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Why do the bands flatten near 1.1 degrees?
3 steps
At the first magic angle the interlayer tunnelling and the kinetic scale are comparable, and the Fermi velocity of the lowest bands vanishes.1
1. Moire bands in twisted double-layer graphene
And which of those two measures the angle directly?
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| Title | Authors | Year | Status |
|---|---|---|---|
| Unconventional superconductivity in magic-angle graphene superlattices | Cao, Y. et al. | 2018 | |
| Moire bands in twisted double-layer graphene | Bistritzer, R. et al. | 2011 | |
| Correlated insulator behaviour at half-filling in magic-angle graphene superlattices | Cao, Y. et al. | 2018 | |
| Graphene bilayer with a twist: electronic structure | Lopes dos Santos, J. M. B. et al. | 2007 | |
| The marvels of moire materials | Andrei, E. Y. et al. | 2021 | |
| Tuning superconductivity in twisted bilayer graphene | Yankowitz, M. et al. | 2019 | |
| Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene | Lu, X. et al. | 2019 | |
| Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene | Sharpe, A. et al. | 2019 | |
| Maximized electron interactions at the magic angle in twisted bilayer graphene | Kerelsky, A. et al. | 2019 | |
| Intrinsic quantized anomalous Hall effect in a moire heterostructure | Serlin, M. et al. | 2020 | |
| Strange Metal in Magic-Angle Graphene with near Planckian Dissipation | Cao, Y. et al. | 2020 |
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50\end{equation}51%52and the Fermi velocity of the lowest bands vanishes at53a sequence of values of $\alpha$, the first of which is−$\alpha \approx 0.605$.54$\alpha \approx 0.605$~\cite{bistritzer2011moire}.5556The same twist fixes the size of the moir\'e cell.57With $a$ the graphene lattice constant,58%59\begin{equation}60 L_s = \frac{a}{2 \sin(\theta / 2)},61 \label{eq:period}62\end{equation}Cao, Y., Fatemi, V., Fang, S., Watanabe, K., Taniguchi, T., Kaxiras, E., & Jarillo-Herrero, P. (2018). Unconventional superconductivity in magic-angle graphene superlattices. Nature, 556(7699), 43–50. https://doi.org/10.1038/nature26160
Cao, Yuan, et al. “Unconventional Superconductivity in Magic-Angle Graphene Superlattices.” Nature, vol. 556, no. 7699, Mar. 2018, pp. 43–50. Crossref, https://doi.org/10.1038/nature26160.
Cao, Yuan, Valla Fatemi, Shiang Fang, et al. 2018. “Unconventional Superconductivity in Magic-Angle Graphene Superlattices.” Nature 556 (7699): 43–50. https://doi.org/10.1038/nature26160.
[1]Y. Cao et al., “Unconventional superconductivity in magic-angle graphene superlattices,” Nature, vol. 556, no. 7699, pp. 43–50, Mar. 2018, doi: 10.1038/nature26160.
1.Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature. 2018 Mar 5;556(7699):43–50. doi:10.1038/nature26160
1.Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
one record · 10.1038/nature26160
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Reviewed 3 min agoClear
The flat-band condition is derived before either measurement is used, and the two measurements are the right ones for it. Two statements stand on nothing in the library, and one result is credited to the wrong paper of a pair.
What works
Coverage1
The half-filling result is credited to the paper beside the one that reports it.
Half filling is credited to the other paper of the pair
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices reports that result, and the note cites Cao et al., Nature 2018 for it, which is the superconductivity paper paper.tex:71-75.
ElaborateFixDismiss
Structure
Sound. Both equations arrive before the sentence that uses them.
Argument
Nothing is concluded that the two cited results do not carry.
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45The competition is governed byone dimensionless ratio,46%47\begin{equation}48 \alpha = \frac{w}{\hbar v_F k_\theta},49 \label{eq:alpha}50\end{equation}51%52and the Fermi velocity of thelowest bands vanishes at asequence of values of53$\alpha$, the first of whichis $\alpha \approx 0.605$ and54$\theta \approx 1.1^\circ$~\cite{bistritzer2011moire}.Twelve handovers were observed on two wards, and each was followed by a short interview with the nurse who gave it. Transcripts were coded by hand twice
“Half of what matters never gets written down. You say it while you walk.”
nurse, ward B
The first pass stayed open. The second kept only the categories both readers agreed on.
Two of the twelve were observed on the same shift, and those two accounts do not agree.
LaTeXpaper.texWord-styleHandover study
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cao2018unconventionalUnconventional superconductivity in magic-angle graphene superlattices
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andrei2021marvelsThe marvels of moire materials
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kaxiras2018flat10.1038/nature00000 · not found at Crossref
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watanabe2020no entry in this libraryAdd by DOI
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50\subsection{Transport}51Transport measurements report an52insulator at half filling, with two53superconducting domes flanking54it~\cite{cao2018correlated}.55
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Does the twist angle drift with temperature in these devices?
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