The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index; none of the 8 sources its claims cite is checked for support yet.
Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect
Open accessAbstract
We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magnetotransport data (Shubnikov-de Haas measurements of the cyclotron mass), and using a tight-binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to midinfrared energies by using fields of less, approximately < 1 V/nm, below the electric breakdown of SiO2. The opening of a gap is clearly seen in the quantum Hall regime.
Overview
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Written from the paper’s full text.
TL;DR
The paper reports that bilayer graphene can be converted into a semiconductor whose band gap is externally tunable by gate bias, with the gap ranging from zero to mid-infrared energies. Magnetotransport measurements and tight-binding modeling show clear gap signatures, including a zero Hall conductivity plateau and an asymmetric cyclotron mass.
Key findings
- In biased bilayer graphene, a plateau at zero Hall conductivity appears at the neutrality point, unlike the pristine case; the longitudinal resistivity at neutrality exceeded 150 kΩ at 4 K for the biased device, compared with 6 kΩ for the unbiased device under the same conditions.
- The cyclotron mass depends asymmetrically on carrier density, and comparison with tight-binding theory yields an interlayer hopping parameter of 0.22 eV and indicates gaps larger than 0.2 eV.
- A small-bias linear fit to the screened theory gives a gap of about 1.2 meV per volt relative to a gate voltage of 25 V, while the theory predicts gap saturation at the interlayer hopping scale.
- The model agrees well with angle-resolved photoemission data, except in the gap saturation regime around densities of about 50 × 10¹² cm⁻².
Methods
- Bilayer graphene devices were prepared by micromechanical cleavage on 300 nm SiO₂ and patterned into Hall bars; carrier density was controlled by a Si backgate and by NH₃ chemical doping, with transport measured by lock-in techniques in fields up to 12 T and temperatures from 4 to 300 K.
- Shubnikov–de Haas oscillations were measured versus temperature and fitted to extract the cyclotron mass as a function of carrier density.
- The data were interpreted with a Bernal-stacked bilayer tight-binding model using in-plane hopping of 3.1 eV and interlayer hopping of 0.22 eV, including a self-consistent Hartree treatment of screening; Hall conductivity was modeled for a zigzag-edged ribbon in a magnetic field.
Limitations
- The paper states that the Hartree approach is reliable only when the gap is small compared with the interlayer hopping; for hole doping it underestimates the cyclotron mass while the unscreened model overestimates it, so the true gap lies between these limits and a better screening treatment is needed when the electrostatic energy becomes comparable to the interlayer hopping.
- The paper notes that the comparison with angle-resolved photoemission data works well except in the gap saturation regime at high density.
- Evident from the text: for the transport devices, the gap values are inferred by fitting a tight-binding/Hartree model to magnetotransport rather than measured directly by a spectroscopic probe.
Model-written summary. Check it against the paper before relying on it.
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Claims the paper makes
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The opening of a gap is clearly seen in the quantum Hall regime.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“which is absent in the unbiased case”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“by comparing the observed behavior with our tightbinding results, we show that the gap can be tuned to values larger than 0.2 eV”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“in the biased device, xx at n 0 exceeded 150 kOhm at 4 K, as compared to 6 kOhm for the unbiased case under the same conditions”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“in a magnetic field, a pronounced plateau at zero Hall conductivity xy 0 is found for the biased bilayer”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the cyclotron mass, m c , in the bilayer biased by chemical doping is an asymmetric function of carrier density, n”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The linear increase of m c with jnj and the pronounced asymmetry between hole-and electron-doping of the biased bilayer are clearly seen here.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We show that the gap can be changed from zero to midinfrared energies by using fields of & 1 V=nm, below the electric breakdown of SiO 2 .”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: The breakdown field for SiO2 is 1 V/nm (i.e., 300 V for the used oxide thickness).
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The linear increase of m c with jnj and the pronounced asymmetry between hole-and electron-doping of the biased bilayer are clearly seen here.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The energy gap is revealed by the appearance of the N 0 plateau at xy 0 [see the curve labeled ''doped'' in Fig. 1(a)].”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- It may state two separate claims as one. 10
- The quote only partly states this claim. 2
- Probably not a substantial claim. 1
In the paper
“The N 0 plateau is strikingly absent, so that a double step of 8e 2 =h in height occurs at n 0, indicating a metallic state at the neutrality point [3].”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
What the sources say
- Not matchedcites [3] 3. K. S. Novoselov et al., Nature Phys. 2, 177 (2006).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Not matched
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this case two flat bands with energies ÿeV=2 and eV=2 appear, similar to the case of zero magnetic field.The other two zero energy bands become dispersive inside the gap, showing the band-crossing phenomenon.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the hole doping region in Fig. 1(b), the Hartree approach underestimates the value of m c whereas the simple unscreened result overestimates it.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The emerged plateau was accompanied by a huge peak in longitudinal resistivity xx , indicating an insulating state”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“which provides a clear signature of a gap and allows its estimate”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“we have cross-checked our theory against angle-resolved photoemission spectroscopy (ARPES) data [8] and found excellent agreement.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
What the sources say
- Not matchedcites [8] 8. Theory of the gap opening within the continuum model was previously given by E. McCann, Phys. Rev. B 74, 161403 (2006).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Zero potential difference and zero gap are expected at n 2n 0 in both unscreened and screened cases, as seen from Eqs. (1) and ( 2) and the fact that nn; 0 0.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The charge in layers 1 and 2 of the bilayer is equal to -ne/2.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that at the zero Hall plateau the current carried around the ribbon loop is zero, I 0, which implies, from the theory view point, a diverging longitudinal resistivity at low T”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This opens a gap of eV in size.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“At this particular density the gap closes and the theoretical value becomes independent of the screening assumptions.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“a more accurate treatment of screening is needed when eV becomes of the order of t ? .”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The coefficient 7:2 10 10 cm ÿ2 =V is determined by the geometry of the resulting capacitor and is in agreement with the values of n 1 found experimentally [1][2][3].”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
What the sources say
- Not matchedcites [1][2][3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- Not matched
The authors state this as an assumption.
The charge in layers 1 and 2 of the bilayer is equal to -ne/2.
“Assuming equal charge ÿne=2 in layers 1 and 2 of the bilayer”
The paper relies on this without support.
The breakdown field for SiO2 is 1 V/nm (i.e., 300 V for the used oxide thickness).
“Note that the breakdown field for SiO 2 is 1 V=nm (i.e., 300 V for the used oxide thickness)”
The authors state this as an assumption.
The electric field induced between the two layers can be considered as a result of the effect of charged surfaces placed above and below bilayer graphene.
“The electric field induced between the two layers can be considered as a result of the effect of charged surfaces placed above and below bilayer graphene .”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Laughlin is cited under the wrong reference number
MinorThe text attributes an argument to Laughlin [14], while the reference list assigns 14 to a note and lists Laughlin at 15.
“As pointed out by Laughlin [14], changing the magnetic flux through the ribbon loop by a flux quantum causes the states to move rigidly towards one edge.”
“14. The unbiased case, in the continuum approximation, was studied in Ref. [5]. 15. R. B. Laughlin, Phys. Rev. B 23, 5632 (1981).”
Citations
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Metadata
- Authors
- Castro, E. V., Novoselov, K. S., Morozov, S. V., Peres, N. M. R., dos Santos, J. M. B. L., Nilsson, J., Guinea, F., Geim, A. K., & Neto, A. H. C.
- Affiliations
- Universidade do Porto (PT)
- University of Manchester (GB)
- University of Minho (PT)
- Boston University (US)
- Consejo Superior de Investigaciones Científicas (ES)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-11-20
- Volume
- 99
- Issue
- 21
- Pages
- 216802-216802
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2113467957
- Cited by
- 2,033
- References
- 14
- Citations by year
- 2026: 54 · 2025: 60 · 2024: 62 · 2023: 68 · 2022: 85 · 2021: 101 · 2020: 134 · 2019: 102 · 2018: 95 · 2017: 121 · 2016: 134 · 2015: 130 · 2014: 142 · 2013: 146 · 2012: 145
- FWCI
- 55.56
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Research Explorer (The University of Manchester) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Graphene research and applications
- Physical Sciences › Materials Science › Materials Chemistry › 2D Materials and Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Quantum and electron transport phenomena
- Keywords
- bilayer graphene, electric field effects, band gap tuning, gate bias, Shubnikov-de Haas effect, cyclotron mass, tight-binding model, quantum Hall effect, electron density
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