Unconventional Superconductivity in Magic-Angle Graphene Superlattices
Nature, 2018 · paper · Materials
Reports superconductivity in bilayer graphene twisted near 1.1°. Doping away from the correlated insulating states gives zero-resistance states with critical temperature up to 1.7 K, with a dome-shaped phase diagram resembling cuprates, at very low carrier densities.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
2 findings
Substance The density of the device M2 I-V data behind the BKT fit (TBKT = 1.0 K) is "n = −1.47 × 10^12 cm−2" in the Fig. 1e caption but "n = −1.44 × 10^12 cm−2" in the text on page 3.
- p. 2 Fig. 1 caption, panel (e)
measured at n = −1.47 × 1012 cm−2
- p. 3 Section 'Superconductivity in MA-TBG', right column
at n = −1.44 × 1012 cm−2
- p. 2 Fig. 1 caption (e)
n = −1.47 × 1012 cm−2 and various temperatures
- p. 2 Fig. 1 caption, panel (e)
measured at n = −1.47 × 1012 cm−2 and various temperatures
Only the authors can say what is right here.
Judge's note: Caption (page 2): "(e) I−V curves for device M2 measured at n = −1.47 × 10^12 cm−2 ... The inset shows the same data plotted in log-log scale ... (TBKT = 1.0 K in this case)". Text (page 3): "The inset shows a tentative fit of the same data ... TBKT = 1.0 K at n = −1.44 × 10^12 cm−2". Both describe the one data set of Fig. 1e and its inset, with the same TBKT. The figure panel carries no density label, and I found no statement elsewhere that explains two densities. Only the authors can say which is right.
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Reference or label Fig. 6 caption prints "TBEC = 1.04ℏ²n3D/m∗ for a 3D bosonic gas" with n3D to the first power; the same caption and the top axis use n3D^(2/3), and the formula needs that exponent.
- p. 9 Fig. 6 caption
TBEC = 1.04ℏ2n3D/m∗
- p. 9 Fig. 6 top axis label
1.52n3D2/3/(gm*/m0)
- p. 9 Fig. 6 caption
TBEC = 1.04ℏ2n3D/m∗ for a 3D bosonic gas
- p. 9 Fig. 6 caption and top axis
n2/3 3D for 3D materials
Judge's note: The caption crop shows "n3D/m*" with no exponent, while "n3D^{2/3}" is typeset with its exponent two lines above and on the top axis ("1.52 n3D^{2/3}/(gm*/m0)"). So this is not an extraction artefact. Internal check: ℏ²n/m* with a 3D density is an energy per length, not an energy; ℏ²n^(2/3)/m* is an energy. The prefactor also matches the 2/3 form: the standard ideal Bose gas result kB·TBEC = 3.31ℏ²nB^(2/3)/mB with nB = n/2 and mB = 2m* gives 3.31/(2 × 2^(2/3)) = 1.04 (the 3.31 coefficient is outside knowledge; the dimensional and internal-consistency argument does not depend on it). The plotted line is unaffected; the caption formula has lost its exponent.
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32 minor (typos and the like; most checked by the judge only)
Reference or label Page 5: "Figures 5a-b show the Shubnikov-de Haas (SdH) oscillations in longitudinal resistance as a function of carrier density", but only Fig. 5a is plotted against density; Fig. 5b shows temperature-dependent traces against 1/B at three fixed densities.
- p. 5 Quantum oscillations section, first paragraph
Figures 5a-b show the Shubnikov-de Haas (SdH)
- p. 8 Fig. 5 caption (b)
Temperature-dependent quantum oscillation traces at charge densities labeled by A, B, and C in (a)
Judge's note: Page 8 image: panel a is Rxx versus n and B⊥ with the Landau fan diagram below it; panel b has the axis 1/B (T−1) and is captioned "Temperature-dependent quantum oscillation traces at charge densities labeled by A, B, and C in (a)". The text later cites "Figures 5b-c" for the oscillations and amplitudes at three densities. Panel b does show SdH oscillations, so the pointer is loose, not wrong; "Fig. 5a" would be exact.
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Reference or label Reference 27 reads "Klemm, R. A. & Luther, A. Theory of the upper critical field in layered superconductors. Phys. Rev. B 12, 3 (1975)"; the first page "3" looks like an issue number, and a third author may be missing.
- p. 11 Reference 27
Phys. Rev. B 12, 3
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that this paper is Klemm, Luther and Beasley, Phys. Rev. B 12, 877 (1975). The page image of p. 11 shows the entry as quoted. A first page of 3 in volume 12 of Phys. Rev. B for this title is implausible on its face, but the true page and author list cannot be checked from the files.
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Reference or label Reference 65: "Perconte, D., Cuellar, F. A., et al. Tunable Klein-like tunnelling of high-temperature superconducting pairs into graphene. Nat. Phys. 14, 2529 (2018).": the page is printed as "2529", which looks like the range 25-29 with the dash missing.
- p. 18 Reference 65
14, 2529 (2018)
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that this article occupies pages 25-29 of Nature Physics volume 14. The crop of page 18 shows "14, 2529 (2018)" with no dash, while the neighbouring entries print ranges with a hyphen ("56-59", "761-764", "756-760"). Within the paper, a four-digit page for an early-2018 issue beside entries that all give ranges is suggestive, but the true pages cannot be verified from the files, so this is a question for the authors.
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Wording Page 3 names "M1 and M2, with twist angles of 1.16° and 1.05° respectively" and then gives Tc as "approximately 1.7 K and 0.5 K for the two devices", the reverse of the device order: M1 is 0.5 K and M2 is 1.7 K.
- p. 3 Section 'Superconductivity in MA-TBG', left column
proximately 1.7 K and 0.5 K for the two devices we stud-
- p. 3 preceding sentence
M1 and M2, with twist angles of
- p. 4 Fig. 2 caption (b)
The highest critical temperature observed in device M1 is Tc = 0.5 K
- p. 3 Section 'Superconductivity in MA-TBG', left column, preceding sentence
two magic-angle devices, M1 and M2, with twist angles of
Judge's note: Fig. 2 caption: "The highest critical temperature observed in device M1 is Tc = 0.5 K" and, for M2, "Tc = 1.7 K". Fig. 1b on page 2 agrees: the M2 (purple) curve reaches zero resistance at the higher temperature. The Tc sentence does not say "respectively", so it is not strictly false, but it follows directly on a sentence that lists M1 then M2 and so invites the wrong assignment. Downgraded from an error to misleading ordering.
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Wording The M1 density window for the periodic oscillations is "−1.47 to −1.67 × 10^12 cm−2" in the main text, while Methods gives "n = −1.70 ∼ −1.60 × 10^12 cm−2 and n = −1.50 ∼ −1.47 × 10^12 cm−2" and Extended Data Fig. 1b is taken at "n=-1.68×10^12 cm-2", just outside the main-text window.
- p. 5 Magnetic field response paragraph
−1.47 to −1.67 × 1012 cm−2
- p. 14 Methods, phase-coherent transport
n = −1.70 ∼−1.60 × 1012 cm−2
- p. 5 Magnetic field response
−1.47 to −1.67 × 1012 cm−2 for M1
- p. 14 Methods, Phase-coherent transport
n = −1.70 ∼−1.60 × 1012 cm−2 and n = −1.50 ∼−1.47 × 1012 cm−2 in device M1
Judge's note: All three values checked on the images of pages 5, 14 and 15. The lower bound differs by 0.01 to 0.03 × 10^12 cm−2. Methods says "most clearly seen" and the main-text range is approximate, so either form could be legitimate. A small inconsistency only.
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Typo Author list prints "Efthimos Kaxiras"; the given name is probably "Efthimios".
- p. 1 Author list
Efthimos Kaxiras
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that this author's given name is spelled Efthimios. The page image shows "Efthimos Kaxiras" in the author list. Nothing in the files gives the full name elsewhere (the reference list uses initials only), so the spelling cannot be checked internally.
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Typo Abstract: "The relative high Tc, given such small Fermi surface" should read "relatively high".
- p. 1 Abstract
The relative high Tc
Judge's note: The abstract crop shows "The relative high Tc". The introduction on the same page writes "The relatively high Tc = 1.7 K", so the adverb is the intended form.
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Typo Two misspellings: Fig. 1 caption "rotatated graphene bilayers" (rotated), and page 5 "the MOtt-like insulator phase crosses over" (Mott-like).
- p. 2 Fig. 1 caption (a)
rotatated graphene
- p. 5 Phase diagram of MA-TBG
MOtt-like insulator phase
- p. 5 Phase diagram of MA-TBG, 1st paragraph
MOtt-like insulator phase crosses over
- p. 5
the MOtt-like insulator phase crosses over
Judge's note: Both are visible on the page images: "rotatated" in the Fig. 1(a) caption on page 2, and "MOtt-like" in the Phase diagram section on page 5, where "Mott-like" is spelled correctly a few lines above.
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Typo Misspellings: "Jospehson coupling" (p. 10; Josephson), "MOtt-like insulator" (p. 5), "rotatated graphene" (Fig. 1 caption, p. 2), "Shubnikov-de Hass" (p. 17; Haas), and "the superconducting quantum flux" (p. 15; the main text on p. 5 has "superconducting flux quantum").
- p. 10 Discussion, left column
induce Jospehson coupling
- p. 10 Summary paragraph, left column
tures to induce Jospehson coupling
- p. 10 Discussion, 1st paragraph
induce Jospehson coupling in the vertical direc-
- p. 10 Discussion
Jospehson coupling
Judge's note: Each seen on the page image or crop: 'Jospehson' on p. 10 while 'Josephson' is spelled correctly later in the same column; 'MOtt-like' on p. 5 beside 'Mott-like' in the same paragraph; 'rotatated' in the Fig. 1 caption; 'Shubnikov-de Hass' on p. 17; 'superconducting quantum flux' on p. 15 against 'superconducting flux quantum' on p. 5. 'staciking boundaries' is also in the Methods text (seen in the text layer only).
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Typo Page 3: "more than 3 orders of magnitudes higher" should read "orders of magnitude".
- p. 3 Superconductivity in MA-TBG, 2nd paragraph
more than 3 orders of magnitudes higher
Judge's note: Seen on the page image. The paper writes "orders of magnitude" on pages 1 and 4.
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Typo Page 4: "but at lower temperatures both devices exhibit signs of superconductivity at the lowest temperatures" states the temperature qualifier twice.
- p. 4 Right column, last paragraph
peratures both devices exhibit signs of superconductivity
Judge's note: The crop shows the full sentence with both "at lower temperatures" and "at the lowest temperatures" in one clause. A redundancy, not a factual problem.
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Typo Page 5: "Such junctions regions may be due to slight density inhomogeneities" should read "junction regions".
- p. 5 Section 'Magnetic field response'
Such junctions regions may be due to
- p. 5 Magnetic field response
Such junctions regions may be due
Judge's note: Seen on the page image.
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Typo Methods (PDF page 15): "where Φ0 = h/2e is the superconducting quantum flux"; the main text (PDF page 5) calls the same quantity "the superconducting flux quantum".
- p. 15 Methods, phase-coherent transport
is the superconducting quantum flux
- p. 5 Magnetic field response
superconducting flux quantum
Judge's note: Crop of page 15 shows "the superconducting quantum flux"; the extracted text of page 5 has "Φ0 = h/2e is the superconducting flux quantum" (not checked on the page 5 image; the wording is plain prose). The standard term is "flux quantum"; the Methods wording has the words transposed. The meaning is unambiguous because the formula h/2e is given both times, so this is a minor terminology inconsistency.
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Typo Discussion, page 9: "the coherence length in MA-BLG" uses an undefined abbreviation; the material is "MA-TBG" everywhere else.
- p. 9 Discussion, right column
the coherence length in MA-BLG
- p. 9 Discussion, coherence length sentence
coherence length in MA-BLG
- p. 9
the coherence length in MA-BLG, of or-
Judge's note: Seen on the page 9 image. A search of the text finds "MA-BLG" only this once and no definition; the surrounding sentences use MA-TBG for the same system.
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Typo Page ranges printed without a dash: reference 9 "Rev. Mod. Phys. 80, 885964 (2008)" and reference 65 "Nat. Phys. 14, 2529 (2018)".
- p. 10 Reference 9
80, 885964
- p. 10 Reference list, entry [9]
Rev. Mod. Phys. 80, 885964
- p. 10 Reference [9]
885964
- p. 12 Reference [51]
158163
Judge's note: Page image of p. 10 shows '885964' with no dash, while neighbouring entries print ranges with a dash ('179-186', '462-466', '1589-1652'). Crop of p. 18 shows '14, 2529 (2018)' while refs 61-63 print '56-59', '761-764', '756-760'. That 885964 is a run-together range is evident from its length; for ref 65 the reading 25-29 is likely but rests on the same pattern. The same defect in reference 51 is handled under C028.
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Typo Reference 4: "Rev. Mod. Phys. 81, 1551(2009)" has no space before the year.
- p. 10 Reference [4]
81, 1551(2009)
Judge's note: Seen on the p. 10 page image; the other entries have a space before the year.
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Typo The same co-author is spelled "Larentiz, S." in reference 20 and "S. Larentis" in reference 21.
- p. 11 Reference 20
Larentiz, S.
- p. 11 Reference 21
S. Larentis
- p. 11 Reference [20]
Larentiz
Judge's note: Both seen on the p. 11 page image, in adjacent entries with largely the same author list (Kim, Fallahazad, Taniguchi, Watanabe, LeRoy, Tutuc). The inconsistency is internal to the paper; which spelling is right (Larentis) is outside knowledge.
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Typo Reference 21 author list contains a stray affiliation mark: "B. J. LeRoy,1, A. H. MacDonald".
- p. 11 Reference 21
B. J. LeRoy,1, A. H. Mac-
Judge's note: Seen on the p. 11 page image. The entry also puts initials first, unlike the surname-first style of the rest of the list.
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Typo Reference 34 prints "Taillefer, D. & Proust, C." while reference 33, from the same group, prints "Taillefer, L.".
- p. 11 Reference 34
Taillefer, D. & Proust, C.
- p. 11 Reference 33
Taillefer, L.
- p. 11 Reference [34]
Taillefer, D. & Proust
Judge's note: Both seen on the p. 11 page image in consecutive entries with overlapping author lists (Doiron-Leyraud, LeBoeuf, Levallois, Vignolle, Proust). The inconsistency is internal; that 'L.' is the right initial is outside knowledge.
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Typo Dashes dropped in reference titles: "Shubnikovde Haas Oscillations" (ref. 33), "de Haasvan Alphen Oscillations" (ref. 34) and "BaFe2(As1xPx)2" (ref. 38; Fig. 6 prints As1-xPx).
- p. 11 Reference 33
Shubnikovde Haas Oscillations
- p. 11 Reference 34
de Haasvan Alphen
- p. 11 Reference 38
BaFe2(As1xPx)2
- p. 11 Reference [34]
de Haasvan Alphen Os-
Judge's note: All three seen on the p. 11 page image, so not an extraction loss. Fig. 6 on p. 9 labels the compound 'BaFe2(As1-xPx)2' with the minus sign.
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Typo Reference 38 ends "Science 336, 1554-1557." with no year.
- p. 11 Reference 38
Science 336, 1554-1557.
Judge's note: Seen on the p. 11 page image; every other journal entry on the page carries a year in parentheses. The missing minus in the title's formula is covered under C023.
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Typo Reference 42 prints the author as "Mannhard, J." (probably Mannhart).
- p. 11 Reference [42]
Mannhard, J.
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the co-author of Caviglia et al., Nature 456, 624 (2008) is J. Mannhart. The page image of p. 11 shows 'Mannhard, J.'; nothing else in the paper spells the name.
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Typo Reference 31 title: "Hofstadters butterfly" lacks the apostrophe (the main text writes "Hofstadter's butterfly").
- p. 11 Reference [31]
Hofstadters butterfly
Judge's note: Seen on the p. 11 page image. The article text on p. 6 writes 'Hofstadter’s' twice.
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Typo Reference 54 prints the volume in parentheses, "Nature (464), 199-208 (2010)", and reference 19 ("J. M. B. Lopes dos Santos, N. M. R. Peres, A. H. Castro Neto, Phys. Rev. B 86, 155449 (2012)") puts initials first and has no title, unlike the rest of the list.
- p. 12 Reference 54
(464), 199-208 (2010)
- p. 11 Reference [19]
J. M. B. Lopes dos Santos, N. M. R. Peres, A. H. Castro
- p. 12 Reference [54]
Nature (464), 199-208 (2010)
Judge's note: Both seen on the page images (p. 12 and p. 11). Other entries give a bold volume without parentheses, surname-first authors and a title. Formatting only.
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Typo Reference 51: "Nature Physics 8, 158163 (2012)" prints the page range without a dash; the journal is written "Nature Physics" here and "Nat. Phys." elsewhere.
- p. 12 Reference 51
8, 158163 (2012)
Judge's note: Seen on the p. 12 page image; other entries on the page print ranges with a dash ('563-567', '199-208'). Refs 35 and 45 use 'Nat. Phys.'. Same kind of defect as C018 but a different entry.
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Typo Reference 49 prints the author as "Chitari, B. L." (probably Chittari).
- p. 12 Reference [49]
Chitari, B. L.
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the co-author of Yankowitz et al., arXiv:1707.09054 is B. L. Chittari. The page image of p. 12 shows 'Chitari, B. L.'; the name appears nowhere else in the paper.
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Typo Methods, Sample Preparation: "since we find that TwBLG tend to relax to Bernal-stacked bilayer graphene at high temperatures" uses the abbreviation "TwBLG", which is never defined; the paper's abbreviation for twisted bilayer graphene is "TBG" (used in the sentences before and after).
- p. 13 Methods, Sample Preparation
since we find that TwBLG tend to relax
- p. 13 Methods, Sample Preparation
we find that TwBLG tend to relax to Bernal-stacked bilayer graphene
- p. 13 Methods, Sample Preparation
TwBLG tend to relax to Bernal-stacked bilayer graphene
Judge's note: Read the full page 13 image: the paragraph has "precisely controlled TBG structure" two sentences earlier and "Electrical connections are made to the TBG" after. A text search finds "TwBLG" only once in the article, and TBG defined in the abstract and Fig. 1 caption. Undefined, inconsistent abbreviation; cosmetic.
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Typo Methods, Sample Preparation: "We use Poly (Bisphenol A carbonate) (PC)/Polydimethylsiloxane (PDMS) stack ... to first pick up an h-BN flake at 90 °C, and then uses the van der Waals force between h-BN and graphene to tear a graphene flake": "uses" should be "use".
- p. 13 Sample preparation
and then uses the van der Waals force
Judge's note: Read on the page 13 image. The subject is "We" and the verb is parallel to "to first pick up", so "uses" does not agree with either construction. Grammar slip only.
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Typo Methods, 'Possible effects due to finite electrical fields': "are interconnected by these AB/BA staciking boundaries": "staciking" should be "stacking".
- p. 14 Methods, 'Possible effects due to finite electrical fields'
AB/BA staciking boundaries
- p. 17 Supplemental quantum oscillation data
Shubnikov-de Hass
- p. 14
interconnected by these AB/BA staciking boundaries
Judge's note: Crop of page 14 shows "staciking" clearly; the sentence before spells "AB/BA stacking boundaries" correctly. The "Shubnikov-de Hass" misspelling that one reviewer attached here is handled in C039.
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Typo Methods, phase-coherent transport (PDF page 16): "are very likely a result of phase-coherent transport (Josephson effect) through a superconductor with insulating puddles and provide further confirm the existence of superconductivity in MA-TBG": "provide further confirm" is ungrammatical ("provide further confirmation of" or "further confirm").
- p. 16 Text below Extended Data Fig. 2, first paragraph
provide further confirm the existence of
- p. 16 Phase-coherent transport, last sentence
provide further confirm the existence of superconductivity
Judge's note: Read on the full page 16 image; the wording is as quoted. Grammar slip only.
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Typo Extended Data Fig. 2 caption: "The data is taken the first derivative with respect to the gate-defined charge density n to enhance the color contrast.": the sentence is ungrammatical (for example "The first derivative of the data is taken with respect to ...").
- p. 16 Extended Data Fig. 2 caption
The data is taken the first derivative with
Judge's note: Read on the full page 16 image; the caption reads as quoted. The intended meaning (the plots show dRxx/dn and dG2/dn, as the colour-bar labels say) is clear, so this is cosmetic.
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Typo PDF page 17: "using the Shubnikov-de Hass (SdH) oscillation frequency in a magnetic field (Fig. 5)": "Hass" should be "Haas", as spelled on PDF page 5 ("Shubnikov-de Haas (SdH)").
- p. 17 Text below Extended Data Fig. 3
Shubnikov-de Hass
- p. 17
Shubnikov-de Hass (SdH) oscillation frequency
Judge's note: Crop of page 17 shows "Shubnikov-de Hass". The extracted text of page 5 has "Shubnikov-de Haas (SdH)", and the abbreviation SdH and the reference titles also give Haas, so the paper's own usage settles the spelling.
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