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The paper argues that doping AB-stacked twisted SnSe2 away from its antiferromagnetic half-filled state produces an intravalley, extended s-wave superconducting state mediated by valley-selective spin fluctuations, establishing M-point moir

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2026-08-01 06:54 UTC pith:G2LOASNA

load-bearing objection First FRG prediction of superconductivity in an M-point moiré material — internally consistent and well-documented, but the extended s-wave mechanism's robustness to twist-angle tuning is untested. the 2 major comments →

arxiv 2607.27492 v1 pith:G2LOASNA submitted 2026-07-29 cond-mat.supr-con cond-mat.str-el

Extended s-wave superconductivity in M-point twisted bilayer SnSe2

Lennart Klebl , Ammon Fischer , Salahudin V. Smailagi\'c , Ming-Rui Li , Henning Schl\"omer , Haoyu Hu , B. Andrei Bernevig , Dante M. Kennes
show 1 more author
Ronny Thomale
This is my paper
classification cond-mat.supr-con cond-mat.str-el
keywords twisted bilayer SnSe2M-valley moiré materialsunconventional superconductivityextended s-wave pairingfunctional renormalization groupspin-fluctuation mechanismantiferromagnetic ordermoiré flat bands
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that AB-stacked twisted bilayer SnSe2, whose low-energy electrons live at three M points and form quasi-one-dimensional Fermi surfaces, becomes superconducting when slightly doped away from an antiferromagnetic state at half filling. Using functional renormalization group simulations of a first-principles Wannier model with long-ranged Coulomb interactions, the authors find an intravalley, extended s-wave superconducting state at electron fillings around two and four electrons per moiré cell, driven by valley-selective spin fluctuations. The pairing is unconventional: the attractive glue comes from high-energy antiferromagnetic fluctuations that connect virtual states away from the Fermi level, so the gap changes sign off-shell while remaining quasi-nodeless on the Fermi surface. If correct, the result casts M-point moiré materials as a tunable quantum simulation platform with phenomenological parallels to iron-pnictide superconductors.

Core claim

The central claim is that the phase diagram of 6.01-degree AB-stacked twisted SnSe2, computed with the functional renormalization group, contains an intravalley extended s-wave superconducting phase flanking an antiferromagnetic dome. At half filling (three electrons per moiré cell) the leading instability is a quasi-one-dimensional antiferromagnetic stripe order; doping to roughly two or four electrons turns the same spin fluctuations into pairing glue. The extended s-wave gap benefits from off-shell scattering: the leading magnetic fluctuations connect particle and hole states detuned from the Fermi level, and the sign change required for attractive pairing takes place away from the Fermi

What carries the argument

The argument rests on a multi-orbital Wannier model of AB-stacked twisted SnSe2 in which the three M-valley bands map onto an approximate Kagome lattice with strong kinetic anisotropy (about 0.19 at 6.01 degrees). The carrier of the mechanism is the banded, quasi-one-dimensional Fermi surface: line-shaped Fermi surfaces keep the antiferromagnetic spin-fluctuation vertex large along an entire strip of transfer momenta parallel to the Fermi surface, not just at a single nesting vector. The functional renormalization group flow with a truncated-unity basis resolves competing particle-particle and particle-hole channels, and a linearized gap equation built from the renormalized magnetic vertex i

Load-bearing premise

The predictions stand or fall on the quasi-one-dimensional, line-shaped Fermi surface of the non-interacting Wannier model at 6.01 degrees (kinetic anisotropy about 0.19); if lattice relaxation, strain, or correlation-driven reconstruction turns those lines into two-dimensional pockets, the extended s-wave phase would move or disappear.

What would settle it

Measure the Fermi surface and pairing gap of gated AB-stacked twisted SnSe2 around fillings two and four electrons per moiré cell using quantum oscillations, angle-resolved photoemission, or tunneling spectroscopy: if the Fermi surface is made of two-dimensional pockets rather than one-dimensional lines, or if the gap shows nodes on the Fermi surface, the predicted off-shell extended s-wave mechanism is falsified. A sharp companion test: the antiferromagnetic fluctuation vector near the m point should remain the dominant magnetic channel, and the superconducting dome should track it as the die

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Gate-tuning a twisted SnSe2 device from half filling toward two or four electrons per moiré cell should reveal superconductivity emerging next to an antiferromagnetic insulating state, with critical scales large enough to be experimentally relevant.
  • The superconducting gap should appear nearly nodeless in probes that sample the Fermi surface, unlike the nodal p- or d-wave states found at lower filling.
  • Because the three valleys are kinetically decoupled, the superconducting state behaves as three weakly Josephson-coupled, highly anisotropic condensates within one sample.
  • The same off-shell pairing mechanism is expected to carry over to other M-valley materials and to systems in the dimensional-crossover regime.
  • The phase diagram gives a concrete route to test spin-fluctuation-mediated pairing: the magnetic dome and the adjacent s-wave superconducting domes should move together as the dielectric environment is varied.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Because the mechanism relies on kinetic anisotropy, varying the twist angle should tune between banded one-dimensional Fermi surfaces and two-dimensional pockets; a testable extension is that the extended s-wave dome shrinks or changes symmetry as the anisotropy decreases.
  • The off-shell sign change implies that energy-resolved spectroscopies might reveal a sign change away from the Fermi level even when the Fermi-surface gap looks nodeless, a distinguishing signature not tested in the paper.
  • The three decoupled intravalley superconductors invite experiments on inter-valley Josephson coupling and collective modes, a direction the authors only hint at.
  • The paper itself flags that the FRG starts from a two-dimensional limit yet predicts quasi-one-dimensional physics; benchmarking against strictly one-dimensional methods such as coupled-wire or sign-problem-free quantum Monte Carlo simulations would settle whether the s-wave phase survives beyond the ladder-type approximation.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper studies a first-principles Wannier model of AB-stacked twisted SnSe2 at θ = 6.01°, with dual-gated Coulomb interactions, using truncated-unity functional renormalization group (TUFRG). The resulting phase diagram as a function of filling ν and dielectric constant ε shows an intravalley antiferromagnetic stripe state at half-filling ν = 3, extended s-wave superconductivity at ν ≈ 2 and ν ≈ 4 flanking the AFM dome, and competing s-, p-, and d-wave states near the lower Van Hove filling. The authors attribute the extended s-wave pairing to valley-selective spin fluctuations with a quasi-one-dimensional, banded character and to off-shell particle-hole states detuned from the Fermi level, drawing an explicit analogy to iron-pnictide superconductors. The Supplemental Material documents the Wannier model, TUFRG implementation, the intraorbital bilinear approximation (IOBI), and the linearized gap equation.

Significance. If robust, the result would extend moiré superconductivity to M-valley systems with intravalley pairing and would provide a concrete, falsifiable prediction for gate-screened twisted SnSe2. The paper has real strengths: the FRG phase diagram is internally consistent, the IOBI treatment reproduces the extended s-wave result on both sides of the dSC region, convergence with rmax was checked, and the simulation code and model data are made available. No superconducting order parameter is fitted to experiment; the phases emerge from the microscopic model. The main significance depends, however, on the claim that the quasi-one-dimensional Fermi surface is essential for the off-shell s-wave mechanism, and this claim has not yet been tested across twist angles or against the static-vertex approximation. The platform-level generalization to all M-point moiré materials therefore rests on an unquantified robustness assumption.

major comments (2)
  1. [Microscopic Pairing Mechanism; Tables S1.1/S1.2] The central mechanistic claim is that the quasi-one-dimensional, banded Fermi surface is essential for the extended s-wave state (main text: 'the quasi-one-dimensional character of AB-stacked tSnSe2 is essential'), but all FRG results are for a single twist angle, θ = 6.01°, where α = |t⧵1/t∥1| ≈ 0.19. Table S1.2 shows that α varies dramatically with θ in the same model: α ≈ 2.01 at 3.89°, 0.48 at 5.09°, and 0.026 at 7.34°. No calculation is presented at any other angle, nor a controlled scan in α with fixed Wannier orbitals. If the sSC dome at ν ≈ 2,4 disappears for α ≈ 0.48 or α ≈ 0.026, the proposed iron-pnictide analogy and the 'quantum simulation platform' statement would apply only in a narrow parameter window. This is a load-bearing robustness gap, not a stylistic issue. I request at least one FRG run at a neighboring angle (e.g., 5.09° or 7.34°) or an explicit α-tuning within the
  2. [Functional renormalization group analysis; Summary & Outlook] The off-shell extended s-wave mechanism is inferred from a frequency-independent, static-vertex FRG flow. The paper argues that at relatively large Λc, pairing receives decisive contributions from virtual states detuned from the Fermi level, with the order parameter changing sign off the Fermi surface. These energy-sensitive processes are exactly where the static approximation is least controlled: the vertex carries no frequency structure, and particle-hole and particle-particle bubbles are evaluated with static propagators. The paper itself acknowledges in the Summary & Outlook that benchmarking against strictly one-dimensional or quantum Monte Carlo methods remains necessary. As it stands, the statement that the system 'overcomes the algebraic energetic penalty for off-shell sign changes' is an inference from a static truncation. A concrete, minimal test would be to verify that the sSC
minor comments (4)
  1. [Footnote [74]; Fig. 2] The sampling range is stated as (ν,ε) ∈ [0,6]×[12,16], but the Fig. 2 ε-axis runs to 60 and the text describes superconducting domes extending to 'large ε (weak coupling)'. Either the axis label or the footnote should be corrected; the discrepancy makes reproducibility unnecessarily confusing.
  2. [Fig. 4 caption] The labels '80 meV' and '180 meV' are not explained in the caption or main text, and the band-structure energy axis in the same panel spans only −14 to 14 meV. Please clarify what these quantities are or remove them.
  3. [Model section; Eq. (1)] The valley-resolved hopping parameters are obtained via Eq. (S1.1) from a continuum model whose detailed derivation is delegated to the in-press Ref. [49]. Since the entire phase diagram depends on those hoppings, it would be helpful to state explicitly in the main text which parts of the Wannier model are independently reproduced in this paper and which are taken from Ref. [49].
  4. [Fig. 2] The labels 'golden circles' and 'purple stars' are used repeatedly in the text, but the figure legend identifies the symbol colors only implicitly. A short legend entry would improve readability.

Circularity Check

0 steps flagged

No circular derivation: the sSC phase is an emergent FRG output, not a refit or self-citation consequence.

full rationale

The derivation chain starts from a non-interacting Wannier model (Eq. 1) whose hoppings are obtained by Wannier projection of an ab initio continuum model (Eq. S1.1), and an interaction (Eq. 2) from a dual-gated Coulomb potential projected to the Wannier basis; neither contains the sSC state. The TUFRG flow (Eqs. S2.13-S2.16) is run with divERGe (public code, Refs. 81-83), with epsilon and nu scanned as control parameters; the leading vertex divergence in Fig. 2 is the output, not an input. The gap equation (3) uses the FRG-generated spin-fluctuation vertex and so is a diagnostic of the same theory, not a separate fit. The self-citations (Ref. 49 for the Wannier model, Refs. 82-83 for the code) overlap with the author list, but the cited model is first-principles-derived, code-reproducible, and makes no assumption of the target superconducting phase; the ~2% density-density truncation is a stated approximation. The authors' own caveats (single twist angle theta=6.01 degrees, kinetic anisotropy alpha~0.19 in Table S1.2, and the need to benchmark FRG against one-dimensional techniques) are robustness concerns, not circularity. No equation reduces to its own output, and no fitted parameter is renamed as a prediction.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

No new particles, forces, or mediators are introduced. The 'extended s-wave' order parameter is a standard superconducting symmetry; the model and method are established, with ε and ξ chosen or tuned. The main external inputs are the Wannier model from Ref [49] and the divERGe code, both from overlapping author groups but publicly available.

free parameters (3)
  • dielectric constant ε = scanned 12–16, baseline 12
    Overall interaction scale is uncertain; treated as a tuning parameter in the phase diagram (Fig. 2).
  • gate screening length ξ = 10 nm
    Set by assumed distance to experimental gates; enters the dual-gated Coulomb potential V(q).
  • FRG divergence threshold = 30 W
    Choice for declaring vertex divergence; affects Λc and phase boundaries (Ref [74]).
axioms (4)
  • domain assumption Truncation to three low-energy conduction bands (one per valley) of the continuum model captures the relevant low-energy physics of AB-stacked tSnSe2.
    Model section; based on Ref [49]; omitted bands could contribute screening or correlations.
  • domain assumption Non-density-density interaction terms from Wannier projection are negligible (≲2% of Hubbard U).
    Model section and SI S1; if violated, the pairing channel could change.
  • domain assumption Static (frequency-independent) two-particle vertex and TUFRG bond truncation provide quantitatively reliable FRG flow.
    FRG section and SI S2; standard but uncontrolled; authors call for QMC/DMRG benchmarks in the Summary.
  • domain assumption Λc is a proxy for transition temperature Tc.
    FRG section; standard in FRG literature.

pith-pipeline@v1.3.0-daily-deepseek · 21569 in / 12037 out tokens · 113165 ms · 2026-08-01T06:54:16.651260+00:00 · methodology

0 comments
read the original abstract

We investigate the emergence of electronic order and unconventional superconductivity in M-valley moir\'e materials. Starting from a first-principles Wannier model of AB-stacked twisted SnSe2, we tackle the (gate-screened) long-ranged Coulomb interaction with functional renormalization group simulations resolving the momentum structure and energy scales of the leading Fermi surface instabilities. Upon doping an antiferromagnetic stripe state at half-filling ($\nu=3$ electrons per moir\'e unit cell) of the moir\'e flat bands, magnetic order gives way to unconventional superconductivity mediated by valley-selective spin fluctuations: Large hole doping ($\nu\approx1$) leads to weak-coupling superconductors with various pairing symmetries, while slight electron- and hole-doping ($\nu\approx2,4$) stabilizes a spin-singlet, extended s-wave state that benefits from scattering between virtual particle and hole states that are detuned from the Fermi level. These findings establish M-point moir\'e materials as a quantum simulation platform with phenomenological parallels to the class of iron pnictide superconductors.

Figures

Figures reproduced from arXiv: 2607.27492 by Ammon Fischer, B. Andrei Bernevig, Dante M. Kennes, Haoyu Hu, Henning Schl\"omer, Lennart Klebl, Ming-Rui Li, Ronny Thomale, Salahudin V. Smailagi\'c.

Figure 1
Figure 1. Figure 1: FIG. 1. Wannier centers, hopping parameters (a), and band struc [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: , we encode the nature of the leading (intravalley) or￾der as color and the critical scale Λc as intensity. Blue, olive, and purple regions correspond to extended 𝑠-wave (𝑠SC), 𝑝- wave (𝑝SC), and 𝑑-wave (𝑑SC) superconductivity, respec￾tively, while magenta indicates a spin density wave; uncol￾ored regions represent a Fermi liquid. The DOS of the non￾interacting (i.e., independent on 𝜖) model (gray) is prov… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Weak-coupling superconductivity in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Microscopic pairing mechanism for extended [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

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Reference graph

Works this paper leans on

85 extracted references · 6 linked inside Pith

  1. [1]

    Y.Cao,V.Fatemi,S.Fang,K.Watanabe,T.Taniguchi,E.Kaxi- ras,andP.Jarillo-Herrero,Unconventionalsuperconductivityin magic-angle graphene superlattices, Nature556, 43 (2018)

    2018

  2. [2]

    J. G. Bednorz and K. A. Müller, Possible highTc superconduc- 6 tivity in the Ba-La-Cu-O system, Zeitschrift für Physik B Con- densed Matter64, 189 (1986)

    1986

  3. [3]

    Steglich, J

    F. Steglich, J. Aarts, C. D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schäfer, Superconductivity in the Presence of Strong Pauli Paramagnetism: CeCu2Si2, Physical Review Let- ters43, 1892 (1979)

    1979

  4. [4]

    Kamihara, T

    Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, Iron- Based Layered Superconductor La[O1-xFx]FeAs (x = 0.05- 0.12) with Tc = 26 K, Journal of the American Chemical So- ciety130, 3296 (2008)

    2008

  5. [5]

    D. M. Kennes, M. Claassen, L. Xian, A. Georges, A. J. Mil- lis, J. Hone, C. R. Dean, D. N. Basov, A. N. Pasupathy, and A. Rubio, Moiré heterostructures as a condensed-matter quan- tum simulator, Nature Physics17, 155 (2021)

    2021

  6. [6]

    Yankowitz, S

    M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T.Taniguchi,D.Graf,A.F.Young,andC.R.Dean,Tuningsu- perconductivity in twisted bilayer graphene, Science363, 1059 (2019)

    2019

  7. [7]

    X. Lu, P. Stepanov, W. Yang, M. Xie, M. A. Aamir, I. Das, C. Urgell, K. Watanabe, T. Taniguchi, G. Zhang, A. Bachtold, A. H. MacDonald, and D. K. Efetov, Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene, Nature574, 653 (2019)

    2019

  8. [8]

    Stepanov, I

    P. Stepanov, I. Das, X. Lu, A. Fahimniya, K. Watanabe, T. Taniguchi, F. H. L. Koppens, J. Lischner, L. Levitov, and D.K.Efetov,Untyingtheinsulatingandsuperconductingorders in magic-angle graphene, Nature583, 375 (2020)

    2020

  9. [9]

    Y.Saito,J.Ge,K.Watanabe,T.Taniguchi,andA.F.Young,In- dependent superconductors and correlated insulators in twisted bilayer graphene, Nature Physics16, 926 (2020)

    2020

  10. [10]

    F. K. de Vries, E. Portolés, G. Zheng, T. Taniguchi, K. Watan- abe,T.Ihn,K.Ensslin,andP.Rickhaus,Gate-definedJosephson junctionsinmagic-angletwistedbilayergraphene,NatureNan- otechnology16, 760 (2021)

    2021

  11. [11]

    M. Oh, K. P. Nuckolls, D. Wong, R. L. Lee, X. Liu, K. Watan- abe,T.Taniguchi,andA.Yazdani,Evidenceforunconventional superconductivity in twisted bilayer graphene, Nature600, 240 (2021)

    2021

  12. [12]

    Bockrath, Evidence for Dirac flat band superconductivity en- abled by quantum geometry, Nature614, 440 (2023)

    H.Tian,X.Gao,Y.Zhang,S.Che,T.Xu,P.Cheung,K.Watan- abe,T.Taniguchi,M.Randeria,F.Zhang,C.N.Lau,andM.W. Bockrath, Evidence for Dirac flat band superconductivity en- abled by quantum geometry, Nature614, 440 (2023)

    2023

  13. [13]

    Di Battista, P

    G. Di Battista, P. Seifert, K. Watanabe, T. Taniguchi, K. C. Fong, A. Principi, and D. K. Efetov, Revealing the Thermal Properties of Superconducting Magic-Angle Twisted Bilayer Graphene, Nano Letters22, 6465 (2022)

    2022

  14. [14]

    Călugăru, N

    D. Călugăru, N. Regnault, M. Oh, K. P. Nuckolls, D. Wong, R. L. Lee, A. Yazdani, O. Vafek, and B. A. Bernevig, Spec- troscopy of Twisted Bilayer Graphene Correlated Insulators, Physical Review Letters129, 117602 (2022)

    2022

  15. [15]

    G. Chen, A. L. Sharpe, P. Gallagher, I. T. Rosen, E. J. Fox, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi, J. Jung, Z. Shi, D. Goldhaber-Gordon, Y. Zhang, and F. Wang, Signa- tures of tunable superconductivity in a trilayer graphene moiré superlattice, Nature572, 215 (2019)

    2019

  16. [16]

    J. M. Park, Y. Cao, K. Watanabe, T. Taniguchi, and P. Jarillo- Herrero, Tunable strongly coupled superconductivity in magic- angle twisted trilayer graphene, Nature590, 249 (2021)

    2021

  17. [17]

    Z. Hao, A. M. Zimmerman, P. Ledwith, E. Khalaf, D. H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, Electric field–tunable superconductivity in alternating- twist magic-angle trilayer graphene, Science371, 1133 (2021)

    2021

  18. [18]

    Y. Cao, J. M. Park, K. Watanabe, T. Taniguchi, and P. Jarillo- Herrero, Pauli-limit violation and re-entrant superconductivity in moiré graphene, Nature595, 526 (2021)

    2021

  19. [19]

    X. Liu, N. J. Zhang, K. Watanabe, T. Taniguchi, and J. I. A. Li, Isospin order in superconducting magic-angle twisted trilayer graphene, Nature Physics18, 522 (2022)

    2022

  20. [20]

    H. Kim, Y. Choi, C. Lewandowski, A. Thomson, Y. Zhang, R. Polski, K. Watanabe, T. Taniguchi, J. Alicea, and S. Nadj-Perge, Evidence for unconventional superconductivity in twisted trilayer graphene, Nature606, 494 (2022)

    2022

  21. [21]

    Zhang, R

    Y. Zhang, R. Polski, C. Lewandowski, A. Thomson, Y. Peng, Y. Choi, H. Kim, K. Watanabe, T. Taniguchi, J. Alicea, F. von Oppen, G. Refael, and S. Nadj-Perge, Promotion of supercon- ductivity in magic-angle graphene multilayers, Science377, 1538 (2022)

    2022

  22. [22]

    H. Zhou, T. Xie, T. Taniguchi, K. Watanabe, and A. F. Young, Superconductivity in rhombohedral trilayer graphene, Nature 598, 434 (2021)

    2021

  23. [23]

    H. Zhou, L. Holleis, Y. Saito, L. Cohen, W. Huynh, C. L. Patterson, F. Yang, T. Taniguchi, K. Watanabe, and A. F. Young, Isospin magnetism and spin-polarized superconductiv- ity in Bernal bilayer graphene, Science375, 774 (2022)

    2022

  24. [24]

    Zhang, R

    Y. Zhang, R. Polski, A. Thomson, É. Lantagne-Hurtubise, C. Lewandowski, H. Zhou, K. Watanabe, T. Taniguchi, J. Al- icea, and S. Nadj-Perge, Enhanced superconductivity in spin– orbit proximitized bilayer graphene, Nature613, 268 (2023)

    2023

  25. [25]

    T. Han, Z. Lu, Z. Hadjri, L. Shi, Z. Wu, W. Xu, Y. Yao, A. A. Cotten,O.SharifiSedeh,H.Weldeyesus,J.Yang,J.Seo,S.Ye, M. Zhou, H. Liu, G. Shi, Z. Hua, K. Watanabe, T. Taniguchi, P.Xiong,D.M.Zumbühl, L.Fu,andL.Ju,Signaturesofchiral superconductivity in rhombohedral graphene, Nature643, 654 (2025)

    2025

  26. [26]

    Y.Choi,Y.Choi,M.Valentini,C.L.Patterson,L.F.W.Holleis, O. I. Sheekey, H. Stoyanov, X. Cheng, T. Taniguchi, K. Watan- abe,andA.F.Young,Superconductivityandquantizedanoma- lous Hall effect in rhombohedral graphene, Nature639, 342 (2025)

    2025

  27. [27]

    Y. Xia, Z. Han, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Superconductivity in twisted bilayer WSe2, Nature637, 833 (2025)

    2025

  28. [28]

    Taniguchi, D

    Y.Guo,J.Pack,J.Swann,L.Holtzman,M.Cothrine,K.Watan- abe, T. Taniguchi, D. G. Mandrus, K. Barmak, J. Hone, A. J. Millis,A.Pasupathy,andC.R.Dean,Superconductivityin5.0 ◦ twisted bilayer WSe2, Nature637, 839 (2025)

    2025

  29. [29]

    Y. Xia, Z. Han, J. Zhu, Y. Zhang, P. Knüppel, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Bandwidth-tuned Mott transition and superconductivity in moiré WSe2, Nature650, 585 (2026)

    2026

  30. [30]

    Y. Guo, J. Cenker, A. Fischer, D. Muñoz-Segovia, J. Pack, L. Holtzman, L. Klebl, K. Watanabe, T. Taniguchi, K. Barmak, J. Hone, A. Rubio, D. M. Kennes, A. J. Millis, A. Pasupathy, and C. R. Dean, Angle evolution of the superconducting phase diagram in twisted bilayer WSe2, Nature652, 622 (2026)

    2026

  31. [31]

    F. Xu, Z. Sun, J. Li, C. Zheng, C. Xu, J. Gao, T. Jia, K. Watan- abe, T. Taniguchi, B. Tong, L. Lu, J. Jia, Z. Shi, S. Jiang, Y. Zhang, Y. Zhang, S. Lei, X. Liu, and T. Li, Signatures of unconventional superconductivity near reentrant and fractional quantumanomalousHallinsulators,arXiv:2504.06972 (2025)

    Pith/arXiv arXiv 2025

  32. [32]

    Z. Sun, F. Xu, J. Li, Y. Jiang, J. Gao, C. Xu, T. Jia, K. Cheng, J. Zhang, W. Tian, K. Watanabe, T. Taniguchi, J. Jia, S. Jiang, Y. Zhang, Y. Zhang, S. Lei, X. Liu, and T. Li, Twist-angle evolutionfromvalley-polarizedfractionaltopologicalphasesto valley-degenerate superconductivity in twisted bilayer mote2, arXiv:2603.16412 (2026)

    arXiv 2026

  33. [33]

    X. Liu, Z. Wang, K. Watanabe, T. Taniguchi, O. Vafek, and J. I. A. Li, Tuning electron correlation in magic-angle twisted 7 bilayer graphene using Coulomb screening, Science371, 1261 (2021)

    2021

  34. [34]

    C. Chen, K. P. Nuckolls, S. Ding, W. Miao, D. Wong, M. Oh, R. L. Lee, S. He, C. Peng, D. Pei, Y. Li, C. Hao, H. Yan, H. Xiao, H. Gao, Q. Li, S. Zhang, J. Liu, L. He, K. Watan- abe,T.Taniguchi,C.Jozwiak,A.Bostwick,E.Rotenberg,C.Li, X.Han,D.Pan,Z.Liu,X.Dai,C.Liu,B.A.Bernevig,Y.Wang, A. Yazdani, and Y. Chen, Strong electron–phonon coupling in magic-angle twi...

    2024

  35. [35]

    Wang, G.-D

    Y.-J. Wang, G.-D. Zhou, S.-Y. Peng, B. Lian, and Z.-D. Song, Molecular Pairing in Twisted Bilayer Graphene Superconduc- tivity, Physical Review Letters133, 146001 (2024)

    2024

  36. [36]

    Klebl, A

    L. Klebl, A. Fischer, L. Classen, M. M. Scherer, and D. M. Kennes, Competition of density waves and superconductivity in twisted tungsten diselenide, Physical Review Research5, L012034 (2023)

    2023

  37. [37]

    Wehling, A

    A.Fischer,L.Klebl,V.Crépel,S.Ryee,A.Rubio,L.Xian,T.O. Wehling, A. Georges, D. M. Kennes, and A. J. Millis, Theory ofIntervalley-CoherentAFMOrderandTopologicalSupercon- ductivity in tWSe2, Physical Review X15, 041055 (2025)

    2025

  38. [38]

    A. V. Chubukov and C. M. Varma, Quantum criticality and superconductivity in twisted transition metal dichalcogenides, Physical Review B111, 014507 (2025)

    2025

  39. [39]

    Qin, W.-X

    W. Qin, W.-X. Qiu, and F. Wu, Topological Chiral Supercon- ductivity Mediated by Intervalley Antiferromagnetic Fluctua- tions in Twisted Bilayer WSe2, Physical Review Letters135, 246002 (2025)

    2025

  40. [40]

    Călugăru, Y

    D. Călugăru, Y. Jiang, H. Hu, H. Pi, J. Yu, M. G. Vergniory, J. Shan, C. Felser, L. M. Schoop, D. K. Efetov, K. F. Mak, and B.A.Bernevig,MoirématerialsbasedonM-pointtwisting,Na- ture643, 376 (2025)

    2025

  41. [41]

    C.Lei,P.T.Mahon,andA.H.MacDonald,MoiréBandTheory forM-ValleyTwistedTransitionMetalDichalcogenides,Physi- cal Review Letters135, 196402 (2025)

    2025

  42. [42]

    K. Bao, H. Wang, Z. Liu, and J. Wang, Anisotropic moiré band flatteningintwistedbilayersofM-valleyMXenes,PhysicalRe- view B112, L041406 (2025)

    2025

  43. [43]

    Ingham, M

    J. Ingham, M. S. Scheurer, and H. D. Scammell, Moiré 𝑀-valley bilayers: Quasi-one-dimensional physics, uncon- ventional spin textures and twisted van Hove singularities, arXiv:2503.11754 (2025)

    Pith/arXiv arXiv 2025

  44. [44]

    Jiang, U

    Y. Jiang, U. Petralanda, G. Skorupskii, Q. Xu, H. Pi, D. Călugăru, H. Hu, J. Xie, R. A. Mustaf, P. Höhn, V. Haase, M. G. Vergniory, M. Claassen, L. Elcoro, N. Regnault, J. Shan, K. F. Mak, D. K. Efetov, E. Morosan, D. M. Kennes, A. Ru- bio, L. Xian, C. Felser, L. M. Schoop, and B. A. Bernevig, 2D Theoretically Twistable Material Database, arXiv:2411.09741 (2024)

    Pith/arXiv arXiv 2024

  45. [45]

    Q. Xu, Y. Gao, T. Zhang, A. Fischer, Y. Jiang, H. Pi, Z. Fan, D. An, K. Zhou, Y. Li, Y. Li, Y. Fu, L. Wang, L. Zhang, B. A. Bernevig,D.M.Kennes,E.Wang,A.Rubio,andL.Xian,Orga- nizing principles for moiré quantum matter, arXiv:2607.24944 (2026)

    Pith/arXiv arXiv 2026

  46. [46]

    Kariyado and A

    T. Kariyado and A. Vishwanath, Flat band in twisted bilayer Bravais lattices, Physical Review Research1, 033076 (2019)

    2019

  47. [47]

    Fujimoto, T

    M. Fujimoto, T. Kawakami, and M. Koshino, Perfect one- dimensional interface states in a twisted stack of three- dimensional topological insulators, Physical Review Research 4, 043209 (2022)

    2022

  48. [48]

    Kariyado, Twisted bilayer BC3: Valley interlocked anisotropic flat bands, Physical Review B107, 085127 (2023)

    T. Kariyado, Twisted bilayer BC3: Valley interlocked anisotropic flat bands, Physical Review B107, 085127 (2023)

    2023

  49. [49]

    Klebl, Z

    M.-R.Li,D.Calugaru,Y.Jiang,H.Pi,A.Fischer,H.Schlömer, L. Klebl, Z. Xia, M. G. Vergniory, D. M. Kennes, K. F. Mak, J. Shan, S. A. Parameswaran, H. Yao, B. A. Bernevig, and H.Hu,Emergentinteractingphasesinthestrong-couplinglimit of twisted𝑚-valley moiré systems: Application to snse2, Phys. Rev. B (2026)

    2026

  50. [50]

    C. D. Beule, L. Peng, E. J. Mele, and S. Adam, Role of electron-electron interactions in 𝑀-valley twisted transition metal dichalcogenides, arXiv:2508.14283 (2025)

    arXiv 2025

  51. [51]

    J. Park, L. Classen, and M. S. Scheurer, Intervalley coher- ence and flavor polarization in three-valley moiré systems, arXiv:2606.16622 (2026)

    arXiv 2026

  52. [52]

    G. R. Stewart, Superconductivity in iron compounds, Reviews of Modern Physics83, 1589 (2011)

    2011

  53. [53]

    Q.Si,R.Yu,andE.Abrahams,High-temperaturesuperconduc- tivity in iron pnictides and chalcogenides, Nature Reviews Ma- terials 1, 16017 (2016)

    2016

  54. [54]

    I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, Un- conventional Superconductivity with a Sign Reversal in the Or- der Parameter of LaFeAsO1-xFx, Physical Review Letters101, 057003 (2008)

    2008

  55. [55]

    Kuroki, H

    K. Kuroki, H. Usui, S. Onari, R. Arita, and H. Aoki, Pnictogen height as a possible switch between high-Tc nodeless and low- Tc nodal pairings in the iron-based superconductors, Physical Review B79, 224511 (2009)

    2009

  56. [56]

    P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, Gap sym- metry and structure of Fe-based superconductors, Reports on Progress in Physics74, 124508 (2011)

    2011

  57. [57]

    Chubukov, Pairing Mechanism in Fe-Based Superconduc- tors,AnnualReviewofCondensedMatterPhysics 3,57(2012)

    A. Chubukov, Pairing Mechanism in Fe-Based Superconduc- tors,AnnualReviewofCondensedMatterPhysics 3,57(2012)

    2012

  58. [58]

    Thomale, C

    R. Thomale, C. Platt, W. Hanke, and B. A. Bernevig, Mech- anism for Explaining Differences in the Order Parameters of FeAs-BasedandFeP-BasedPnictideSuperconductors,Physical Review Letters106, 187003 (2011)

    2011

  59. [59]

    Platt, R

    C. Platt, R. Thomale, and W. Hanke, Superconducting state of the iron pnictide LiFeAs: A combined density-functional and functional-renormalization-groupstudy,PhysicalReviewB 84, 235121 (2011)

    2011

  60. [60]

    Xiang, F

    Y.-Y. Xiang, F. Wang, D. Wang, Q.-H. Wang, and D.-H. Lee, High-temperature superconductivity at the FeSe/SrTiO3 inter- face, Physical Review B86, 134508 (2012)

    2012

  61. [61]

    R.Thomale,C.Platt,J.Hu,C.Honerkamp,andB.A.Bernevig, Functional renormalization-group study of the doping depen- denceofpairingsymmetryintheironpnictidesuperconductors, Physical Review B80, 180505 (2009)

    2009

  62. [62]

    Song and B

    Z.-D. Song and B. A. Bernevig, Magic-Angle Twisted Bilayer Graphene as a Topological Heavy Fermion Problem, Physical Review Letters129, 047601 (2022)

    2022

  63. [63]

    Datta, M

    A. Datta, M. J. Calderón, A. Camjayi, and E. Bascones, Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene, Nature Communications14, 5036 (2023)

    2023

  64. [64]

    Georges, B

    G.Rai,L.Crippa,D.Călugăru,H.Hu,F.Paoletti,L.de’Medici, A. Georges, B. A. Bernevig, R. Valentí, G. Sangiovanni, and T. Wehling, Dynamical correlations and order in magic-angle twisted bilayer graphene, Phys. Rev. X14, 031045 (2024)

    2024

  65. [65]

    J. B. Profe, J. Vučičević, P. P. Stavropoulos, M. Rösner, R. Va- lentí, and L. Klebl, Exact downfolding and its perturbative ap- proximation, Phys. Rev. Res.8, 023091 (2026)

    2026

  66. [66]

    Metzner, M

    W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden, and K. Schönhammer, Functional renormalization group approach to correlated fermion systems, Reviews of Modern Physics84, 299 (2012)

    2012

  67. [67]

    C.Platt,W.Hanke,andR.Thomale,Functionalrenormalization group for multi-orbital Fermi surface instabilities, Advances in Physics62, 453 (2013)

    2013

  68. [68]

    Tissier, and N

    N.Dupuis,L.Canet,A.Eichhorn,W.Metzner,J.M.Pawlowski, 8 M. Tissier, and N. Wschebor, The nonperturbative functional renormalizationgroupanditsapplications,PhysicsReportsThe NonperturbativeFunctionalRenormalizationGroupandItsAp- plications,910, 1 (2021)

    2021

  69. [69]

    Husemann and M

    C. Husemann and M. Salmhofer, Efficient parametrization of the vertex function,Ω scheme, and the𝑡,𝑡′ Hubbard model at van Hove filling, Physical Review B79, 195125 (2009)

    2009

  70. [70]

    Lichtenstein, D

    J. Lichtenstein, D. Sánchez de la Peña, D. Rohe, E. Di Napoli, C. Honerkamp, and S. A. Maier, High-performance functional Renormalization Group calculations for interacting fermions, Computer Physics Communications213, 100 (2017)

    2017

  71. [71]

    J.Beyer,J.B.Profe,andL.Klebl,Referenceresultsforthemo- mentumspacefunctionalrenormalizationgroup,TheEuropean Physical Journal B95, 65 (2022)

    2022

  72. [72]

    J. B. Profe and D. M. Kennes, TU2FRG: A scalable approach for truncated unity functional renormalization group in generic fermionic models, The European Physical Journal B95, 60 (2022)

    2022

  73. [73]

    Fischer, L

    A. Fischer, L. Klebl, J. B. Profe, A. Rothstein, L. Waldecker, B. Beschoten, T. O. Wehling, and D. M. Kennes, Spin and chargefluctuationinducedpairinginABCBtetralayergraphene, Physical Review Research6, L012003 (2024)

    2024

  74. [74]

    The initial (minimal) scale is set to Λini = 103𝑊 (Λmin = 10−4𝑊)

    Wesample(𝜈,𝜖)∈[0 ,6]×[12,16]onaregular 51×49meshand usethedivERGelibrary[82,83]fortheFRGflow.Themodel’s dispersion (vertex) is sampled on a regular540×540(36×36) momentum mesh in the primitive zone, and the TU cutoff dis- tance is set to𝑟max = 2.01 lattice constants; convergence was checked with𝑟max = 8.01. The initial (minimal) scale is set to Λini = 103...

  75. [75]

    W.Cho,R.Thomale,S.Raghu,andS.A.Kivelson,Bandstruc- ture effects on the superconductivity in Hubbard models, Phys- ical Review B88, 064505 (2013)

    2013

  76. [76]

    Schollwöck, The density-matrix renormalization group, Re- views of Modern Physics77, 259 (2005)

    U. Schollwöck, The density-matrix renormalization group, Re- views of Modern Physics77, 259 (2005)

    2005

  77. [77]

    A.SzaszandJ.Motruk,Phasediagramoftheanisotropictrian- gular lattice hubbard model, Phys. Rev. B103, 235132 (2021)

    2021

  78. [78]

    Li and H

    Z.-X. Li and H. Yao, Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications, Annual Review of Condensed Matter Physics10, 337 (2019)

    2019

  79. [79]

    D.Călugăru,K.Vasiliou,H.Hu,B.A.Bernevig,W.Krauth,and S. A. Parameswaran, Mixed-dimensional quantum monte carlo studies of m-point moiré materials, arXiv:2606.12508 (2026)

    Pith/arXiv arXiv 2026

  80. [80]

    Vasiliou, D

    K. Vasiliou, D. Călugăru, J. S. Hofmann, and S. A. Parameswaran, Hidden antiferromagnetism, persistent val- ley fluctuations, and 𝑢(6) crossovers in triangular-lattice m- point moiré materials via determinantal quantum monte carlo, arXiv:2606.12530 (2026)

    Pith/arXiv arXiv 2026

Showing first 80 references.