Fractal Butterflies of Chiral Fermions in Bilayer Graphene: Phase Transitions and Emergent Properties

Areg Ghazaryan; Tapash Chakraborty

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Fractal Butterflies of Chiral Fermions in Bilayer Graphene: Phase Transitions and Emergent Properties

Areg Ghazaryan, Tapash Chakraborty

Mesoscale and Nanoscale Physics · Submitted 4 Feb 2015

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

The authors' main claim Interestingly, the butterfly spectra exhibits remarkable phase transitions between the FQHE gap and the butterfly gap for chiral electrons in bilayer graphene, by varying either the periodic potential strength or the bias voltage.

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arXiv ID1502.01373 (version 1)

Pith ID3XWNN5SI, Pith's permanent record of this paper and its review

CitationAreg Ghazaryan, Tapash Chakraborty. "Fractal Butterflies of Chiral Fermions in Bilayer Graphene: Phase Transitions and Emergent Properties." arXiv:1502.01373 (2015). https://pith.science/paper/3XWNN5SI

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,662 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.05 · mentions code or data availability 0.02.

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

We report on our studies of fractal butterflies in biased bilayer graphene in the fractional quantum Hall effect (FQHE) regime. We have considered the case when the external periodic potential is present in one layer and have illustrated the effect of varying both the periodic potential strength and the bias voltage on the FQHE and the butterfly energy gaps. Interestingly, the butterfly spectra exhibits remarkable phase transitions between the FQHE gap and the butterfly gap for chiral electrons in bilayer graphene, by varying either the periodic potential strength or the bias voltage. We also find that, in addition to those phase transitions, by varying the bias voltage one can essentially control the periodic potential strength experienced by the electrons.

background contribution method result interpretation main claim

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 report on our studies of fractal butterflies in biased bilayer graphene in the fractional quantum Hall effect (FQHE) regime.	contribution 1.00	0.93	0.08	asserted 0.95
s1	We have considered the case when the external periodic potential is present in one layer and have illustrated the effect of varying both the periodic potential strength and the bias voltage on the FQHE and the butterfly energy gaps.	contribution 0.70	0.90	0.07	asserted 0.98
s2	Interestingly, the butterfly spectra exhibits remarkable phase transitions between the FQHE gap and the butterfly gap for chiral electrons in bilayer graphene, by varying either the periodic potential strength or the bias voltage.	result 0.99	0.87	0.56	asserted 1.00
s3	We also find that, in addition to those phase transitions, by varying the bias voltage one can essentially control the periodic potential strength experienced by the electrons.	result 0.96	0.94	0.26	asserted 0.98

What kind of paper the classifier reports this is: simulation study 0.49 · evidence from simulation or computation 0.88.

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Original abstract

We report on our studies of fractal butterflies in biased bilayer graphene in the fractional quantum Hall effect (FQHE) regime. We have considered the case when the external periodic potential is present in one layer and have illustrated the effect of varying both the periodic potential strength and the bias voltage on the FQHE and the butterfly energy gaps. Interestingly, the butterfly spectra exhibits remarkable phase transitions between the FQHE gap and the butterfly gap for chiral electrons in bilayer graphene, by varying either the periodic potential strength or the bias voltage. We also find that, in addition to those phase transitions, by varying the bias voltage one can essentially control the periodic potential strength experienced by the electrons.

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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

What it cites · 6 sentences without a confident label

Uses the method or tool of 2 papers

After that we use the center of mass (CM) translation algebra [ref] and the eigenstates of CM translations to bring the Hamiltonian matrix into block diagonal form, where each block can then be diagonalized using the exact diagonalization procedure [ref] .

Fractional Quantum Hall Effect in Hofstadter Butterflies of Dirac Fermions · Introduction · 1.00
After that we use the center of mass (CM) translation algebra [ref] and the eigenstates of CM translations to bring the Hamiltonian matrix into block diagonal form, where each block can then be diagonalized using the exact diagonalization procedure [ref] .

Spin Transitions in Graphene Butterflies at an Integer Filling Factor · Introduction · 1.00

Cites as background 1 paper

That arrangement resulted in the Moiré pattern which actually introduces a large-scale periodicity in the Hamiltonian of the system, and the fractal butterfly pattern was the result of splitting of the Moiré minibands (secondary Dirac cones) by the magnetic field that are exhibited in the magnetoconductance probe [ref] .

Fractal Butterflies of Dirac Fermions in Monolayer and Bilayer graphene · Introduction · 0.93

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