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Independently Tunable Flat Bands and Correlations in a Graphene Double Moir\'e System

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A four-layer graphene stack can host two spatially separated twisted-bilayer flat bands, and a capacitance model lets each band's chemical potential be measured independently.

desk verdict A new double-moiré platform with credible independent flat bands; the thermodynamic extraction is plausible, but the separate-layer model needs a clearer defense and the theory comparison is explicitly a fit. read the letter →

arxiv 2411.18785 v1 pith:454AIFFF submitted 2024-11-27 cond-mat.mes-hall

Yimeng Wang , Jihang Zhu , G. William Burg , Anand Swain , Kenji Watanabe , Takashi Taniguchi , Yuebing Zheng , Allan H. MacDonald
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Emanuel Tutuc
This is my paper · ORCID
classification cond-mat.mes-hall
keywords doublemoirésystemtwistedbilayergrapheneflatbandschemicalpotentialcorrelatedinsulatorchargeneutralitygapmagicanglethermodynamicmeasurement
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports that a stack of four graphene layers, with a small twist angle between the top pair and between the bottom pair but a deliberately large twist angle between the two pairs, forms two separated twisted-bilayer-graphene (TBG) flat-band systems in a single device. Using a dual-gated channel and an electrostatic model in which the two TBG subsystems share only an interlayer capacitance, the authors extract the chemical potential as a function of carrier density for each TBG across twist angles from 0.91° to 1.57°. They find that correlated insulating states at integer numbers of electrons per moiré unit cell are strongest for twists near the magic angle, while gapped states at charge neutrality are more robust at larger twist angles, and that the valence flat band is flatter than the conduction band. The result opens a way to study flat-band correlations while keeping two flat bands independently tunable in one stack.

What carries the argument

The central mechanism is the two-capacitor electrostatic model of the double moiré system, written as Eq. (1): $V_{\rm BG}C_{\rm BG}=en_{\rm B}+\frac{\mu_{\rm B}}{e}(C_{\rm BG}+C_{\rm IL})-\frac{\mu_{\rm T}}{e}C_{\rm IL}$ and $V_{\rm TG}C_{\rm TG}=en_{\rm T}+\frac{\mu_{\rm T}}{e}(C_{\rm TG}+C_{\rm IL})-\frac{\mu_{\rm B}}{e}C_{\rm IL}$, where $C_{\rm IL}$ is the interlayer capacitance between the two TBG subsystems. Because each layer's chemical potential appears in the other layer's gate equation only through $C_{\rm IL}$, tracing a constant-$\mu$ resistance line while the other layer is incompressible converts gate voltages into $(\mu_{\rm B}, n_{\rm B})$ points, and the dimensions of incompressible-state diamonds in the $(V_{\rm TG}, V_{\rm BG})$ plane give the gap sizes $E_{g,\nu}$. The extracted value $C_{\rm IL}=1.6\,\mu{\rm F/cm^2}$ corresponds to a 0.55 nm vacuum separation between the TBG mid-planes, supporting the weak-coupling picture.

What would settle it

A decisive test would be a double-moiré device with the middle twist angle deliberately reduced below about 5°: if interlayer tunneling matters, constant-$\mu$ traces from the top layer would no longer give identical $\mu_{\rm B}$ versus $n_{\rm B}$ curves at different top-layer fillings, and the diamond-edge slopes would deviate from the capacitance-only prediction. Alternatively, Landau-fan spectroscopy at matched densities could reveal tunnel-induced anticrossings between the two subsystems.

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Extended reading notes

Core claim

Two sets of flat bands, one from each twisted bilayer pair, coexist in a four-layer graphene double moiré system and can be gated separately. The paper's central claim is that because the middle interface has a large rotational mismatch, electron tunneling across it is suppressed and the two subsystems conserve their carrier numbers separately, interacting only electrostatically; this allows a thermodynamic analysis (Eq. 1) that converts resistance maps in the two-gate plane into chemical potential versus density curves for each TBG. The resulting data, spanning twist angles 0.91°–1.57°, show that correlated insulators at quarter-multiple moiré fillings appear only near the magic angle, whereas charge-neutrality gaps grow with twist angle away from it, and the hole-side flat band is flatter than the electron side. These trends are reproduced by a self-consistent Hartree calculation that uses a twist-angle-dependent ratio of same-sublattice to different-sublattice interlayer tunneling and a non-local tunneling term. No superconductivity was observed down to 95 mK in these samples, which the authors tie to the flatter valence band and to the different dielectric environment of the double-moiré stack.

Load-bearing premise

Carrier number is separately conserved in each twisted bilayer pair, so the two systems interact only through an interlayer capacitance; if electrons tunnel across the middle interface in non-negligible amounts, the extracted chemical potentials and gap sizes shift.

Editorial extensions

If this is right

  • A single four-layer device can host two flat-band systems at different twist angles, so flat-band correlations can be studied in one stack without mixing the bands.
  • The extracted $\mu$ versus $n$ curves across 0.91°–1.57° provide a thermodynamic reference for TBG flat bands away from the magic angle that agrees with earlier near-magic-angle measurements.
  • The different twist-angle dependence of charge-neutrality gaps and integer-filling gaps indicates that the two types of gaps come from different broken-symmetry states.
  • Because the valence flat band is flatter than the conduction band, the data support the view that superconductivity in these systems is favored on the valence side.
  • Correlated insulators survive in one TBG while another TBG sits nearby, showing that the proximity of a second flat-band system does not by itself destroy the correlated state.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A structural measurement (for example scanning tunneling or transmission electron imaging) could test the model's implicit assumption directly by checking whether lattice corrugation across the stack varies with twist angle in the way the tuned tunneling ratio $\alpha$ implies.
  • If the middle twist angle were deliberately reduced below about 5°, the capacitance-only analysis should break down; the deviation would give a quantitative measure of residual interlayer tunneling between the two TBGs.
  • The same architecture could be reused with one TBG replaced by another kind of two-dimensional system, turning the remaining TBG into a built-in low-temperature chemical-potential sensor for its neighbor.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This manuscript reports transport measurements on a double moiré system of four graphene layers, in which the top and bottom pairs form twisted bilayer graphene (TBG) with small twist angles and the middle interface has a large rotational mismatch. The authors observe resistance peaks in the (VTG, VBG) plane that they attribute to integer fillings of the top and bottom TBG flat bands. Using a thermodynamic model of two capacitively coupled layers with separately conserved densities (Eq. 1), they extract chemical potential versus density curves for each TBG, identify correlated insulators near half and quarter fillings, and report a twist-angle dependence of gaps at neutrality and at integer fillings. They compare the extracted gaps with self-consistent Hartree calculations and find qualitative agreement after adjusting phenomenological parameters. The paper concludes that the two flat bands are independently tunable, and that valence flat bands are flatter than conduction flat bands.

Significance. The paper proposes a new architecture for studying two moiré flat bands in one device and provides a data set spanning twist angles from 0.91° to 1.57°. The temperature dependence in Fig. 4 confirms that some observed resistance peaks are correlated insulators, and the comparison with previous chemical potential measurements of TBG is valuable. However, the central quantitative claim of layer-resolved chemical potentials rests on the assumption of separately conserved densities in the two TBG subsystems, which is undermined by the edge-contact geometry. The Hartree comparison is a parameter fit rather than a prediction. If the contact issue could be resolved or the analysis redone under a common-μ model, the empirical observations might still be of interest, but as presented the main claim is not established.

major comments (3)
  1. [Eq. (1) and SM Sec. I] The thermodynamic model in Eq. (1) assumes that the top and bottom TBG subsystems have separately conserved carrier numbers and are coupled only by an interlayer capacitance C_IL. This assumption is not justified by the device geometry. The samples are four-layer stacks etched into a Hall bar with edge contacts, which contact all graphene layers and thus short the two TBG subsystems at the contacts. Since the channel is shorted to ground (SM Sec. I), the electrochemical potentials of the two subsystems are equal at the contacts and charge can be exchanged between them through the contacts. Consequently, n_T and n_B are not independently conserved, and Eq. (1) is not the correct starting point; a dual-gated conductor with total density and displacement field as independent variables is the standard description. The consistency check after Eq. (3), namely identical μ_B vs n_B at different integer ν_T, does not rule out a common-μ model, because a pinned Fermi level would yield the same apparent bottom-layer relation while the top-layer density changes. This issue directly affects the central claim of measuring layer-resolved chemical potentials and the assignment of resistance peaks to independent layer fillings.
  2. [Fig. 3(c)-(d) and SM Sec. V] The comparison with the self-consistent Hartree approximation is presented as a validation, but the model parameters are set to match the data. As stated in the text, α is set to 0.3 for θ=0.91°, 0.6 for θ=0.99°–1.57°, and 1.0 for θ=1.7° specifically to reproduce the measured Eg,±1, and wNL is arbitrarily set to −20 meV. The paper itself notes that this choice is not a rigorous determination. Therefore, the agreement in Fig. 3(c)-(d) is a fit, not a parameter-free prediction, and it does not provide independent confirmation of the extracted gap sizes or their twist-angle dependence. The manuscript should either constrain α and wNL from independent data or present the curves as fits with an explicit discussion of the parameter uncertainty.
  3. [Figs. 3(b)-(d) and SM Sec. II] The extracted chemical potential curves, gap sizes Eg,ν, and bandwidth measures Δμp and Δμn are reported without error bars or uncertainty propagation. The capacitance values CTG, CBG, and CIL enter directly into Eqs. (2) and (3), and the extraction relies on assumptions such as Δμ_X << eΔV in SM Eq. (S5). The sample-to-sample scatter in Fig. 3 is significant, so without a quantitative uncertainty estimate the claimed twist-angle trends, including the minimum of Eg,0 near the magic angle, are not firmly established. The authors should provide error bars derived from capacitance uncertainties and sample-to-sample variations.
minor comments (4)
  1. [SM Sec. III] SM Sec. III refers to 'Fig. S7(d)' for the boundary of the νT = 0 state, but Fig. S7 is the µ vs n plot; the intended figure appears to be Fig. S5(d).
  2. [General] The main text contains typos, e.g., 'exprimental' in the caption of Fig. 3, and the manuscript would benefit from a careful proofread.
  3. [Fig. 3(d)] In Fig. 3(d), the scattered literature data are not fully identified in the caption; specify which symbols correspond to Refs. 27, 29, 30, and 32.
  4. [Last paragraph] The discussion of superconductivity uses the observed electron-hole asymmetry to speculate that flatter valence bands favor superconductivity, but no superconductivity is observed in this study; this statement should be labeled as a conjecture rather than a conclusion of the present data.

Circularity Check

1 steps flagged · score 5.0 of 10

The Hartree comparison in Fig. 3(c)-(d) is a fitted input presented as a 'prediction': alpha is set per twist angle to reproduce the measured Eg,+/-1, and the SM admits the choice is not a rigorous determination. The central experimental double-moiré extraction itself is not circular.

  1. fitted input called prediction [Main text, Hartree comparison paragraph near Fig. 3(c)-(d); SM Sec. V 'Bistritzer-MacDonald model parameters'.]
    "We compare our exprimental data with the predictions of a self-consistent Hartree approximation ... To qualitatively match the observed variations in insulating gaps across different twist angles, we set α = 0.3 for θ = 0.91◦, α = 0.6 for θ = 0.99◦ to 1.57◦ and α = 1 for θ = 1.7◦, where α is the ratio between same and different sublattice interlayer tunneling and is introduced as a phenomenological parameter (SM. Sec. V [41–43])."

    The theory curves are labeled 'predictions' and are said to 'agree well with experimental measurements,' but α is assigned per twist angle to match the measured Eg,±1, the same gaps being compared. SM Sec. V confirms: 'The specific model parameters α = 0.3 ... are chosen to qualitatively match experimental insulating gaps Eg,±1' and calls the choice 'not a rigorous determination.' Because the main text states the gap features 'are directly influenced by the varying α values,' the Eg,±1 agreement is imposed by the fit, not predicted. ∆µp,n is not the direct fit target and has some independent content, but the fitted-parameter circularity for the gap comparison stands.

full rationale

The core experimental analysis is self-contained rather than circular. Equation (1) is a standard dual-gate thermodynamic model for two capacitively coupled layers; CIL is obtained from diamond-edge slopes (SM Sec. II), and the μB(nB) curves are extracted from constant-μ traces via Eq. (3). The consistency check that μB vs nB is identical at different integer νT is an internal validation of the weak-coupling assumption, not a definitional identity. The experimental finding of two independently tunable TBG subsystems and the twist-angle dependence of correlated insulators do not reduce to the model's outputs. However, the Hartree 'predictions' in Fig. 3(c)-(d) are partially circular: α is chosen per twist angle to reproduce the measured Eg,±1, and the SM expressly disavows the choice as a rigorous determination, so the claimed agreement of calculated gap sizes with experiment is a fit renamed as prediction. The author-group citation [40] for the Hartree scheme is not what carries the argument; the circularity is the parameter fit. Score 5 reflects one important predict-by-fit step while the central experimental thermodynamic extraction remains independent. A separate physical concern about edge contacts shorting the four-layer stack would be a correctness issue, not a circularity of the derivation chain, and is not scored here.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The physical model of two capacitively coupled subsystems with separately conserved densities is the main assumption. The theory comparison introduces two fitted parameters (alpha and wNL) that are adjusted to data, so the 'predictions' in Fig. 3 are not parameter-free. No new fundamental entities are postulated.

free parameters (2)
  • alpha (ratio of same-to-different sublattice interlayer tunneling) = 0.3 for theta=0.91 deg; 0.6 for theta=0.99-1.57 deg; 1.0 for theta=1.7 deg
    Chosen in SM Sec. V to qualitatively match experimental insulating gaps Eg,+1 and Eg,-1. The paper states this is a phenomenological parameter and the choice is not a rigorous determination.
  • wNL (non-local interlayer tunneling strength) = -20 meV (constant)
    Set to a constant for simplicity in the Hartree calculation. The paper states the rigorous value should be twist-angle dependent and experimentally determined.
assumptions (4)
  • domain assumption The two TBG subsystems have separately conserved particle numbers and are electrostatically coupled by a capacitance CIL.
    Invoked in Eq. (1) of the main text and SM Sec. I; this is load-bearing for the chemical potential extraction.
  • domain assumption Electron tunneling between the two TBGs across the large-angle middle interface is negligible and acts only as disorder.
    Stated in the main text after the device description; justifies separate particle-number conservation.
  • domain assumption Resistance peaks in the (VTG, VBG) map correspond to incompressible states of one or both TBGs at integer fillings of the moiré bands.
    Used to assign filling factors and to extract gaps from diamond boundaries.
  • domain assumption The Hartree approximation is adequate for computing insulating gaps when the flat bands are empty or fully filled.
    Used for the dashed curves in Fig. 3(c)-(d); justification is given in the main text with Ref. 40.

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Pith. "Pith review of Independently Tunable Flat Bands and Correlations in a Graphene Double Moir\'e System." pith.science (2026). https://pith.science/paper/454AIFFF

@misc{pith2026241118785,
  author       = {Pith},
  title        = {Pith review of: Independently Tunable Flat Bands and Correlations in a Graphene Double Moir\'e System},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/454AIFFF}},
  note         = {Machine review of arXiv:2411.18785}
}
read the original abstract

We report on a double moir\'e system consisting of four graphene layers, where the top and bottom pairs form small-twist-angle bilayer graphene, and the middle interface has a large rotational mismatch. This system shows clear signatures of two sets of spatially separated flat bands associated with the top and bottom twisted bilayer graphene (TBG) subsystems, each independently tunable. Thermodynamic analysis reveals weak correlations between layers that allow the chemical potential to be measured as a function of carrier density for each constituent TBG. We find that correlated insulating states at integer number of electrons per moir\'e unit cell are most robust near magic angle, whereas gapped states at neutrality are more robust at larger twist angles.

Figures

Figures reproduced from arXiv: 2411.18785 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Brillouin zones of the top (blue) and bottom (red) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. (a), the chemical potential of a constituent TBG close to the magic angle is plotted as a function of car￾rier density and moir´e band filling factor (top axis). We observe jumps near half fillings ν = ±1/2 which we as￾sociate with broken flavor symmetry states induced by strong electron interactions [27, 29, 30]. The jumps oc￾1.0 1.2 1.4 1.6 0 100 200  () p , exp. Ref. 27 n , exp. Ref. 29 p , theory Ref. 30… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (a) shows a contour plot of Rxx as a function of VTG and VBG in a sample with θT = 1.57◦ and θB = 0.99◦ measured at T = 95 mK. The most prominent resistance peaks around VTG = ±8 V signal that the top TBG is incompressible with νT = ±1 [PITH_FULL_IMAGE:figures/full_fi…

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  1. Many-body perturbation theory for moir\'{e} systems

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Reference graph

Works this paper leans on

46 extracted references · 17 canonical work pages · cited by 1 Pith paper

  1. [1]

    Bistritzer \ and\ author A

    author author R. Bistritzer \ and\ author A. H. \ MacDonald ,\ https://doi.org/10.1073/pnas.1108174108 journal journal Proc. Natl. Acad. Sci. \ volume 108 ,\ pages 12233 ( year 2011 ) NoStop

    doi:10.1073/pnas.1108174108 2011

  2. [2]

    Cao , author V

    author author Y. Cao , author V. Fatemi , author S. Fang , author K. Watanabe , author T. Taniguchi , author E. Kaxiras ,\ and\ author P. Jarillo-Herrero ,\ https://doi.org/10.1038/nature26160 journal journal Nature \ volume 556 ,\ pages 43 ( year 2018 a ) NoStop

    doi:10.1038/nature26160

  3. [3]

    Cao , author V

    author author Y. Cao , author V. Fatemi , author A. Demir , author S. Fang , author S. L. \ Tomarken , author J. Y. \ Luo , author J. D. \ Sanchez-Yamagishi , author K. Watanabe , author T. Taniguchi , author E. Kaxiras , author R. C. \ Ashoori ,\ and\ author P. Jarillo-Herrero ,\ https://doi.org/10.1038/nature26154 journal journal Nature \ volume 556 ,\ ...

    doi:10.1038/nature26154

  4. [4]

    Lu , author P

    author author X. Lu , author P. Stepanov , author W. Yang , author M. Xie , author M. A. \ Aamir , author I. Das , author C. Urgell , author K. Watanabe , author T. Taniguchi , author G. Zhang , author A. Bachtold , author A. H. \ MacDonald ,\ and\ author D. K. \ Efetov ,\ https://doi.org/10.1038/s41586-019-1695-0 journal journal Nature \ volume 574 ,\ pa...

    doi:10.1038/s41586-019-1695-0

  5. [5]

    author author A. L. \ Sharpe , author E. J. \ Fox , author A. W. \ Barnard , author J. Finney , author K. Watanabe , author T. Taniguchi , author M. A. \ Kastner ,\ and\ author D. Goldhaber-Gordon ,\ https://doi.org/10.1126/science.aaw3780 journal journal Science \ volume 365 ,\ pages 605 ( year 2019 ) NoStop

    doi:10.1126/science.aaw3780

  6. [6]

    author author K. P. \ Nuckolls , author M. Oh , author D. Wong , author B. Lian , author K. Watanabe , author T. Taniguchi , author B. A. \ Bernevig ,\ and\ author A. Yazdani ,\ https://doi.org/10.1038/s41586-020-3028-8 journal journal Nature \ volume 588 ,\ pages 610 ( year 2020 ) NoStop

    doi:10.1038/s41586-020-3028-8

  7. [7]

    Xie , author A

    author author Y. Xie , author A. T. \ Pierce , author J. M. \ Park , author D. E. \ Parker , author E. Khalaf , author P. Ledwith , author Y. Cao , author S. H. \ Lee , author S. Chen , author P. R. \ Forrester , author K. Watanabe , author T. Taniguchi , author A. Vishwanath , author P. Jarillo-Herrero ,\ and\ author A. Yacoby ,\ https://doi.org/10.1038/...

    doi:10.1038/s41586-021-04002-3

  8. [8]

    Cao , author D

    author author Y. Cao , author D. Chowdhury , author D. Rodan-Legrain , author O. Rubies-Bigorda , author K. Watanabe , author T. Taniguchi , author T. Senthil ,\ and\ author P. Jarillo-Herrero ,\ https://doi.org/10.1103/PhysRevLett.124.076801 journal journal Phys. Rev. Lett. \ volume 124 ,\ pages 076801 ( year 2020 ) NoStop

    doi:10.1103/physrevlett.124.076801

Show all 46 references
  1. [9]

    Jaoui , author I

    author author A. Jaoui , author I. Das , author G. Di Battista , author J. Díez-Mérida , author X. Lu , author K. Watanabe , author T. Taniguchi , author H. Ishizuka , author L. Levitov ,\ and\ author D. K. \ Efetov ,\ https://doi.org/10.1038/s41567-022-01556-5 journal journal...

    doi

  2. [10]

    Yankowitz , author S

    author author M. Yankowitz , author S. Chen , author H. Polshyn , author Y. Zhang , author K. Watanabe , author T. Taniguchi , author D. Graf , author A. F. \ Young ,\ and\ author C. R. \ Dean ,\ https://doi.org/10.1126/science.aav1910 journal journal Science \ volume 363 ,\ p...

    doi

  3. [11]

    Saito , author J

    author author Y. Saito , author J. Ge , author K. Watanabe , author T. Taniguchi ,\ and\ author A. F. \ Young ,\ https://doi.org/10.1038/s41567-020-0928-3 journal journal Nat. Phys. \ volume 16 ,\ pages 926 ( year 2020 ) NoStop

    2020 doi

  4. [12]

    Stepanov , author I

    author author P. Stepanov , author I. Das , author X. Lu , author A. Fahimniya , author K. Watanabe , author T. Taniguchi , author F. H. L. \ Koppens , author J. Lischner , author L. Levitov ,\ and\ author D. K. \ Efetov ,\ https://doi.org/10.1038/s41586-020-2459-6 journal jou...

    doi

  5. [13]

    author author H. S. \ Arora , author R. Polski , author Y. Zhang , author A. Thomson , author Y. Choi , author H. Kim , author Z. Lin , author I. Z. \ Wilson , author X. Xu , author J.-H. \ Chu , author K. Watanabe , author T. Taniguchi , author J. Alicea ,\ and\ author S. Nad...

    doi

  6. [14]

    Chen , author L

    author author G. Chen , author L. Jiang , author S. Wu , author B. Lyu , author H. Li , author B. L. \ Chittari , author K. Watanabe , author T. Taniguchi , author Z. Shi , author J. Jung , author Y. Zhang ,\ and\ author F. Wang ,\ https://doi.org/10.1038/s41567-018-0387-2 jou...

    doi

  7. [15]

    Chen , author A

    author author G. Chen , author A. L. \ Sharpe , author P. Gallagher , author I. T. \ Rosen , author E. J. \ Fox , author L. Jiang , author B. Lyu , author H. Li , author K. Watanabe , author T. Taniguchi , author J. Jung , author Z. Shi , author D. Goldhaber-Gordon , author Y....

    doi

  8. [16]

    author author J. M. \ Park , author Y. Cao , author K. Watanabe , author T. Taniguchi ,\ and\ author P. Jarillo-Herrero ,\ https://doi.org/10.1038/s41586-021-03192-0 journal journal Nature \ volume 590 ,\ pages 249 ( year 2021 a ) NoStop

    doi

  9. [17]

    author author J. M. \ Park , author Y. Cao , author L.-Q. \ Xia , author S. Sun , author K. Watanabe , author T. Taniguchi ,\ and\ author P. Jarillo-Herrero ,\ https://doi.org/10.1038/s41563-022-01287-1 journal journal Nat. Mater. \ volume 21 ,\ pages 877 ( year 2022 ) NoStop

    doi

  10. [18]

    author author G. W. \ Burg , author E. Khalaf , author Y. Wang , author K. Watanabe , author T. Taniguchi ,\ and\ author E. Tutuc ,\ https://doi.org/10.1038/s41563-022-01286-2 journal journal Nat. Mater. \ volume 21 ,\ pages 884 ( year 2022 ) NoStop

    doi

  11. [19]

    Zhang , author R

    author author Y. Zhang , author R. Polski , author C. Lewandowski , author A. Thomson , author Y. Peng , author Y. Choi , author H. Kim , author K. Watanabe , author T. Taniguchi , author J. Alicea , author F. von Oppen , author G. Refael ,\ and\ author S. Nadj-Perge ,\ https:...

    doi

  12. [20]

    author author G. W. \ Burg , author J. Zhu , author T. Taniguchi , author K. Watanabe , author A. H. \ MacDonald ,\ and\ author E. Tutuc ,\ https://doi.org/10.1103/PhysRevLett.123.197702 journal journal Phys. Rev. Lett. \ volume 123 ,\ pages 197702 ( year 2019 ) NoStop

    doi

  13. [21]

    Liu , author Z

    author author X. Liu , author Z. Hao , author E. Khalaf , author J. Y. \ Lee , author Y. Ronen , author H. Yoo , author D. Haei Najafabadi , author K. Watanabe , author T. Taniguchi , author A. Vishwanath ,\ and\ author P. Kim ,\ https://doi.org/10.1038/s41586-020-2458-7 journ...

    doi

  14. [22]

    Chen , author M

    author author S. Chen , author M. He , author Y.-H. \ Zhang , author V. Hsieh , author Z. Fei , author K. Watanabe , author T. Taniguchi , author D. H. \ Cobden , author X. Xu , author C. R. \ Dean ,\ and\ author M. Yankowitz ,\ https://doi.org/10.1038/s41567-020-01062-6 journ...

    doi

  15. [23]

    Xu , author M

    author author S. Xu , author M. M. \ Al Ezzi , author N. Balakrishnan , author A. Garcia-Ruiz , author B. Tsim , author C. Mullan , author J. Barrier , author N. Xin , author B. A. \ Piot , author T. Taniguchi , author K. Watanabe , author A. Carvalho , author A. Mishchenko , ...

    doi

  16. [24]

    Waters , author E

    author author D. Waters , author E. Thompson , author E. Arreguin-Martinez , author M. Fujimoto , author Y. Ren , author K. Watanabe , author T. Taniguchi , author T. Cao , author D. Xiao ,\ and\ author M. Yankowitz ,\ https://doi.org/10.1038/s41586-023-06290-3 journal journal...

    doi

  17. [25]

    Kim , author I

    author author S. Kim , author I. Jo , author D. C. \ Dillen , author D. A. \ Ferrer , author B. Fallahazad , author Z. Yao , author S. K. \ Banerjee ,\ and\ author E. Tutuc ,\ https://doi.org/10.1103/PhysRevLett.108.116404 journal journal Phys. Rev. Lett. \ volume 108 ,\ pages...

    doi

  18. [26]

    Lee , author B

    author author K. Lee , author B. Fallahazad , author J. Xue , author D. C. \ Dillen , author K. Kim , author T. Taniguchi , author K. Watanabe ,\ and\ author E. Tutuc ,\ https://doi.org/10.1126/science.1251003 journal journal Science \ volume 345 ,\ pages 58 ( year 2014 ) NoStop

    doi

  19. [27]

    author author J. M. \ Park , author Y. Cao , author K. Watanabe , author T. Taniguchi ,\ and\ author P. Jarillo-Herrero ,\ https://doi.org/10.1038/s41586-021-03366-w journal journal Nature \ volume 592 ,\ pages 43 ( year 2021 b ) NoStop

    doi

  20. [28]

    Wang , author J

    author author Y. Wang , author J. Herzog-Arbeitman , author G. W. \ Burg , author J. Zhu , author K. Watanabe , author T. Taniguchi , author A. H. \ MacDonald , author B. A. \ Bernevig ,\ and\ author E. Tutuc ,\ https://doi.org/10.1038/s41567-021-01419-5 journal journal Nat. P...

    doi

  21. [29]

    Wong , author K

    author author D. Wong , author K. P. \ Nuckolls , author M. Oh , author B. Lian , author Y. Xie , author S. Jeon , author K. Watanabe , author T. Taniguchi , author B. A. \ Bernevig ,\ and\ author A. Yazdani ,\ https://doi.org/10.1038/s41586-020-2339-0 journal journal Nature \...

    doi

  22. [30]

    Zondiner , author A

    author author U. Zondiner , author A. Rozen , author D. Rodan-Legrain , author Y. Cao , author R. Queiroz , author T. Taniguchi , author K. Watanabe , author Y. Oreg , author F. von Oppen , author A. Stern , author E. Berg , author P. Jarillo-Herrero ,\ and\ author S. Ilani ,\...

    doi

  23. [31]

    Choi , author J

    author author Y. Choi , author J. Kemmer , author Y. Peng , author A. Thomson , author H. Arora , author R. Polski , author Y. Zhang , author H. Ren , author J. Alicea , author G. Refael , author F. von Oppen , author K. Watanabe , author T. Taniguchi ,\ and\ author S. Nadj-Pe...

    doi

  24. [32]

    Yu , author B

    author author J. Yu , author B. A. \ Foutty , author Z. Han , author M. E. \ Barber , author Y. Schattner , author K. Watanabe , author T. Taniguchi , author P. Phillips , author Z.-X. \ Shen , author S. A. \ Kivelson ,\ and\ author B. E. \ Feldman ,\ https://doi.org/10.1038/s...

    doi

  25. [33]

    Oh , author K

    author author M. Oh , author K. P. \ Nuckolls , author D. Wong , author R. L. \ Lee , author X. Liu , author K. Watanabe , author T. Taniguchi ,\ and\ author A. Yazdani ,\ https://doi.org/10.1038/s41586-021-04121-x journal journal Nature \ volume 600 ,\ pages 240 ( year 2021 ) NoStop

    doi

  26. [34]

    author author K. P. \ Nuckolls , author R. L. \ Lee , author M. Oh , author D. Wong , author T. Soejima , author J. P. \ Hong , author D. Călugăru , author J. Herzog-Arbeitman , author B. A. \ Bernevig , author K. Watanabe , author T. Taniguchi , author N. Regnault , author M....

    doi

  27. [35]

    Min , author G

    author author H. Min , author G. Borghi , author M. Polini ,\ and\ author A. H. \ MacDonald ,\ @noop journal journal Phys. Rev. B \ volume 77 ,\ pages 041407(R) ( year 2008 ) NoStop

    2008

  28. [36]

    author author R. T. \ Weitz , author M. T. \ Allen , author B. E. \ Feldman , author J. Martin ,\ and\ author A. Yacoby ,\ @noop journal journal Science \ volume 330 ,\ pages 812 ( year 2010 ) NoStop

    2010

  29. [37]

    Velasco Jr , author L

    author author J. Velasco Jr , author L. Jing , author W. Bao , author Y. Lee , author P. Kratz , author V. Aji , author M. Bockrath , author C. Lau , author C. Varma , author R. Stillwell , et al. ,\ @noop journal journal Nat. Nanotechnol. \ volume 7 ,\ pages 156 ( year 2012 ) NoStop

    2012

  30. [38]

    author author A. H. \ MacDonald , author J. Jung ,\ and\ author F. Zhang ,\ @noop journal journal Phys. Scr. \ volume 2012 ,\ pages 014012 ( year 2012 ) NoStop

    2012

  31. [39]

    Bao , author J

    author author W. Bao , author J. Velasco , author F. Zhang , author L. Jing , author B. Standley , author D. Smirnov , author M. Bockrath , author A. H. \ MacDonald ,\ and\ author C. N. \ Lau ,\ https://doi.org/10.1073/pnas.1205978109 journal journal Proc. Natl. Acad. Sci. \ v...

    doi

  32. [40]

    Zhu , author I

    author author J. Zhu , author I. Torre , author M. Polini ,\ and\ author A. H. \ MacDonald ,\ https://doi.org/10.48550/arXiv.2401.02872 \ note arXiv:2401.02872 [cond-mat] NoStop ( year 2024 )

    2024 doi arXiv

  33. [41]

    Koshino, N

    M. Koshino, N. F. Q. Yuan, T. Koretsune, M. Ochi, K. Kuroki, and L. Fu, Phys. Rev. X , 8, 031087 (2018)

    2018

  34. [42]

    Kang and O

    J. Kang and O. Vafek, Phys. Rev. B , 107, 075408 (2023)

    2023

  35. [43]

    Vafek and J

    O. Vafek and J. Kang, Phys. Rev. B , 107, 075123 (2023)

    2023

  36. [44]

    Xie \ and\ author A

    author author M. Xie \ and\ author A. H. \ MacDonald ,\ https://doi.org/10.1103/PhysRevLett.127.196401 journal journal Phys. Rev. Lett. \ volume 127 ,\ pages 196401 ( year 2021 ) NoStop

    2021 doi

  37. [45]

    Keimer , author S

    author author B. Keimer , author S. A. \ Kivelson , author M. R. \ Norman , author S. Uchida ,\ and\ author J. Zaanen ,\ https://doi.org/10.1038/nature14165 journal journal Nature \ volume 518 ,\ pages 179 ( year 2015 ) NoStop

    2015 doi

  38. [46]

    Su , author M

    author author R. Su , author M. Kuiri , author K. Watanabe , author T. Taniguchi ,\ and\ author J. Folk ,\ https://doi.org/10.1038/s41563-023-01653-7 journal journal Nat. Mater. \ volume 22 ,\ pages 1332 ( year 2023 ) NoStop

    2023 doi

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