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REVIEW 3 major objections 3 minor 56 references

Tunable Superconductivity Mediated by Heavy-Electron Plasmons: Band-Structure and Quantum-Geometric Engineering

T0 review · 3 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Heavy-electron plasmons—collective charge oscillations of a heavy band—can mediate pairing of light electrons, and with a moderate phonon boost, transition temperatures above 20 K become possible.

desk verdict The interband quantum-geometric plasmon mediator is the real contribution; the metallic >20 K numbers rest on an uncontrolled heavy-band limit. read the letter →

arxiv 2607.18157 v1 pith:FZACYJKO submitted 2026-07-20 cond-mat.supr-con

Sang Hyun Park , Junyeong Ahn This is my paper · ORCID
classification cond-mat.supr-con
keywords superconductivityplasmon-mediatedpairingheavy-electronplasmonsflatbandsquantummetricEliashbergtheoryrandom-phaseapproximationtwo-carriersystems
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 argues that in a two-dimensional system containing both heavy and light electrons, the collective charge oscillations (plasmons) of the heavy electrons provide a retarded attractive interaction that can bind light electrons into Cooper pairs. The central result is that the optimal transition temperature is set by a competition between the plasmon energy scale and how strongly retardation suppresses the repulsive Coulomb interaction, giving dome-shaped Tc curves in carrier density and mass. A moderate phonon attraction acting together with the plasmon raises Tc from roughly 0.1 K to above 20 K. The paper also shows that in gapped flat bands, interband plasmons—governed by the quantum metric—can mediate pairing without free carriers, and that nontrivial quantum geometry in the light band suppresses static screening, enhancing the net attraction. If correct, the work reframes flat bands as tunable pairing mediators rather than simply hosts of superconductivity.

What carries the argument

The screened Coulomb interaction W(q,iν) in RPA with separate polarizations for light and heavy electrons, combined with the isotropic linearized Eliashberg equations. The key analytic object is the heavy-electron plasmon frequency Ωp(q), whose mass/density dependence enters both the prefactor and the retardation correction in the McMillan–Allen–Dynes form of Tc. In the interband case, the polarization is expressed through the Hilbert–Schmidt quantum distance d_Q, whose small-q expansion gives the BZ-integrated quantum metric; this single quantity controls the interband plasmon dispersion and the electron–plasmon coupling. For the light band, the static polarizability entering the screening

What would settle it

Momentum-resolved electron energy-loss spectroscopy on a candidate material (e.g., alternating-twist multilayer graphene or a dice-lattice electride) should reveal a gapped or acoustic interband/intraband plasmon with frequency matching the model's Ωp(q); if the mode is overdamped or absent in the predicted density window, the mechanism is falsified.

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Extended reading notes

Core claim

The paper establishes design principles for plasmon-mediated superconductivity in two-carrier systems. Light electrons pair via the retarded interaction generated by heavy-electron plasmons, described by the RPA-screened Coulomb interaction and solved with isotropic Eliashberg equations. In metallic heavy bands, Tc shows a dome in carrier density and heavy mass: flattening the heavy band lowers the plasmon frequency, improving retardation and suppressing the Coulomb repulsion, but too low a frequency reduces the energy scale; the optimum balances these. The plasmon channel alone reaches only about 0.1 K, but a phonon coupling of λ_ph=0.4 cooperates with it, boosting Tc above 20 K. For insula

Load-bearing premise

The quantitative high-Tc predictions assume that an extremely heavy metallic band (mass up to 10^4 m0, Fermi energy ~0.1 meV) can still be treated as a coherent Fermi gas with well-defined plasmons, and that vertex corrections and non-s-wave pairing channels are negligible; if competing orders or strong correlations dominate that band instead, the predicted Tc window collapses.

Editorial extensions

If this is right

  • Flat-band systems can serve as tunable pairing mediators: the collective-mode spectrum, not the narrow bandwidth, sets the superconducting energy scale.
  • Optimal Tc is a balance, not a maximization: raising the plasmon frequency alone (via density or dispersion) eventually hurts Tc because it weakens the retardation-driven reduction of the Coulomb repulsion.
  • A moderate phonon attraction combined with the plasmon can yield Tc above 20 K, even though each mechanism alone gives only ~0.1 K, suggesting a cooperative route to higher Tc.
  • Interband plasmons in gapped flat bands survive without free carriers, potentially avoiding competing metallic orders; the BZ-integrated quantum metric is the tunable control knob for pairing strength.
  • Layer separation beyond about 3 Å kills the plasmonic pairing, so engineering must place light and heavy electrons in the same layer (e.g., distinct mirror-symmetry sectors).

Reading between the lines

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

  • The same retardation argument that makes heavy plasmons attractive should apply to any slow collective charge mode, so the design principle might extend to excitons, magnons, or polaritons, with the Tc ceiling set by the mode frequency and coupling.
  • The predicted >20 K regime rests on treating a heavy band of m_h ~ 10^4 m0 as a coherent Fermi gas; if such a band is instead in a correlated or ordered state (as the paper itself worries), the high-Tc window would be inaccessible—a direct test would be to measure the plasmon dispersion and its damping in candidate moiré or dice materials.
  • Quantum-geometric suppression of screening suggests a testable corollary: systems with larger BZ-integrated quantum metric should show enhanced Tc at fixed density, which could be probed by twist-angle or strain tuning in twisted multilayer graphene.
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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 / 3 minor

Summary. The paper investigates superconductivity mediated by heavy-electron plasmons in two-carrier 2D systems. It considers a metallic model in which heavy intraband plasmons provide a retarded effective attraction for a lighter electron band, and an insulating model in which gapped interband plasmons of flat bands play the same role. The theoretical framework is RPA screening (Eqs. (1)–(3)) combined with linearized isotropic Eliashberg equations (Eq. (5)); the authors augment the plasmon channel by a phonon with λ_ph = 0.4. The central findings are a dome-shaped Tc as a function of carrier densities and masses, a plasmon-only Tc of order 0.1 K, a cooperative phonon–plasmon regime with Tc above 20 K (Fig. 2), quantum-geometric control of interband plasmon pairing (Sec. III and Eq. (13)), and suppression of screening by the light-band quantum metric (Sec. IV). The paper closes with layer-separation/dielectric-environment analysis and candidate material platforms.

Significance. The conceptual contribution is genuinely interesting: flat bands and heavy-electron bands are positioned not as hosts of superconductivity but as tunable bosonic mediators, with the superconducting scale set by collective-mode parameters rather than the narrow bandwidth. The analytic formulas (e.g., Eq. (8) and Eq. (13)) and transparent parameter scans are strengths, and the paper is explicit about several approximations (vertex corrections, competing orders, isotropic channel). If the quantitative claims can be placed on a controlled footing, the work would be a useful design principle for plasmon-mediated pairing in moiré and layered systems. At present, however, the headline >20 K numbers are not reproducible because a key parameter is unspecified, and the metallic high-Tc regime appears to lie outside the range where the RPA/Fermi-gas treatment is controlled.

major comments (3)
  1. [II, phonon term after Eq. (6), Figs. 2d–f, 3c–e, 5c–d] The phonon contribution is introduced as λ_ph ω_ph²/(ν_n²+ω_ph²), but the numerical value of ω_ph is never stated anywhere in the manuscript. All the high-Tc results with λ_ph = 0.4 depend on this frequency, and the claim that the phonon alone gives Tc ∼ 0.1 K is not verifiable without it. Moreover, the Eliashberg Matsubara cutoff is E_F,l/ħ; the phonon must lie within this window to act in a retarded manner, and no such check is given. Please specify ω_ph (and the ε_env used in Figs. 2–4) and report the sensitivity of Tc to these choices.
  2. [II, Figs. 2a–f] The metallic high-Tc regime uses m_h up to 10^4 m0 and n_h ≈ 10^15 cm^-2. For these values T_F,h = ħ²π n_h/(m_h k_B) ≈ 3 mK, while the claimed Tc is about 20 K, so the heavy carriers are non-degenerate at the transition. The 2D Wigner–Seitz radius is r_s ≈ 3×10^4/ε_env for m_h = 10^4 m0 and remains large for m_h ≳ 100 m0 even with ε_env ~ 10. Thus the heavy band is in a strong-coupling/Wigner-crystal regime where the RPA polarization of Eq. (2) and the Fermi-liquid picture are not controlled. The abstract notes that flattening favors competing orders, but the calculation itself contains no breakdown scale. Please add a validity analysis (T_F,h/Tc, r_s, Landau damping) and either restrict quantitative claims to the controlled parameter region or present the high-mass results explicitly as an extrapolation.
  3. [VI.B and Eqs. (5), (14)] The authors acknowledge that vertex corrections and anisotropic channels are neglected and may be quantitatively important. In the present parameter regime this is not a minor refinement: the effective boson energy for the heavy plasmon can be comparable to or larger than the light-electron Fermi energy, and the isotropic one-loop approximation is not protected by Migdal's theorem. The quantitative Tc values should be accompanied by an estimate of the small parameter of the theory (e.g., the ratio of plasmon energy to the relevant Fermi energy, or an effective Migdal parameter) at the optimal parameters, so the reader can assess whether the numbers are order-of-magnitude reliable.
minor comments (3)
  1. [Eq. (8) and Sec. II] The notation λ is used both as the dynamical frequency-dependent function λ(iν_n) and as a 'static attraction' in Eq. (8) and the McMillan discussion. Please define clearly which quantity is plotted and which is used in Eq. (7), and specify the sign convention for the attractive part.
  2. [Figs. 2–3] Please state the value of ε_env (and any other fixed parameters) used for the calculations in Figs. 2 and 3; Fig. 5 shows that ε_env is a parameter, but the earlier figures do not state the chosen value.
  3. [Sec. III, after Eq. (13)] The statement that the plasmon energy 'reaches a maximum energy and exhibits an oscillatory behavior' would benefit from a brief explanation tying the oscillations to zeros of the average quantum distance d_Q(q), rather than referring only to Ref. [29].

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central derivation is a self-contained RPA + Eliashberg calculation with scanned inputs; the one self-citation is not load-bearing.

full rationale

The derivation chain is self-contained. The screened interaction W(q, iνn) is defined by RPA in Eq. (1) from the polarizations in Eq. (2); the static-light-electron approximation leads to Eq. (3), and Eq. (4) is an algebraic rewriting using the heavy-plasmon pole. The analytic λ(x) in Eq. (8) follows directly from Eq. (4) by the stated Fermi-surface average, not from an input fitted to Tc. The Eliashberg equations in Eq. (5) are standard external machinery, and the McMillan/Anderson-Morel discussion is a subsequent interpretation, not an input. All quantitative results are obtained by solving these equations with scanned physical parameters (n_h, m_h, n_l, ζ, t, λ_ph); no target Tc or experimental datum is used to set model inputs. The tunable metric model in Eq. (9) is taken from prior work, but it is an explicitly stated model Hamiltonian, not a uniqueness theorem or a disguised ansatz imported to force the conclusion. The only paper-specific self-citation, Ref. [19] (an experimental observation of chiral/slow plasmons in twisted bilayer graphene), is used merely to support the tunability of plasmons in 2D materials and is not load-bearing for any derived result. The paper's own caveats in Sec. VI B about vertex corrections and competing orders concern validity regimes and quantitative reliability, not circularity. No step reduces to its own input by construction, and no fitted prediction is relabeled as a derivation.

Assumptions & free parameters 10 free parameters · 6 assumptions · 0 invented entities

No data fitting is performed: model inputs are scanned rather than inferred from a target result, so the circularity burden is low. The main load-bearing choices are the static-screening ansatz, the isotropic one-loop Eliashberg treatment, and the absence of competing-order feedback. No new particles, mediators, or conserved quantities are introduced.

free parameters (10)
  • heavy band mass m_h = scanned 50–10000 m0
    Controls heavy plasmon frequency; flattening enhances retardation and Tc. Scanned, not fitted.
  • heavy carrier density n_h = scanned 10^12–10^17 cm^-2
    Sets the intraband plasmon scale and the position of the Tc dome; scanned.
  • light carrier density n_l = fixed at 5×10^14 cm^-2 for most figures; scanned in Fig. 2(b-c,e-f)
    Sets E_F,l and the Thomas-Fermi screening wavevector κ; scanned.
  • light band mass m_l = m0 (fixed)
    Pairing electron mass; fixed to the bare electron mass in all presented calculations.
  • phonon coupling λ_ph = 0.4
    Ad hoc moderate coupling added in Fig. 2(d-f); not derived from a material or phonon model.
  • phonon frequency ω_ph = not stated
    The term λ_ph ω_ph^2/(ν_n^2+ω_ph^2) is used, but ω_ph is never specified; required to reproduce Tc values.
  • heavy quantum metric parameter ζ_h = scanned 0.1–10
    Tunable-metric model parameter controlling the BZ-averaged quantum distance in Sec. III; scanned.
  • light quantum metric parameter ζ_l = scanned 0.01–10
    Controls the suppression of static screening from light electrons in Sec. IV; scanned.
  • gap/hybridization t = scanned 1–100 meV
    Interband gap 2t in Eq. (9); sets the gapped interband plasmon energy scale.
  • environment dielectric constant ε_env = scanned 1–20 ε_0
    Screens the bare Coulomb interaction; dependence analyzed in Sec. V.
assumptions (6)
  • domain assumption The screened Coulomb interaction is computed in the random-phase approximation including both carrier species (Eq. 1).
    Standard approximation for collective modes; used throughout Sections II–IV.
  • domain assumption The light-electron polarization is replaced by its static Thomas-Fermi limit Π_l(q,0) = −2N_F,l when deriving the effective interaction Eq. (3).
    Assumes light electrons respond instantaneously; valid only for energies below E_F,l, while the Eliashberg cutoff is E_F,l/ħ.
  • domain assumption Pairing is treated with linearized isotropic Eliashberg equations (Eq. 5), retaining only the s-wave channel.
    Neglects anisotropic pairing channels and vertex corrections; acknowledged in Sec. VI B as potentially important.
  • domain assumption The metallic heavy band is treated as a coherent 2D parabolic Fermi gas with mass m_h up to 10^4 m0.
    No stability or competing-order analysis is included; the authors note flattening favors competing orders in Sec. VI C.
  • domain assumption Interband polarization of insulating flat bands is given by Eq. (11), proportional to a constant gap and BZ-averaged quantum distance.
    Applies to two-band models with exactly constant gap and flat bands; candidate materials deviate.
  • domain assumption Effective dielectric constant ε_env represents all high-energy and environmental screening, with no frequency dependence.
    Used in v_q; scanned in Sec. V.

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Pith. "Pith review of Tunable Superconductivity Mediated by Heavy-Electron Plasmons: Band-Structure and Quantum-Geometric Engineering." pith.science (2026). https://pith.science/paper/FZACYJKO

@misc{pith2026260718157,
  author       = {Pith},
  title        = {Pith review of: Tunable Superconductivity Mediated by Heavy-Electron Plasmons: Band-Structure and Quantum-Geometric Engineering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FZACYJKO}},
  note         = {Machine review of arXiv:2607.18157}
}
abstract

Conventional superconductivity derives its pairing glue from lattice vibrations, tying its characteristic scales to chemistry and atomic masses. Plasmons$-$the collective oscillations of electrons$-$can instead be reshaped through electronic structure engineering, but the principles governing optimal plasmon-mediated pairing remain unclear. Here, we establish such principles for two-carrier systems in which heavy-electron plasmons mediate the pairing of light electrons. Within the random-phase approximation and Eliashberg theory, we calculate the optimal $T_c$ of minimal metallic models and show that it is controlled by a competition between the plasmon energy scale and retardation-driven suppression of the repulsion, yielding optimal carrier densities and band masses. While the plasmon channel alone reaches only $T_c\sim$ 0.1 K, a moderate phonon attraction cooperates with it, boosting $T_c$ by two orders of magnitude to above 20 K. However, the band flattening needed for slow metallic plasmons also favors the development of competing orders. We therefore consider an insulating system in which coherent interband transitions between flat bands generate gapped interband plasmons without free carriers. The heavy-band quantum metric governs the dispersion and electron-plasmon pairing strength of the interband plasmon, while the quantum geometry of the light band suppresses static screening and enhances the net attraction. Because layer separation rapidly weakens pairing, we propose systems with coexisting light and heavy electrons living in different mirror-symmetry sectors of the same layer as promising platforms. Our results establish a new role for flat-band systems in superconductivity: rather than hosting the paired electrons themselves, they can serve as a tunable pairing mediator whose collective charge excitations set the superconducting energy scale beyond their narrow bandwidth.

Figures

Figures reproduced from arXiv: 2607.18157 by the authors.

Figure 1
Figure 1. FIG. 1. Tunable superconductivity mediated by heavy [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Calculations of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Quantum-geometric control of interband-plasmon-mediated superconductivity in gapped flat bands. (a) Schematic of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Enhancement of heavy-electron-plasmon-mediated superconductivity by light-electron quantum geometry. (a) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Dependence on layer separation and screening from [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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Works this paper leans on

56 extracted references · 2 linked inside Pith

  1. [1]

    Bardeen, L

    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Mi- croscopic Theory of Superconductivity, Physical Review 106, 162 (1957)

    1957

  2. [2]

    Eliashberg, Interactions between electrons and lattice vibrations in a superconductor, Sov

    G. Eliashberg, Interactions between electrons and lattice vibrations in a superconductor, Sov. Phys. JETPL11, 696 (1960)

    1960

  3. [3]

    J. P. Carbotte, Properties of boson-exchange supercon- ductors, Reviews of Modern Physics62, 1027 (1990)

    1990

  4. [4]

    N. W. Ashcroft, Metallic Hydrogen: A High- Temperature Superconductor?, Physical Review Letters 21, 1748 (1968)

    1968

  5. [5]

    A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Kseno- fontov, and S. I. Shylin, Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride sys- tem, Nature525, 73 (2015)

    2015

  6. [6]

    A. P. Drozdov, P. P. Kong, V. S. Minkov, S. P. Besedin, M. A. Kuzovnikov, S. Mozaffari, L. Balicas, F. F. Bal- akirev, D. E. Graf, V. B. Prakapenka, E. Greenberg, D. A. Knyazev, M. Tkacz, and M. I. Eremets, Super- conductivity at 250 K in lanthanum hydride under high pressures, Nature569, 528 (2019)

    2019

  7. [7]

    Somayazulu, M

    M. Somayazulu, M. Ahart, A. K. Mishra, Z. M. Geballe, M. Baldini, Y. Meng, V. V. Struzhkin, and R. J. Hem- ley, Evidence for Superconductivity above 260 K in Lan- thanum Superhydride at Megabar Pressures, Physical Review Letters122, 027001 (2019)

    2019

  8. [8]

    J. A. Flores-Livas, L. Boeri, A. Sanna, G. Profeta, R. Arita, and M. Eremets, A perspective on conven- tional high-temperature superconductors at high pres- sure: Methods and materials, Physics Reports A Per- spective on Conventional High-Temperature Supercon- ductors at High Pressure: Methods and Materials,856, 1 (2020)

    2020

Show all 56 references
  1. [9]

    K. Gao, T. F. T. Cerqueira, A. Sanna, Y.-W. Fang, Ð. Dangić, I. Errea, H.-C. Wang, S. Botti, and M. A. L. Marques, The maximum Tc of conventional superconduc- tors at ambient pressure, Nature Communications16, 8253 (2025)

    2025

  2. [10]

    Takada, Plasmon Mechanism of Superconductivity in Two- and Three-Dimensional Electron Systems, Journal of the Physical Society of Japan45, 786 (1978)

    Y. Takada, Plasmon Mechanism of Superconductivity in Two- and Three-Dimensional Electron Systems, Journal of the Physical Society of Japan45, 786 (1978)

    1978

  3. [11]

    Akashi and R

    R. Akashi and R. Arita, Development of Density- FunctionalTheoryforaPlasmon-AssistedSuperconduct- ing State: Application to Lithium Under High Pressures, Physical Review Letters111, 057006 (2013)

    2013

  4. [12]

    Ruhman and P

    J. Ruhman and P. A. Lee, Superconductivity at very low density: The case of strontium titanate, Physical Review B94, 224515 (2016)

    2016

  5. [13]

    Fatemi and J

    V. Fatemi and J. Ruhman, Synthesizing Coulombic su- perconductivity in van der Waals bilayers, Physical Re- view B98, 094517 (2018)

    2018

  6. [14]

    Sharma, M

    G. Sharma, M. Trushin, O. P. Sushkov, G. Vignale, and S. Adam, Superconductivity from collective excitations in magic-angle twisted bilayer graphene, Physical Review Research2, 022040 (2020)

    2020

  7. [15]

    in ’t Veld, M

    Y. in ’t Veld, M. I. Katsnelson, A. J. Millis, and M. Rös- ner, Enhancing plasmonic superconductivity in layered materials via dynamical Coulomb engineering, npj 2D Materials and Applications10, 30 (2026)

    2026

  8. [16]

    Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Cas- tro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, Gate-tuning of graphene plasmons revealed by infrared nano-imaging, Nature486, 82 (2012)

    2012

  9. [17]

    S. S. Sunku, G. X. Ni, B. Y. Jiang, H. Yoo, A. Stern- bach, A. S. McLeod, T. Stauber, L. Xiong, T. Taniguchi, K. Watanabe, P. Kim, M. M. Fogler, and D. N. Basov, Photonic crystals for nano-light in moiré graphene super- lattices (supp. mat.), Science362, 1153 (2018)

    2018

  10. [18]

    N. C. Hesp, I. Torre, D. Rodan-Legrain, P. Novelli, Y. Cao, S. Carr, S. Fang, P. Stepanov, D. Barcons-Ruiz, H. Herzig Sheinfux, K. Watanabe, T. Taniguchi, D. K. Efetov, E. Kaxiras, P. Jarillo-Herrero, M. Polini, and F. H. Koppens, Observation of interband collective ex- citati...

    2021

  11. [19]

    Huang, X

    T. Huang, X. Tu, C. Shen, B. Zheng, J. Wang, H. Wang, 10 K.Khaliji, S.H.Park, Z.Liu, T.Yang, Z.Zhang, L.Shao, X. Li, T. Low, Y. Shi, and X. Wang, Observation of chiral and slow plasmons in twisted bilayer graphene, Nature 605, 63 (2022)

    2022

  12. [20]

    Xiong, C

    L. Xiong, C. Forsythe, M. Jung, A. S. McLeod, S. S. Sunku, Y. M. Shao, G. X. Ni, A. J. Sternbach, S. Liu, J. H. Edgar, E. J. Mele, M. M. Fogler, G. Shvets, C. R. Dean, and D. N. Basov, Photonic crystal for graphene plasmons, Nature Communications10, 4780 (2019)

    2019

  13. [21]

    Xiong, Y

    L. Xiong, Y. Li, M. Jung, C. Forsythe, S. Zhang, A. S. McLeod, Y. Dong, S. Liu, F. L. Ruta, C. Li, K. Watan- abe, T. Taniguchi, M. M. Fogler, J. H. Edgar, G. Shvets, C. R. Dean, and D. N. Basov, Programmable Bloch po- laritons in graphene, Science Advances7, 1 (2021)

    2021

  14. [22]

    Grabowski and L

    M. Grabowski and L. J. Sham, Superconductivity from nonphonon interactions, Physical Review B29, 6132 (1984)

    1984

  15. [23]

    Grimaldi, L

    C. Grimaldi, L. Pietronero, and S. Strässler, Nonadi- abatic Superconductivity: Electron-Phonon Interaction Beyond Migdal’s Theorem, Physical Review Letters75, 1158 (1995)

    1995

  16. [24]

    Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo- Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature556, 80 (2018)

    2018

  17. [25]

    Bultinck, E

    N. Bultinck, E. Khalaf, S. Liu, S. Chatterjee, A. Vish- wanath, and M. P. Zaletel, Ground State and Hidden SymmetryofMagic-AngleGrapheneatEvenIntegerFill- ing, Physical Review X10, 031034 (2020)

    2020

  18. [26]

    G. Chen, A. L. Sharpe, E. J. Fox, Y.-H. Zhang, S. Wang, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi, Z. Shi, T. Senthil, D. Goldhaber-Gordon, Y. Zhang, and F. Wang, Tunable correlated Chern insulator and fer- romagnetism in a moiré superlattice, Nature579, 56 (2020)

    2020

  19. [27]

    E. C. Regan, D. Wang, C. Jin, M. I. Bakti Utama, B. Gao, X. Wei, S. Zhao, W. Zhao, Z. Zhang, K. Yu- migeta, M. Blei, J. D. Carlström, K. Watanabe, T. Taniguchi, S. Tongay, M. Crommie, A. Zettl, and F. Wang, Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlatt...

    2020

  20. [28]

    He, Y.-H

    M. He, Y.-H. Zhang, Y. Li, Z. Fei, K. Watanabe, T. Taniguchi, X. Xu, and M. Yankowitz, Competing cor- related states and abundant orbital magnetism in twisted monolayer-bilayergraphene,NatureCommunications12, 4727 (2021)

    2021

  21. [29]

    Shavit and J

    G. Shavit and J. Alicea, Quantum Geometric Kohn- Luttinger Superconductivity, Physical Review Letters 134, 176001 (2025)

    2025

  22. [30]

    Jahin and S.-Z

    A. Jahin and S.-Z. Lin, Enhanced Kohn-Luttinger super- conductivity in geometric bands, Physical Review B113, 014504 (2026)

    2026

  23. [31]

    E. R. Margine and F. Giustino, Anisotropic Migdal- Eliashberg theory using Wannier functions, Physical Re- view B87, 024505 (2013)

    2013

  24. [32]

    W. L. McMillan, Transition Temperature of Strong- Coupled Superconductors, Physical Review167, 331 (1968)

    1968

  25. [33]

    P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Physical Re- view B12, 905 (1975)

    1975

  26. [34]

    Morel and P

    P. Morel and P. W. Anderson, Calculation of the Su- perconducting State Parameters with Retarded Electron- Phonon Interaction, Physical Review125, 1263 (1962)

    1962

  27. [35]

    J. S. Hofmann, D. Chowdhury, S. A. Kivelson, and E. Berg, Heuristic bounds on superconductivity and how to exceed them, npj Quantum Materials7, 83 (2022)

    2022

  28. [36]

    J. S. Hofmann, E. Berg, and D. Chowdhury, Supercon- ductivity, Charge Density Wave, and Supersolidity in Flat Bands with a Tunable Quantum Metric, Physical Review Letters130, 226001 (2023)

    2023

  29. [37]

    J. P. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Communications in Math- ematical Physics76, 289 (1980)

    1980

  30. [38]

    Nashabeh and L

    L. Nashabeh and L. Fu, Prediction of superconduc- tivity in mass-asymmetric electron-hole bilayers (2026), arXiv:2601.07729 [cond-mat]

    2026

  31. [39]

    K. Ochi, H. Tajima, K. Iida, and H. Aoki, Resonant pair- exchange scattering and BCS-BEC crossover in a system composed of dispersive and heavy incipient bands: A Feshbach analogy, Physical Review Research4, 013032 (2022)

    2022

  32. [40]

    Tajima, H

    H. Tajima, H. Aoki, A. Perali, and A. Bianconi, Emer- gent Fano-Feshbach resonance in two-band superconduc- tors with an incipient quasiflat band: Enhanced critical temperature evading particle-hole fluctuations, Physical Review B109, L140504 (2024)

    2024

  33. [41]

    Peotta and P

    S. Peotta and P. Törmä, Superfluidity in topologically nontrivial flat bands, Nature Communications6, 8944 (2015)

    2015

  34. [42]

    Liang, T

    L. Liang, T. I. Vanhala, S. Peotta, T. Siro, A. Harju, and P. Törmä, Band geometry, Berry curvature, and super- fluid weight, Physical Review B95, 024515 (2017)

    2017

  35. [43]

    F. Xie, Z. Song, B. Lian, and B. A. Bernevig, Topology- BoundedSuperfluidWeightinTwistedBilayerGraphene, Physical Review Letters124, 167002 (2020)

    2020

  36. [44]

    Riolo, F

    R. Riolo, F. H. L. Koppens, P. Jarillo-Herrero, G. Mazza, A. H. MacDonald, and M. Polini, Polariton-induced superconductivity in two-dimensional metals (2025), arXiv:2511.00608 [cond-mat]

    2025

  37. [45]

    D. J. Scalapino, E. Loh, and J. E. Hirsch, D -wave pairing near a spin-density-wave instability, Physical Review B 34, 8190 (1986)

    1986

  38. [46]

    D. J. Scalapino, A common thread: The pairing inter- action for unconventional superconductors, Reviews of Modern Physics84, 1383 (2012)

    2012

  39. [47]

    Khalaf, A

    E. Khalaf, A. J. Kruchkov, G. Tarnopolsky, and A. Vish- wanath, Magic angle hierarchy in twisted graphene multilayers, Physical Review B100, 85109 (2019), arXiv:1901.10485

    2019 arXiv

  40. [48]

    C. Lei, L. Linhart, W. Qin, F. Libisch, and A. H. Mac- Donald, Mirror symmetry breaking and lateral stacking shifts in twisted trilayer graphene, Physical Review B 104, 035139 (2021)

    2021

  41. [49]

    J. M. Park, Y. Cao, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Tunable strongly coupled supercon- ductivity in magic-angle twisted trilayer graphene, Na- ture590, 249 (2021)

    2021

  42. [50]

    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, Science 371, 1133 (2021)

    2021

  43. [51]

    A. T. Pierce, Y. Xie, J. M. Park, Z. Cai, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, and A. Yacoby, Tunable interplay between light and heavy electrons in twisted 11 trilayer graphene, Nature Physics , 1 (2025)

    2025

  44. [52]

    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 superconductivity in magic-angle graphene multilayers, Science377, 1538 (2022)

    2022

  45. [53]

    J. M. Park, Y. Cao, L.-Q. Xia, S. Sun, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Robust supercon- ductivity in magic-angle multilayer graphene family, Na- ture Materials21, 877 (2022)

    2022

  46. [54]

    Sutherland, Localization of electronic wave functions due to local topology, Physical Review B34, 5208 (1986)

    B. Sutherland, Localization of electronic wave functions due to local topology, Physical Review B34, 5208 (1986)

    1986

  47. [55]

    S. Geng, X. Wang, R. Guo, C. Qiu, F. Chen, Q. Wang, K. Li, P. Hao, H. Liang, Y. Huang, Y. Wu, S. Cui, Z. Sun, T. K. Kim, C. Cacho, D. S. Dessau, B. T. Zhou, and H. Li, Experimental realization of dice-lattice flat band at the Fermi level in layered electride YCl, Nature Com- m...

    2026

  48. [56]

    S. Wang, S. D. Sarma, and J. D. Sau, Evolution from an acoustic-plasmon-mediated superconductivity to an acoustic-phonon-mediated superconductivity in bilayers (2026), arXiv:2607.10835 [cond-mat.supr-con]

    2026 arXiv

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