Protected Majorana Zero Modes at the Gapless Edge of Abelian Quantum Hall States

Chetan Nayak; David J. Clarke; Jennifer Cano; Maissam Barkeshli; Meng Cheng

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Chirality-Protected Majorana Zero Modes at the Gapless Edge of Abelian Quantum Hall States

Jennifer Cano, Meng Cheng, Maissam Barkeshli, David J. Clarke, Chetan Nayak

Strongly Correlated Electrons · Submitted 28 May 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the $\nu=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity.

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arXiv ID1505.07825 (version 2)

Pith ID2DANTDKF, Pith's permanent record of this paper and its review

CitationChetan Nayak, David J. Clarke, Jennifer Cano, Maissam Barkeshli, Meng Cheng. "Chirality-Protected Majorana Zero Modes at the Gapless Edge of Abelian Quantum Hall States." arXiv:1505.07825 (2015). https://pith.science/paper/2DANTDKF

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.31 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.22 · compares with prior results 0.15 · mentions code or data availability 0.02.

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We show that the $\nu=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a function of the relevant length scales, in spite of the presence of gapless excitations, including gapless fermions. These results are compatible with charge conservation, but do not require it. We discuss generalizations to other integer and fractional quantum Hall states, and classify possible mechanisms for appearance of Majorana zero modes at domain walls.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that the $\nu=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity.	result 0.85	0.92	0.92	asserted 0.96
s1	This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase.	interpretation 0.67	0.76	0.08	asserted 1.00
s2	Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions.	result 0.94	0.78	0.17	asserted 1.00
s3	Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a function of the relevant length scales, in spite of the presence of gapless excitations, including gapless fermions.	result 0.95	0.86	0.24	asserted 1.00
s4	These results are compatible with charge conservation, but do not require it.	interpretation 0.79	0.68	0.04	asserted 0.55
s5	We discuss generalizations to other integer and fractional quantum Hall states, and classify possible mechanisms for appearance of Majorana zero modes at domain walls.	contribution 0.80	0.82	0.05	asserted 0.69

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.80.

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full text
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We show that the $\nu=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a function of the relevant length scales, in spite of the presence of gapless excitations, including gapless fermions. These results are compatible with charge conservation, but do not require it. We discuss generalizations to other integer and fractional quantum Hall states, and classify possible mechanisms for appearance of Majorana zero modes at domain walls.

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6 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Cites it as background 4 papers

Recent years have seen significant advances in our understanding of critical many-body systems with boundaries, such as classical [ref] and quantum magnets [ref] , and gapless quantum systems with topologically protected boundary states [ref] .

Boundary operator product expansion coefficients of the three-dimensional Ising universality class · Introduction · 0.87
0d wall between gapless edges were also studied in [ref] .

A mathematical theory of gapless edges of 2d topological orders. Part II · Classification of 0+1D walls and examples · 0.88
There are several factors contributing to an interest in this topic, including questions about the existence of topologically protected boundary states in gapless quantum systems [ref] , appearance of conical defects in the study of entanglement properties [ref] , mapping of questions about open quantum systems to more conventional statistical mechanics problems with defects [ref] , and the use of extended operators to characterize phases of matter [ref] .

Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model · Introduction · 0.98

What it cites · 11 sentences without a confident label

Builds on 4 papers

Case 2 generalizes the topological degeneracy of parafermionic zero modes in Abelian quantum Hall states [ref] .

Exotic non-Abelian anyons from conventional fractional quantum Hall states · Classification of domain walls on the edge of an Abelian quantum Hall state · 0.93
Case 2 generalizes the topological degeneracy of parafermionic zero modes in Abelian quantum Hall states [ref] .

Topological Nematic States and Non-Abelian Lattice Dislocations · Classification of domain walls on the edge of an Abelian quantum Hall state · 0.93
Case 2 generalizes the topological degeneracy of parafermionic zero modes in Abelian quantum Hall states [ref] .

Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states · Classification of domain walls on the edge of an Abelian quantum Hall state · 0.93

Uses the method or tool of 2 papers

Following Ref. [ref] , we can define Majorana fermion operators.

Exotic non-Abelian anyons from conventional fractional quantum Hall states · Ground state degeneracy of an edge with multiple domain walls · 0.96
Alternatively, a measurement-only scheme [ref] can be used to manipulate quantum information.

Measurement-Only Topological Quantum Computation · Discussion · 0.92

Cites as background 7 papers

We begin by recalling some facts about the edge phases of the $ν=8$ integer quantum Hall state [ref] .

Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases · Edge Phases of the $ν=8$ integer quantum Hall state · 0.90
Majorana zero modes have been the focus of recent theoretical and experimental efforts [ref] , motivated in part by their potential applications to topological quantum information processing [ref] .

New directions in the pursuit of Majorana fermions in solid state systems · Introduction. · 1.00
Majorana zero modes have been the focus of recent theoretical and experimental efforts [ref] , motivated in part by their potential applications to topological quantum information processing [ref] .

Search for Majorana fermions in superconductors · Introduction. · 1.00

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