Localization of Dirac electrons by Moire patterns in graphene bilayers

Didier Mayou; Guy Trambly de Laissardi\`ere; Laurence Magaud

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Localization of Dirac electrons by Moire patterns in graphene bilayers

Guy Trambly de Laissardière, Didier Mayou, Laurence Magaud

Mesoscale and Nanoscale Physics · Submitted 8 Apr 2009

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

The authors' main claim The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moire patterns.

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arXiv ID0904.1233 (version 2)

Pith IDG7MRJ7CU, Pith's permanent record of this paper and its review

CitationDidier Mayou, Guy Trambly de Laissardi\`ere, Laurence Magaud. "Localization of Dirac electrons by Moire patterns in graphene bilayers." arXiv:0904.1233 (2009). https://pith.science/paper/G7MRJ7CU

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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,565 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.15 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio and tight-binding approaches are combined and show that the spatially periodic coupling between the two Dirac electron gazes can renormalize strongly their velocity. We investigate in particular small angles of rotation and show that the velocity tends to zero in this limit. The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moire patterns.

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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 study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers.	contribution 0.92	0.78	0.04	asserted 0.78
s1	Ab initio and tight-binding approaches are combined and show that the spatially periodic coupling between the two Dirac electron gazes can renormalize strongly their velocity.	result 0.84	0.93	0.36	asserted 1.00
s2	We investigate in particular small angles of rotation and show that the velocity tends to zero in this limit.	result 0.96	0.92	0.31	asserted 0.89
s3	The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moire patterns.	result 0.95	0.92	0.41	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.51 · evidence from simulation or computation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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S sections
T body sentences
C citations
R cross-paper relations

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 study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio and tight-binding approaches are combined and show that the spatially periodic coupling between the two Dirac electron gazes can renormalize strongly their velocity. We investigate in particular small angles of rotation and show that the velocity tends to zero in this limit. The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moire patterns.

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How later papers used it

154 later papers cite it

Evidence: substantial. 151 of the citing papers share no author with it, and 44 of those carry a confident label from Pith's citation classifier.

Pith read 13 of the 276 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

6 later papers by other authors are listed below: 3 used its method or tool and 3 used its data or values.

Uses its method or tool 3 of 27 papers with this label

Calculated the electronic bands of moiré graphene using a tight-binding model from this paper to study the effective interaction matrix at different twist angles.

Anomalous enhancement of large-momentum scattering by electron-electron interaction in moir\'e superlattices (2025) · 1.00 · paraphrased: the licence does not allow quoting
Based its tight-binding model of rotated double-layer graphene on a Slater-Koster parametrization from this paper.

Theory of the Raman spectrum of rotated double-layer graphene (2013) · 0.91 · paraphrased: the licence does not allow quoting
Described the matrix element between orbitals with Slater-Koster two-centre integrals as used previously for twisted bilayer graphene in this paper.

Mach--Zehnder-like interferometry with graphene nanoribbon networks (2023) · 1.00 · paraphrased: the licence does not allow quoting

Uses its data or values 3 of 13 papers with this label

The intra- and interlayer hopping matrix elements $t_ij$ have been determined by fitting the dispersion relations of graphene monolayer and graphene AB-stacked bilayer obtained from ab initio calculations [ref] .

Stoner ferromagnetism in low-angle twisted bilayer graphene at three-quarters filling (2024) · Model Hamiltonian · 0.80
Used the tight-binding parameters given in this paper.

Unfolding energy spectra of multi-periodicity materials (2017) · 0.92 · paraphrased: the licence does not allow quoting
Chose an isotropic decay length for the transfer integrals from this paper so that the next-nearest in-plane overlap becomes 0.1t0.

Pressure-Induced Metal-Insulator Transition in Twisted Bi-layer Graphene (2018) · 0.90 · paraphrased: the licence does not allow quoting

How the literature uses it

4 arXiv papers cite this in 5 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 · 3 sentences without a confident label

Compares with it 1 paper

Finally, we note that the analytic results presented here are in agreement with the numerical solution to this problem provided recently by Campenara et al. [ref] ; special cases of these results have been found in Ref. [ [ref] ] (the case $p=1$, $δ=3$, $γ=2$) and more recently in Ref. [ [ref] ] (the case $δ=1$).

Electronic structure of turbostratic graphene · Commensuration conditions of the twisted bilayer · 0.87

Cites it as background 1 paper

When the twist angle between the two graphene layers approaches the so-called magic angle, $θ≈1.1^∘$, extremely narrow, nearly flat, bands appear at low energies [ref] .

Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene · Introduction · 0.87

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