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Probing the flat-band limit of the superconducting proximity effect in Twisted Bilayer Graphene Josephson junctions

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

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Pith's one-line read Even in twisted bilayer graphene's flattest bands, the superconducting proximity effect remains strong and the critical current decouples from normal-state conductance.

desk verdict Careful experiment with a real anomaly in Ic-GN scaling, but the interaction-driven explanation is underdetermined because the supercurrent is edge-dominated in the relevant domes. read the letter →

arxiv 2502.04785 v1 pith:FLJ54E2L submitted 2025-02-07 cond-mat.supr-con cond-mat.str-el

A. Diez-Carlon , J. Diez-Merida , P. Rout , D. Sedov , P. Virtanen , S. Banerjee , R. P. S. Penttila , P. Altpeter
show 8 more authors
K. Watanabe T. Taniguchi S.-Y. Yang K. T. Law T. T. Heikkila P. Torma M. S. Scheurer D. K. Efetov
This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el PACS 74.50.+r74.45.+c73.22.Pr
keywords twistedbilayergrapheneflat-bandsuperconductivityJosephsonjunctionproximityeffectcriticalcurrentquantumgeometrydiodemoirématerials
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

Twisted bilayer graphene is two graphene layers stacked at a small twist angle, creating moiré bands that can be made nearly flat, with a width below 10 meV. This paper asks whether those flat bands can still carry a supercurrent when placed between two superconducting electrodes, and it argues that they can: critical currents in the flattest devices are only about a factor of five below those in the dispersive bands, and the $I_c R_N$ product reaches comparable values. It also claims that inside the flat bands the critical current $I_c$ stops following the normal-state conductance $G_N$, which is what would be expected if an interaction-induced excess supercurrent, independent of $G_N$, contributes alongside the usual transport term. If correct, this would mean flat-band weak links are not inherently dead for proximity superconductivity, and that quantum geometry and multiband pairing help determine where superconducting domes form.

What carries the argument

The load-bearing object is the contact-induced pair correlator $\phi_{\mathbf R}=\int_{\mathrm{u.c.}} da\,\langle c_{\downarrow,-}(\mathbf R+a)\cdot c_{\uparrow,+}(\mathbf R+a)\rangle$, a response function of the twisted bilayer graphene bands to the pairing field imposed by the superconducting lead. Computed in a two-band continuum model of twisted bilayer graphene, it splits into a kinetic factor $\phi^{\mathrm{disp}}$ that encodes band dispersion and a Bloch-overlap factor $\phi^{\mathrm{QG}}$ determined by the quantum metric, so the calculation can isolate single-band atomic, single-band geometric, multiband, and interband contributions. For the interaction-induced current, a free-energy expansion around an exact flat band yields $I_c^{\mathrm{int}}\propto \Delta_S^2/U\, e^{-L/L_Q}$ with the coherence length set by the averaged minimal quantum metric $\xi_Q$, and no dependence on the normal-state conductance; this is the mechanism the paper invokes to explain the $I_c$-$G_N$ decoupling. An inversion of the measured interference patterns is used to show that the supercurrent is edge-concentrated in the diode regions.

What would settle it

Make a junction whose supercurrent path and conductance probe coincide, for instance a narrow gate-defined channel with wide superconducting contacts, and compare $I_c$ and $G_N$ across the flat-band dome: if the decoupling disappears, the interaction-induced excess current is not the explanation, while if it persists, the claim survives.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the superconducting proximity effect remains strong in the flat-band limit of twisted bilayer graphene: even for a junction with bandwidth $w<10$ meV the measured critical current reaches $I_c\sim65$ nA, compared with $\sim350$ nA in the dispersive bands, and $I_c R_N$ is comparable at specific fillings. The accompanying anomaly is that $I_c$ and $G_N$ decouple inside the flat bands: as doping moves away from the charge-neutrality point, $G_N$ keeps rising while $I_c$ peaks and falls, and in the domes between $\nu=\pm2$ and $\nu=\pm4$ the current is larger than the small normal conductance would suggest. The paper attributes this excess to strong electron interactions, which produce a critical-current contribution $I_c^{\mathrm{int}}$ that scales with the attractive interaction and not with $G_N$, and it shows that a free-energy estimate gives the observed tens of nanoamperes. Interference patterns at the domes also show a Josephson diode effect, with $I_c^+(B)\neq|I_c^-(B)|$ and $I_c^+(B)=|I_c^-(-B)|$, which the paper reads as spontaneous breaking of $C_{2z}$ and spinless time-reversal symmetry, consistent with a sublattice-polarized state.

Load-bearing premise

The argument assumes that the measured two-terminal normal-state conductance $G_N$ is the correct baseline for the noninteracting supercurrent, so that the observed mismatch with $I_c$ can be attributed to an interaction-driven excess current rather than to the actual edge-dominated supercurrent path having a different conductance than the bulk value.

Editorial extensions

If this is right

  • If the flat-band proximity effect is as strong as reported, flat-band Josephson junctions can serve as superconducting elements even where the Fermi velocity is essentially zero.
  • The collapse of the $I_c\propto G_N$ rule in flat bands means future estimates of critical currents in moiré superconductors cannot be based on normal-state conductance alone.
  • The quantum-geometric and multiband contributions that reproduce dome-shaped $I_c$ regions suggest why intrinsic superconducting domes in twisted bilayer graphene appear between half-filling and the band edges.
  • The programmable Josephson diode, switchable by reversing the magnetic field, makes the observed flat-band domes a candidate platform for superconducting diode devices.
  • The correlation between the diode efficiency and the $I_c$ dome implies that the symmetry-broken phase and the enhanced supercurrent share the same filling range, which a complete theory of interactions in twisted bilayer graphene will need to explain.

Reading between the lines

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

  • If the decoupling mechanism is generic, the same $I_c$-$G_N$ breaking should appear in other flat-band weak links, such as small-angle twisted trilayer graphene or kagome metals, whenever an interaction-induced term dominates.
  • Because the diode appears only in the flat-band domes and the supercurrent there is edge-concentrated, a natural experiment is to vary edge termination or width: if the diode efficiency tracks the edge-to-bulk ratio, the edge channel plays a causal role, whereas if it tracks filling only, the bulk correlated state is responsible.
  • The pair-correlator calculation suggests that the dome positions shift toward the band edges as the bandwidth decreases; mining the existing dataset of intrinsic twisted bilayer graphene superconductors for the same trend would test whether proximity domes and intrinsic domes share a geometric origin.
  • A quantitative theory that includes interactions ought to reproduce both the dome shape and the integer-filling suppression; if it does, the same formalism may connect the diode's symmetry-broken state to the ground states identified in other twisted bilayer graphene experiments.
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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. The manuscript reports transport measurements of NbTiN/TBG/NbTiN Josephson junctions at three twist angles (0.94°, 1.00°, 1.24°) and compares them with control devices at larger twist angles and with monolayer graphene. The central empirical findings are (i) that the critical current remains substantial in the flat-band limit, forming dome-shaped superconducting regions near half-filling and near the band edges, and (ii) that Ic does not scale with the two-terminal normal-state conductance GN in the flat bands, in contrast to the dispersive bands and to the control devices. The authors attribute this anomalous scaling to an interaction-induced excess critical current I_c^int, and support the interpretation with Ginzburg-Landau estimates and with continuum-model calculations of a superconducting pair correlator that separates dispersion, quantum-geometric, and multiband contributions. They also report a Josephson diode effect in the flat-band domes and attribute it to inversion-symmetry breaking in the TBG weak link.

Significance. If the interpretation is correct, the paper provides the first systematic evidence that flat-band weak links can sustain proximity supercurrents with strength comparable to dispersive-band junctions, and that interactions can decouple the critical current from the normal-state conductance. The dataset is substantial: three magic-angle devices, three larger-twist TBG controls, one graphene control, magnetic interference patterns, and temperature and field dependence. The continuum-model correlator calculations offer a useful framework for separating dispersion, quantum-geometric, and multiband contributions. However, the central explanatory claim rests on an assumption about the spatial structure of the normal-state conductance that the paper itself shows to be violated, and the quantitative estimate of I_c^int is fitted rather than predicted. The empirical observations are solid and deserve publication; the interpretation needs to be strengthened or reframed.

major comments (3)
  1. [Section II.B and Supplementary L (Figs. S25-S26)] The claim that the violation of the Ic-GN scaling in the flat-band domes signals an interaction-induced excess critical current assumes that the two-terminal conductance GN is the correct non-interacting baseline. Supplementary L shows, however, that in the very same filling range (e.g., the ν = -2 to -3.5 dome of D2, Fig. S26) the supercurrent is strongly edge-dominated, with the left edge carrying up to three times the bulk supercurrent (Fig. S26d). Because GN is measured across all parallel channels while the supercurrent flows primarily through edge channels, a non-interacting junction with spatially varying channel transparency or filling-dependent edge conductance could produce the observed decoupling between Ic and GN. The manuscript does not provide a spatially resolved GN profile nor a model of how a non-interacting inhomogeneous junction would scale Ic with a properly weighted conductance. This alternative should be ruled out or incorporated before the interaction interpretation is presented as the conclusion.
  2. [Supplementary E] The quantitative support for I_c^int is not independent. The Ginzburg-Landau formula is taken from the self-cited preprint arXiv:2410.23121, and the parameters U ~ 10 micro-eV and xi_q = 40 nm are chosen to reproduce the measured Ic ~ 50 nA; the paper itself labels this an order-of-magnitude check. As such, the calculation cannot be adduced as evidence for the interaction origin of the excess current. The authors should either derive I_c^int from a microscopic model of TBG with realistic parameters or provide a distinct experimental signature that discriminates the interaction mechanism from the inhomogeneous-baseline alternative.
  3. [Section II.C and Supplementary F] The comparison between the computed pair correlator phi_R and the measured critical current is heuristic: the paper assumes a monotonic relation between phi_R and Ic without deriving the current from the correlator. As the authors note in Supplementary F, the correlator is a response function, not the supercurrent. The qualitative agreement with dome positions is suggestive, but the calculation should be framed as a qualitative indicator rather than as a test of the quantum-geometric and multiband mechanisms, or it should be extended to compute Ic directly.
minor comments (4)
  1. [Supplementary E] The displayed equation for I_c^int is garbled by missing division bars; it should read I_c^int = (8e/ℏ)(W L_ξ/A_m)(Δ_S^2/U)(1 - U/(4 k_B T)) exp(-L/L_ξ).
  2. [Abstract] The phrase 'the first detailed study of the SC proximity effect in the flat-band limit' should be qualified with respect to the gate-defined TBG Josephson junctions in Refs. [28,29], whose geometry differs but which also probe proximity in flat bands.
  3. [Fig. 5d-e] The error bars on the diode efficiency are shown but their derivation is not described; Supplementary K discusses extraction but not the error estimate.
  4. [Section II.A] In the sentence 'this is seen in Fig. 1f, were we measure the differential resistance', 'were' should be 'where'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the main empirical observations are direct measurements; the interaction-excess interpretation is explicitly tentative and its GL estimate is an order-of-magnitude check, not a fitted prediction.

full rationale

The paper's central observations — strong proximity effect in the flat bands and the Ic versus GN scaling violation — are direct transport measurements, not outputs of a fitted model. The theoretical support for the 'excess critical current' interpretation is presented in Supplementary E as a Ginzburg-Landau derivation that explicitly yields a GN-independent term; the parameters (U~10 μeV, xi=40 nm) are chosen to show that plausible scales can give Ic~50 nA, and the text explicitly labels this an 'order of magnitude check' and states that 'a thorough analysis ... would require a more microscopic theory'. No fitted parameter is renamed as a prediction. The quantum-geometric/multiband correlator calculation (Supplementary F) is parameter-free after the Bistritzer-MacDonald model and is compared qualitatively with the data, so it is not circular. The self-citations to Refs. [7,8,9,13] support the GL framework but are not the sole load-bearing basis for the measured claims; the JDE interpretation is a literature-based symmetry classification rather than a self-referential derivation. The alternative explanation raised by the Dynes-Fulton edge-current analysis is a plausible correctness challenge to the GN baseline, not a circularity: it does not amount to Eq. X = Eq. Y by construction or to a fitted parameter presented as a prediction. Therefore no circular step is identified.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central empirical findings are supported by the measurements and controls, but the theoretical interpretation introduces three free parameters (U, xi_q, T) chosen to reproduce the observed Ic magnitude in the Ginzburg-Landau estimate. The paper relies on standard TBG modeling (Bistritzer-MacDonald) and on a monotonicity assumption linking a computed correlator to Ic. No new physical entities are introduced.

free parameters (3)
  • attractive interaction U = ~10 micro-eV
    In Supplementary E, U is set to ~10 micro-eV to make the Ginzburg-Landau estimate of I_c^int approach the experimentally observed Ic ~ 50 nA.
  • quantum metric length xi_q = 40 nm
    Set in Supplementary E to get I_c^int ~ 50 nA, quoted as consistent with Refs [8,9].
  • temperature T for GL estimate = 100 mK
    Used in Supplementary E to evaluate the I_c^int formula; the experimental base temperature is 35 mK, so 100 mK is a chosen scale.
assumptions (5)
  • domain assumption The superconducting pair correlator phi_R is a monotonic function of the critical current Ic, so comparing phi_R with Ic is valid.
    Stated in Supplementary F.1: 'As we expect a monotonic relation between phi_R and the critical current, the main features ... are expected to be captured by phi_R.' This is load-bearing for the theory-data comparison in Fig. 4.
  • domain assumption The contact-induced pairing amplitude is slowly varying within a unit cell and can be represented as local, Delta(R+a) approximately Delta(R), with a Debye cutoff ~50 meV for the NbTiN phonon-mediated pairing.
    Used in the derivation in Supplementary F.1 and F.3 to define the pairing correlator and restrict the calculation to the flat bands.
  • standard math The Bistritzer-MacDonald continuum model with parameters t=2.97 eV, w_AA=110 meV, w_AB=80 meV accurately describes TBG bands and Bloch states.
    Standard model for TBG, parameters from literature; used for all numerical calculations of band structure and correlators.
  • domain assumption The symmetry-based classification of possible symmetry-broken states in TBG at fillings |nu|>2 is exhaustive enough to conclude that a sublattice-polarized phase with opposite Chern numbers is the only candidate consistent with the observed Josephson diode effect.
    In Section II.D, after ruling out valley polarization and intervalley coherent or Kekule spiral states based on their symmetries, the authors conclude a sublattice-polarized phase emerges as the only candidate. This assumes no other phases outside the listed set can break C2x and spinless TRS while preserving the observations.
  • domain assumption TBG satisfies spinless time-reversal symmetry with xi_{k,eta,n}=xi_{-k,-eta,n} and u*_{k,eta,n}=u_{-k,-eta,n}.
    Used in the derivation of the pairing correlator in Supplementary F.1 to reduce the expression to a single valley.

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Pith. "Pith review of Probing the flat-band limit of the superconducting proximity effect in Twisted Bilayer Graphene Josephson junctions." pith.science (2026). https://pith.science/paper/FLJ54E2L

@misc{pith2026250204785,
  author       = {Pith},
  title        = {Pith review of: Probing the flat-band limit of the superconducting proximity effect in Twisted Bilayer Graphene Josephson junctions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FLJ54E2L}},
  note         = {Machine review of arXiv:2502.04785}
}
read the original abstract

While extensively studied in normal metals, semimetals and semiconductors, the superconducting (SC) proximity effect remains elusive in the emerging field of flat-band systems. In this study we probe proximity-induced superconductivity in Josephson junctions (JJs) formed between superconducting NbTiN electrodes and twisted bilayer graphene (TBG) weak links. Here the TBG acts as a highly tunable topological flat-band system, which due to its twist-angle dependent bandwidth, allows to probe the SC proximity effect at the crossover from the dispersive to the flat-band limit. Contrary to our original expectations, we find that the SC remains strong even in the flat-band limit, and gives rise to broad, dome shaped SC regions, in the filling dependent phase diagram. In addition, we find that unlike in conventional JJs, the critical current Ic strongly deviates from a scaling with the normal state conductance GN. We attribute these findings to the onset of strong electron interactions, which can give rise to an excess critical current, and also work out the potential importance of quantum geometric terms as well as multiband pairing mechanisms. Our results present the first detailed study of the SC proximity effect in the flat-band limit and shed new light on the mechanisms that drive the formation of SC domes in flat-band systems.

Figures

Figures reproduced from arXiv: 2502.04785 by the authors.

Figure 1
Figure 1. Superconducting proximity effect in a TBG Josephson junction. a, [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Strength of the proximity effect and relation between critical current and normal conductance. a, Product of the critical current and normal-state resistance, 𝐼ୡ𝑅୒, as a function of the moiré filling factor ν. b, Critical current 𝐼ୡ in blue (left axis) and normal-state conductance 𝐺୒ in red (right axis), both as a function of ν. Following the same color code, the dashed vertical arrows indicate whether the correspon… view at source ↗
Figure 5
Figure 5. Josephson diode effect and inversion symmetry breaking at the | [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

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Reference graph

Works this paper leans on

73 extracted references · 60 canonical work pages · cited by 1 Pith paper

  1. [1]

    P. G. De Gennes, Boundary Effects in Superconductors, Rev. Mod. Phys. 36, 225 (1964)

    work page 1964

  2. [2]

    K. K. Likharev, Superconducting weak links, Rev. Mod. Phys. 51, 101 (1979)

    1979

  3. [3]

    T. M. Klapwijk, Proximity Effect From an Andreev Perspective, J. Supercond. 17, 593 (2004)

    work page 2004

  4. [5]

    A. A. Golubov, M. Yu. Kupriyanov, and E. Il’ichev, The current-phase relation in Josephson junctions, Rev. Mod. Phys. 76, 411 (2004)

    work page 2004

  5. [6]

    Li et al., Realization of flat band with possible nontrivial topology in electronic Kagome lattice, Sci

    Z. Li et al., Realization of flat band with possible nontrivial topology in electronic Kagome lattice, Sci. Adv. 4, eaau4511 (2018)

    work page 2018

  6. [7]

    Kang et al., Dirac fermions and flat bands in the ideal kagome metal FeSn, Nat

    M. Kang et al., Dirac fermions and flat bands in the ideal kagome metal FeSn, Nat. Mater. 19, 163 (2020)

    work page 2020

  7. [8]

    Balents, C

    L. Balents, C. R. Dean, D. K. Efetov, and A. F. Young, Superconductivity and strong correlations in moiré flat bands, Nat. Phys. 16, 725 (2020)

    work page 2020

  8. [9]

    Mukherjee, A

    S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, and R. R. Thomson, Observation of a Localized Flat-Band State in a Photonic Lieb Lattice, Phys. Rev. Lett. 114, 245504 (2015)

    work page 2015

Show all 73 references
  1. [10]

    Julku, S

    A. Julku, S. Peotta, T. I. Vanhala, D.-H. Kim, and P. Törmä, Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band, Phys. Rev. Lett. 117, 045303 (2016)

    2016

  2. [11]

    Ahmadkhani and M

    S. Ahmadkhani and M. V. Hosseini, Superconducting proximity effect in flat band systems, J. Phys. Condens. Matter 32, 315504 (2020)

    2020

  3. [12]

    Z. C. F. Li, Y. Deng, S. A. Chen, D. K. Efetov, and K. T. Law, Flat Band Josephson Junctions with Quantum Metric, arXiv:2404.09211

    arXiv

  4. [14]

    Peotta and P

    S. Peotta and P. Törmä, Superfluidity in topologically nontrivial flat bands, Nat. Commun. 6, 1 (2015)

    2015

  5. [15]

    Törmä, S

    P. Törmä, S. Peotta, and B. A. Bernevig, Superfluidity and Quantum Geometry in Twisted Multilayer Systems, Nat. Rev. Phys. 4, 528 (2022)

    2022

  6. [16]

    Tian et al., Evidence for Dirac flat band superconductivity enabled by quantum geometry, Nature 614, 440 (2023)

    H. Tian et al., Evidence for Dirac flat band superconductivity enabled by quantum geometry, Nature 614, 440 (2023)

    2023

  7. [17]

    Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature 556, 43 (2018)

    2018

  8. [18]

    Lu et al., Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene, Nature 574, 653 (2019)

    X. Lu et al., Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene, Nature 574, 653 (2019). 15

    2019

  9. [19]

    Cao et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature 556, 80 (2018)

    Y. Cao et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature 556, 80 (2018)

    2018

  10. [20]

    Yankowitz, S

    M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Tuning superconductivity in twisted bilayer graphene, Science 363, 1059 (2019)

    2019

  11. [21]

    Serlin, C

    M. Serlin, C. L. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. F. Young, Intrinsic quantized anomalous Hall effect in a moiré heterostructure, Science 367, 900 (2020)

    2020

  12. [22]

    K. P. Nuckolls, M. Oh, D. Wong, B. Lian, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Strongly correlated Chern insulators in magic-angle twisted bilayer graphene, Nat. 2020 5887839 588, 610 (2020)

    2020

  13. [23]

    I. Das, X. Lu, J. Herzog-Arbeitman, Z.-D. Song, K. Watanabe, T. Taniguchi, B. A. Bernevig, and D. K. Efetov, Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene, Nat. Phys. 17, 710 (2021)

    2021

  14. [25]

    Bussmann-Holder, H

    A. Bussmann-Holder, H. Keller, A. Simon, and A. Bianconi, Multi-Band Superconductivity and the Steep Band/Flat Band Scenario, Condens. Matter 4, 4 (2019)

    2019

  15. [26]

    Christos, S

    M. Christos, S. Sachdev, and M. S. Scheurer, Nodal band-off-diagonal superconductivity in twisted graphene superlattices, Nat. Commun. 14, 1 (2023)

    2023

  16. [27]

    Khasanov, B.-B

    R. Khasanov, B.-B. Ruan, Y.-Q. Shi, G.-F. Chen, H. Luetkens, Z.-A. Ren, and Z. Guguchia, Tuning of the flat band and its impact on superconductivity in Mo5Si3−xPx, Nat. Commun. 15, 2197 (2024)

    2024

  17. [28]

    F. K. de Vries, E. Portolés, G. Zheng, T. Taniguchi, K. Watanabe, T. Ihn, K. Ensslin, and P. Rickhaus, Gate-defined Josephson junctions in magic-angle twisted bilayer graphene, Nat. Nanotechnol. 16, 7 (2021)

    2021

  18. [29]

    Rodan-Legrain, Y

    D. Rodan-Legrain, Y. Cao, J. M. Park, S. C. de la Barrera, M. T. Randeria, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Highly tunable junctions and non-local Josephson effect in magic-angle graphene tunnelling devices, Nat. Nanotechnol. 16, 7 (2021)

    2021

  19. [30]

    Díez-Mérida et al., Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene, Nat

    J. Díez-Mérida et al., Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene, Nat. Commun. 14, 1 (2023)

    2023

  20. [34]

    Bistritzer and A

    R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. U. S. A. 108, 12233 (2011). 16

    2011

  21. [35]

    J. Hu, C. Wu, and X. Dai, Proposed Design of a Josephson Diode, Phys. Rev. Lett. 99, 067004 (2007)

    2007

  22. [36]

    F. Ando, Y. Miyasaka, T. Li, J. Ishizuka, T. Arakawa, Y. Shiota, T. Moriyama, Y. Yanase, and T. Ono, Observation of superconducting diode effect, Nat. 2020 5847821 584, 373 (2020)

    2020

  23. [37]

    Nadeem, M

    M. Nadeem, M. S. Fuhrer, and X. Wang, The superconducting diode effect, Nat. Rev. Phys. 5, 558 (2023)

    2023

  24. [38]

    J.-X. Lin, P. Siriviboon, H. D. Scammell, S. Liu, D. Rhodes, K. Watanabe, T. Taniguchi, J. Hone, M. S. Scheurer, and J. I. A. Li, Zero-field superconducting diode effect in small-twist- angle trilayer graphene, Nat. Phys. 18, 10 (2022)

    2022

  25. [39]

    Tseng, X

    C.-C. Tseng, X. Ma, Z. Liu, K. Watanabe, T. Taniguchi, J.-H. Chu, and M. Yankowitz, Anomalous Hall effect at half filling in twisted bilayer graphene, Nat. Phys. 18, 1038 (2022)

    2022

  26. [40]

    Hu, Z.-T

    J.-X. Hu, Z.-T. Sun, Y.-M. Xie, and K. T. Law, Josephson Diode Effect Induced by Valley Polarization in Twisted Bilayer Graphene, Phys. Rev. Lett. 130, 266003 (2023)

    2023

  27. [41]

    Jiang, X

    Y. Jiang, X. Lai, K. Watanabe, T. Taniguchi, K. Haule, J. Mao, and E. Y. Andrei, Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene, Nature 573, 91 (2019)

    2019

  28. [42]

    Y. Cao, D. Rodan-Legrain, J. M. Park, N. F. Q. Yuan, K. Watanabe, T. Taniguchi, R. M. Fernandes, L. Fu, and P. Jarillo-Herrero, Nematicity and competing orders in superconducting magic-angle graphene, Science 372, 264 (2021)

    2021

  29. [43]

    K. P. Nuckolls et al., Quantum textures of the many-body wavefunctions in magic-angle graphene, Nature 620, 525 (2023)

    2023

  30. [44]

    Bultinck, E

    N. Bultinck, E. Khalaf, S. Liu, S. Chatterjee, A. Vishwanath, and M. P. Zaletel, Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling, Phys. Rev. X 10, 031034 (2020)

    2020

  31. [45]

    Christos, S

    M. Christos, S. Sachdev, and M. S. Scheurer, Correlated Insulators, Semimetals, and Superconductivity in Twisted Trilayer Graphene, Phys. Rev. X 12, 021018 (2022)

    2022

  32. [47]

    M. R. Sinko, S. C. De La Barrera, O. Lanes, K. Watanabe, T. Taniguchi, S. Tan, D. Pekker, M. Hatridge, and B. M. Hunt, Superconducting contact and quantum interference between two-dimensional van der Waals and three-dimensional conventional superconductors, Phys. Rev. Mater. 5...

    2021

  33. [49]

    Golod and V

    T. Golod and V. M. Krasnov, Demonstration of a superconducting diode-with-memory, operational at zero magnetic field with switchable nonreciprocity, Nat. Commun. 13, 1 (2022). 17

    2022

  34. [50]

    Tafuri, Fundamentals and Frontiers of the Josephson Effect, Vol

    F. Tafuri, Fundamentals and Frontiers of the Josephson Effect, Vol. 286 (Springer International Publishing, 2019)

    2019

  35. [51]

    J. R. Clem, Josephson junctions in thin and narrow rectangular superconducting strips, Phys. Rev. B - Condens. Matter Mater. Phys. 81, (2010)

    2010

  36. [55]

    Chen et al., Current induced hidden states in Josephson junctions, Nat

    S. Chen et al., Current induced hidden states in Josephson junctions, Nat. Commun. 15, 8059 (2024)

    2024

  37. [56]

    Alvarado, P

    M. Alvarado, P. Burset, and A. L. Yeyati, Intrinsic nonmagnetic ${\ensuremath{\phi}}_{0}$ Josephson junctions in twisted bilayer graphene, Phys. Rev. Res. 5, L032033 (2023)

    2023

  38. [57]

    Sainz-Cruz, P

    H. Sainz-Cruz, P. A. Pantaleón, V. T. Phong, A. Jimeno-Pozo, and F. Guinea, Junctions and Superconducting Symmetry in Twisted Bilayer Graphene, Phys. Rev. Lett. 131, 016003 (2023)

    2023

  39. [58]

    C.-Z. Chen, J. J. He, M. N. Ali, G.-H. Lee, K. C. Fong, and K. T. Law, Asymmetric Josephson effect in inversion symmetry breaking topological materials, Phys. Rev. B 98, 075430 (2018)

    2018

  40. [59]

    Endres, A

    M. Endres, A. Kononov, H. S. Arachchige, J. Yan, D. Mandrus, K. Watanabe, T. Taniguchi, and C. Schönenberger, Current–Phase Relation of a WTe2 Josephson Junction, Nano Lett. 23, 4654 (2023). 18 Acknowledgements: With thank Srijit Goswami for help in sample fabrication. D.K.E. ...

    2023

  41. [60]

    Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4, 80799 München, Germany

  42. [61]

    Munich Center for Quantum Science and Technology (MCQST), München, Germany

  43. [62]

    Institute for Theoretical Physics III, University of Stuttgart, 70550 Stuttgart, Germany

  44. [63]

    Box 35 (YFL), FI-40014 University of Jyväskylä, Finland

    Department of Physics and Nanoscience Center, University of Jyväskylä, P.O. Box 35 (YFL), FI-40014 University of Jyväskylä, Finland

  45. [64]

    Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland

  46. [65]

    Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

  47. [66]

    International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

  48. [67]

    Southern University of Science and Technology, Shenzhen 518055, P.R. China

  49. [68]

    laser-and-stack

    Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China *E-mail: dmitri.efetov@lmu.de Table of Contents A.- Methods B.- Additional information about devices D1-3 C.- Transport characterization of devices D1-3 D.- Conventional features in TBG JJs...

  50. [69]

    D. J. Thoen, B. G. C. Bos, E. A. F. Haalebos, T. M. Klapwijk, J. J. A. Baselmans, and A. Endo, Superconducting NbTin Thin Films With Highly Uniform Properties Over a \varnothing 100 mm Wafer, IEEE Trans. Appl. Supercond. 27, 1 (2017)

    2017

  51. [70]

    J. G. Kroll et al., Magnetic-Field-Resilient Superconducting Coplanar-Waveguide Resonators for Hybrid Circuit Quantum Electrodynamics Experiments, Phys. Rev. Appl. 11, 064053 (2019)

    2019

  52. [71]

    Dubos, H

    P. Dubos, H. Courtois, B. Pannetier, F. K. Wilhelm, A. D. Zaikin, and G. Schön, Josephson critical current in a long mesoscopic S-N-S junction, Phys. Rev. B 63, 064502 (2001)

    2001

  53. [72]

    Tinkham, Introduction to Superconductivity (Dover, Mineola, 1996)

    M. Tinkham, Introduction to Superconductivity (Dover, Mineola, 1996)

    1996

  54. [73]

    H. B. Heersche, P. Jarillo-Herrero, J. B. Oostinga, L. M. K. Vandersypen, and A. F. Morpurgo, Bipolar supercurrent in graphene, Nature 446, 56 (2007)

    2007

  55. [74]

    J. R. Williams, D. A. Abanin, L. Dicarlo, L. S. Levitov, and C. M. Marcus, Quantum Hall conductance of two-terminal graphene devices, Phys. Rev. B - Condens. Matter Mater. Phys. 80, (2009)

    2009

  56. [75]

    Virtanen, R

    P. Virtanen, R. P. S. Penttilä, P. Törmä, A. Díez-Carlón, D. K. Efetov, and T. T. Heikkilä, Superconducting Junctions with Flat Bands, arXiv:2410.23121

    arXiv

  57. [76]

    S. A. Chen and K. T. Law, Ginzburg-Landau Theory of Flat-Band Superconductors with Quantum Metric, Phys. Rev. Lett. 132, 026002 (2024)

    2024

  58. [77]

    J.-X. Hu, S. A. Chen, and K. T. Law, Anomalous Coherence Length in Superconductors with Quantum Metric, https://arxiv.org/abs/2308.05686v5

    arXiv

  59. [78]

    Bistritzer and A

    R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. U. S. A. 108, 12233 (2011)

    2011

  60. [79]

    Hazra et al., Superconducting properties of NbTiN thin films deposited by high- temperature chemical vapor deposition, Phys

    D. Hazra et al., Superconducting properties of NbTiN thin films deposited by high- temperature chemical vapor deposition, Phys. Rev. B 97, 144518 (2018)

    2018

  61. [80]

    Portolés, S

    E. Portolés, S. Iwakiri, G. Zheng, P. Rickhaus, T. Taniguchi, K. Watanabe, T. Ihn, K. Ensslin, and F. K. de Vries, A tunable monolithic SQUID in twisted bilayer graphene, Nat. Nanotechnol. 2022 1711 17, 1159 (2022)

    2022

  62. [81]

    R. Jha, M. Endres, K. Watanabe, T. Taniguchi, M. Banerjee, C. Schönenberger, and P. Karnatak, Large Tunable Kinetic Inductance in a Twisted Graphene Superconductor, arXiv:2403.02320

    arXiv

  63. [82]

    Iwakiri et al., Tunable quantum interferometer for correlated moiré electrons, Nat

    S. Iwakiri et al., Tunable quantum interferometer for correlated moiré electrons, Nat. Commun. 15, 1 (2024)

    2024

  64. [83]

    R. C. Dynes and T. A. Fulton, Supercurrent Density Distribution in Josephson Junctions, Phys. Rev. B 3, 3015 (1971)

    1971

  65. [84]

    S. Hart, H. Ren, T. Wagner, P. Leubner, M. Mühlbauer, C. Brüne, H. Buhmann, L. W. Molenkamp, and A. Yacoby, Induced superconductivity in the quantum spin Hall edge, Nat. Phys. 10, 638 (2014)

    2014

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.