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Mirror winding number and helical edge modes in honeycomb lattice with hopping-energy texture

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Toshikaze Kariyado, Xiao Hu

Mesoscale and Nanoscale Physics · Submitted 29 Jul 2016

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

The authors' main claim We illustrate possible topological phases in honeycomb lattice with textures in electron hopping energy between nearest-neighboring sites and show that they are characterized by the mirror winding number intimately related to the chiral (or sublattice) symmetry.

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arXiv ID1607.08706 (version 1)
Pith IDIJQGW4SD, Pith's permanent record of this paper and its review
CitationToshikaze Kariyado, Xiao Hu. "Mirror winding number and helical edge modes in honeycomb lattice with hopping-energy texture." arXiv:1607.08706 (2016). https://pith.science/paper/IJQGW4SD
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,700 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We illustrate possible topological phases in honeycomb lattice with textures in electron hopping energy between nearest-neighboring sites and show that they are characterized by the mirror winding number intimately related to the chiral (or sublattice) symmetry. Analytic wave functions of zero-energy edge modes in ribbon geometry are provided, which are classified into even and odd sectors with respect to the mirror operation with the mirror plane perpendicular to the edge, and evolve into the topological helical edge states at finite momenta. Intriguingly our results demonstrate that in order to achieve the topological phase one can decorate the edge in a way adaptive to the bulk hopping texture. This paves a new way to tailoring graphene in the topological point of view.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We illustrate possible topological phases in honeycomb lattice with textures in electron hopping energy between nearest-neighboring sites and show that they are characterized by the mirror winding number intimately related to the chiral (or sublattice) symmetry. contribution 0.64 0.89 0.66 asserted 0.87
s1 Analytic wave functions of zero-energy edge modes in ribbon geometry are provided, which are classified into even and odd sectors with respect to the mirror operation with the mirror plane perpendicular to the edge, and evolve into the topological helical edge states at finite momenta. result 0.65 0.93 0.18 asserted 1.00
s2 Intriguingly our results demonstrate that in order to achieve the topological phase one can decorate the edge in a way adaptive to the bulk hopping texture. result 0.81 0.93 0.31 asserted 1.00
s3 This paves a new way to tailoring graphene in the topological point of view. interpretation 0.95 0.27 0.13 asserted 0.85

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

What was examined, and what was not

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  • C citations
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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 illustrate possible topological phases in honeycomb lattice with textures in electron hopping energy between nearest-neighboring sites and show that they are characterized by the mirror winding number intimately related to the chiral (or sublattice) symmetry. Analytic wave functions of zero-energy edge modes in ribbon geometry are provided, which are classified into even and odd sectors with respect to the mirror operation with the mirror plane perpendicular to the edge, and evolve into the topological helical edge states at finite momenta. Intriguingly our results demonstrate that in order to achieve the topological phase one can decorate the edge in a way adaptive to the bulk hopping texture. This paves a new way to tailoring graphene in the topological point of view.

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2 arXiv papers cite this in 4 sentences

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