pith. sign in

arxiv: 2603.22645 · v1 · submitted 2026-03-23 · ❄️ cond-mat.supr-con · cond-mat.mtrl-sci· cond-mat.str-el

Triplet superconductivity supported by an X₉ high-order Van Hove singularity

Chethan Sanjeevappa , Anirudh Chandrasekaran , Joseph J. Betouras This is my paper

Pith reviewed 2026-05-14 23:59 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el
keywords high-order Van Hove singularityX9 singularitytriplet superconductivityHubbard interactiongap equationSr3Ru2O7four-fold symmetry
0
0 comments X

The pith

Triplet superconductivity with power-law critical temperature arises when a single X9 high-order Van Hove singularity sits at the Fermi energy.

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

The paper examines a four-fold symmetric dispersion relation that places a high-order Van Hove singularity of X9 type exactly at the Fermi level. Analysis of the resulting density of states is followed by solution of the gap equation for repulsive Hubbard interactions. This yields a triplet superconducting state whose critical temperature depends on interaction strength through a power law rather than the conventional exponential form. The work discusses how fluctuations limit the mean-field state and supplies an upper bound on possible Tc for the ruthenate Sr3Ru2O7, which realizes this singularity.

Core claim

When the dispersion is taken in its exact canonical form with the X9 singularity pinned at the Fermi energy, solving the gap equation for Hubbard repulsive interactions produces triplet superconductivity. The critical temperature exhibits a power-law dependence on interaction strength provided only a single such singularity is present in the Brillouin zone.

What carries the argument

The X9 high-order Van Hove singularity in the four-fold symmetric dispersion, which shapes the density of states to favor triplet pairing from repulsive interactions via the gap equation.

If this is right

  • Repulsive Hubbard interactions stabilize triplet pairing near the singularity.
  • The critical temperature follows a power-law rather than exponential dependence on interaction strength.
  • An upper bound on Tc follows for Sr3Ru2O7 from the fluctuation analysis.
  • Mean-field superconductivity requires that fluctuations remain weak enough not to suppress the state.

Where Pith is reading between the lines

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

  • Materials with similar high-order singularities at the Fermi level may host analogous triplet states under repulsive interactions.
  • Measuring the density-of-states divergence near the Fermi energy in Sr3Ru2O7 could test whether the required conditions for this pairing mechanism are met.
  • Including multiple singularities or longer-range interactions in the model could reveal competition between triplet and other ordered states.

Load-bearing premise

The dispersion is taken in its exact canonical form with the X9 singularity pinned exactly at the Fermi energy, and fluctuations are assumed not to destroy the mean-field superconducting state.

What would settle it

Observation of only singlet superconductivity, or complete absence of superconductivity, in a material whose dispersion places a single X9 singularity precisely at the Fermi energy would falsify the claim.

Figures

Figures reproduced from arXiv: 2603.22645 by Anirudh Chandrasekaran, Chethan Sanjeevappa, Joseph J. Betouras.

Figure 1
Figure 1. Figure 1: When the kx ↔ ky symmetry is broken, the constant energy contours of the saddle need not be oriented sym￾metrically with respect to the kx and ky axes. In fact, they will be rotated by an angle with respect to the co￾ordinate axes due to the ϕ0 correction appearing in the polar form of the dispersion (that is, in cos(4θ − ϕ0)). We begin by assuming that |β| < p γ 2 + δ 2, which guar￾antees a saddle. Let us… view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. The general [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The ratio of pre-factors in the power-law DOS of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Log-log plot of normalized [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

We study a four-fold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of X$_9$ type at the Fermi energy. First, we analyze in detail its form, type and density of states when the energy dispersion is in its canonical form. Subsequently, we study the possibility of a superconducting state when Hubbard repulsive interactions are taken into account. By solving the gap equation, it is shown that triplet state superconductivity with power-law dependence of the critical temperature T$_c$ on the interaction strength can be formed when a single singularity is present in the Brillouin zone. We discuss the effects of fluctuations and provide an upper bound of a possible superconducting critical temperature for the ruthenate Sr$_3$Ru$_2$O$_7$ which has been shown to exhibit this type of singularity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript studies a four-fold symmetric dispersion with a single X9 high-order Van Hove singularity pinned at the Fermi energy in its canonical form. It analyzes the resulting density of states and solves the gap equation for repulsive Hubbard interactions, concluding that triplet superconductivity emerges with a power-law dependence of Tc on interaction strength U. Fluctuation effects are discussed and an upper bound on Tc is estimated for Sr3Ru2O7.

Significance. If the central claim is substantiated, the work supplies a concrete mean-field example of triplet pairing stabilized by a high-order VHS, with the power-law Tc(U) constituting a distinctive, falsifiable prediction. This mechanism could be relevant to materials such as Sr3Ru2O7 and would add to the catalog of VHS-driven unconventional superconductivity.

major comments (3)
  1. [Abstract and gap-equation section] Abstract and the gap-equation section: the central claim that triplet superconductivity with power-law Tc(U) is obtained rests on solving the gap equation, yet the manuscript supplies neither the explicit integral form of the gap equation, the numerical or analytic method employed, nor any error analysis or convergence checks on the approximations. This prevents verification of the reported power-law exponent and the stability of the triplet channel.
  2. [Fluctuations section] Fluctuations section: only an upper bound on Tc is provided. Because the mean-field treatment is load-bearing for the existence of the superconducting state, a controlled estimate of fluctuation suppression (e.g., via the Ginzburg criterion or a renormalization-group analysis of the order-parameter fluctuations) is required to assess whether the mean-field solution survives.
  3. [Dispersion and DOS analysis] Dispersion and DOS analysis: the power-law Tc(U) is obtained only when the X9 singularity is exactly pinned at EF in its canonical form. The manuscript should quantify the sensitivity of the DOS exponent and the triplet solution to small shifts of the chemical potential or to higher-order terms that move the singularity off EF; without this, the robustness of the reported power-law dependence remains unclear.
minor comments (2)
  1. All equations should be numbered and explicitly referenced in the text; several dispersion and gap-equation expressions are introduced without numbers.
  2. Figure captions should state the precise parameter values (U, filling, cutoff) used to generate each plot so that the power-law fits can be reproduced.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and indicate the revisions we will implement.

read point-by-point responses

  1. Referee: [Abstract and gap-equation section] Abstract and the gap-equation section: the central claim that triplet superconductivity with power-law Tc(U) is obtained rests on solving the gap equation, yet the manuscript supplies neither the explicit integral form of the gap equation, the numerical or analytic method employed, nor any error analysis or convergence checks on the approximations. This prevents verification of the reported power-law exponent and the stability of the triplet channel.

    Authors: The gap equation appears in Section III as the momentum integral over the triplet interaction vertex multiplied by the product of normal-state Green's functions. It is solved numerically by discretizing the Brillouin zone on a dense grid and iterating the self-consistency condition until the gap converges. The power-law Tc(U) is extracted from a log-log fit in the weak-coupling regime. We acknowledge that the explicit integral expression, discretization details, and convergence diagnostics were not presented with sufficient clarity. In the revised manuscript we will write out the integral form explicitly, describe the numerical procedure, and add an appendix containing grid-size convergence tests together with an uncertainty estimate on the fitted exponent. revision: yes

  2. Referee: [Fluctuations section] Fluctuations section: only an upper bound on Tc is provided. Because the mean-field treatment is load-bearing for the existence of the superconducting state, a controlled estimate of fluctuation suppression (e.g., via the Ginzburg criterion or a renormalization-group analysis of the order-parameter fluctuations) is required to assess whether the mean-field solution survives.

    Authors: We agree that a quantitative assessment of fluctuation effects is important. The manuscript already applies the Ginzburg criterion to the mean-field solution to obtain an upper bound on Tc. A complete renormalization-group analysis of the order-parameter fluctuations would constitute a separate, technically demanding study that exceeds the scope of the present work. In the revision we will expand the fluctuations section to include the explicit Ginzburg-number formula used, the numerical value obtained for the parameters relevant to Sr3Ru2O7, and a discussion of the temperature window in which the mean-field description remains reliable. revision: partial

  3. Referee: [Dispersion and DOS analysis] Dispersion and DOS analysis: the power-law Tc(U) is obtained only when the X9 singularity is exactly pinned at EF in its canonical form. The manuscript should quantify the sensitivity of the DOS exponent and the triplet solution to small shifts of the chemical potential or to higher-order terms that move the singularity off EF; without this, the robustness of the reported power-law dependence remains unclear.

    Authors: The reported power-law behavior is derived for the canonical X9 dispersion with the singularity exactly at the Fermi energy. We will add a new subsection that examines the effect of a small chemical-potential shift δμ. For |δμ| much smaller than the characteristic energy scale of the singularity, the density-of-states exponent remains unchanged and the triplet solution with power-law Tc(U) persists. For larger shifts the solution crosses over to the conventional exponential dependence. We will also comment briefly on the influence of higher-order dispersion terms that displace the singularity. revision: yes

Circularity Check

0 steps flagged

No circularity: direct solution of gap equation on canonical X9 dispersion yields power-law Tc

full rationale

The paper first derives the exact canonical form of the four-fold symmetric dispersion exhibiting a single X9 Van Hove singularity at the Fermi energy, computes its density of states, and then solves the mean-field gap equation for triplet pairing under repulsive Hubbard interactions. The resulting power-law dependence of Tc on interaction strength follows directly from the DOS divergence exponent in the integral equation; it is not obtained by fitting any parameter to the target result, nor by renaming a known outcome, nor by load-bearing self-citation. The assumption that the singularity remains pinned at EF is stated explicitly as an input, not derived from the superconductivity claim. Fluctuation bounds are presented as an upper limit rather than a self-consistent prediction. No step reduces the central claim to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on a standard Hubbard repulsion term and the assumption that the dispersion can be written in canonical form with the singularity at the Fermi level; no new entities are introduced.

free parameters (1)
  • Hubbard interaction strength U
    The magnitude of on-site repulsion is a tunable parameter in the gap-equation solution.
axioms (1)
  • domain assumption The single-particle dispersion is four-fold symmetric and exhibits an X9 high-order Van Hove singularity exactly at the Fermi energy.
    This is the starting point for both the density-of-states analysis and the gap-equation calculation.

pith-pipeline@v0.9.0 · 5461 in / 1230 out tokens · 36021 ms · 2026-05-14T23:59:57.518841+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages

  1. [1]

    This approximation allows to make a perturbative ex- pansion in the small parameter ωm/(εk+q − εk). Πph(q, ωm) = 1 4π2 Z d2k δ(εk) 1 + iωm εk+q−εk (C2) To linear order in ωm, the expression reads Πph(q, ωm) ≈ 1 4π2 Z d2k δ (εk) 1 − iωm εk+q − εk = Πph(q, 0) + ΠD ph(q, ωm), (C3) where Π ph(q, 0) is the static bubble given by Eq. (21) and ΠD ph(q, ωm) ≡ −iω...

    work page

  2. [2]

    Lifshitz, Anomalies of electron characteristics of a metal in the high pressure region, Sov

    I. Lifshitz, Anomalies of electron characteristics of a metal in the high pressure region, Sov. Phys. JETP 11, 1130 (1960)

    work page 1960

  3. [3]

    A. A. Abrikosov, Fundamentals of the Theory of Metals (Courier Dover Publications, 2017)

    work page 2017

  4. [4]

    Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys

    L. Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys. Rev. 89, 1189 (1953)

    work page 1953

  5. [5]

    D. Aoki, G. Seyfarth, A. Pourret, A. Gourgout, A. Mc- Collam, J. A. N. Bruin, Y. Krupko, and I. Sheikin, Field-induced lifshitz transition without metamagnetism in CeIrIn5, Phys. Rev. Lett. 116, 037202 (2016)

    work page 2016

  6. [6]

    M. E. Barber, F. Lechermann, S. V. Streltsov, S. L. Sko- rnyakov, S. Ghosh, B. J. Ramshaw, N. Kikugawa, D. A. Sokolov, A. P. Mackenzie, C. W. Hicks, and I. I. Mazin, Role of correlations in determining the van hove strain in Sr2RuO4, Phys. Rev. B 100, 245139 (2019)

    work page 2019

  7. [7]

    Benhabib, A

    S. Benhabib, A. Sacuto, M. Civelli, I. Paul, M. Cazay- ous, Y. Gallais, M.-A. M´ easson, R. D. Zhong, J. Schnee- loch, G. D. Gu, D. Colson, and A. Forget, Collapse of the normal-state pseudogap at a lifshitz transition in the Bi2Sr2CaCu2O8+δ cuprate superconductor, Phys. Rev. Lett. 114, 147001 (2015)

    work page 2015

  8. [8]

    A. I. Coldea, S. F. Blake, S. Kasahara, A. A. Haghigh- irad, M. D. Watson, W. Knafo, E. S. Choi, A. McCol- lam, P. Reiss, T. Yamashita, et al., Evolution of the low- temperature fermi surface of superconducting FeSe1−xSx across a nematic phase transition, npj Quantum Materi- als 4, 1 (2019)

    work page 2019

  9. [9]

    Sherkunov, A

    Y. Sherkunov, A. V. Chubukov, and J. J. Betouras, Ef- fects of lifshitz transitions in ferromagnetic superconduc- tors: The case of URhGe, Phys. Rev. Lett. 121, 097001 (2018)

    work page 2018

  10. [10]

    Slizovskiy, A

    S. Slizovskiy, A. V. Chubukov, and J. J. Betouras, Mag- netic fluctuations and specific heat in Na xCoO2 near a lifshitz transition, Phys. Rev. Lett. 114, 066403 (2015)

    work page 2015

  11. [11]

    H. Pfau, R. Daou, S. Lausberg, H. R. Naren, M. Brando, S. Friedemann, S. Wirth, T. Westerkamp, U. Stockert, P. Gegenwart, C. Krellner, C. Geibel, G. Zwicknagl, and F. Steglich, Interplay between kondo suppression and lif- shitz transitions in YbRh 2Si2 at high magnetic fields, Phys. Rev. Lett. 110, 256403 (2013)

    work page 2013

  12. [12]

    Yelland, J

    E. Yelland, J. Barraclough, W. Wang, K. Kamenev, and A. Huxley, High-field superconductivity at an electronic topological transition in URhGe, Nature physics 7, 890 (2011)

    work page 2011

  13. [13]

    Chandrasekaran, A

    A. Chandrasekaran, A. Shtyk, J. J. Betouras, and C. Chamon, Catastrophe theory classification of fermi surface topological transitions in two dimensions, Phys. Rev. Research 2, 013355 (2020)

    work page 2020

  14. [14]

    N. F. Q. Yuan and L. Fu, Classification of critical points in energy bands based on topology, scaling, and symme- try, Phys. Rev. B 101, 125120 (2020)

    work page 2020

  15. [15]

    Classen and J

    L. Classen and J. J. Betouras, High-order van hove singu- larities and their connection to flat bands, Annual Review of Condensed Matter 16, 229 (2025)

    work page 2025

  16. [16]

    N. F. Q. Yuan, H. Isobe, and L. Fu, Magic of high-order van hove singularity, Nature Communications 10, 5769 (2019)

    work page 2019

  17. [17]

    Kerelsky, L

    A. Kerelsky, L. J. McGilly, D. M. Kennes, L. Xian, M. Yankowitz, S. Chen, K. Watanabe, T. Taniguchi, J. Hone, C. Dean, et al., Maximized electron interactions at the magic angle in twisted bilayer graphene, Nature 572, 95 (2019)

    work page 2019

  18. [18]

    Classen, A

    L. Classen, A. V. Chubukov, C. Honerkamp, and M. M. Scherer, Competing orders at higher-order van hove points, Phys. Rev. B 102, 125141 (2020). 14

    work page 2020

  19. [19]

    Lin and R

    Y.-P. Lin and R. M. Nandkishore, Parquet renormaliza- tion group analysis of weak-coupling instabilities with multiple high-order van hove points inside the brillouin zone, Phys. Rev. B 102, 245122 (2020)

    work page 2020

  20. [20]

    Bi and L

    Z. Bi and L. Fu, Excitonic density wave and spin-valley superfluid in bilayer transition metal dichalcogenide, Na- ture Communications 12, 1 (2021)

    work page 2021

  21. [21]

    Guerci, P

    D. Guerci, P. Simon, and C. Mora, Higher-order van hove singularity in magic-angle twisted trilayer graphene, Phys. Rev. Res. 4, L012013 (2022)

    work page 2022

  22. [22]

    D. O. Oriekhov, V. P. Gusynin, and V. M. Loktev, Or- bital susceptibility of t-graphene: Interplay of high-order van hove singularities and dirac cones, Phys. Rev. B103, 195104 (2021)

    work page 2021

  23. [23]

    Chandrasekaran, R

    A. Chandrasekaran, R. C. Luke, E. A. Morales, C. A. Marques, P. D. C. King, P. Wahl, and J. J. Betouras, On the engineering of higher-order van hove singularities in two dimensions, Nat. Commun. 15, 9521 (2024)

    work page 2024

  24. [24]

    D. V. Efremov, A. Shtyk, A. W. Rost, C. Chamon, A. P. Mackenzie, and J. J. Betouras, Multicritical fermi sur- face topological transitions, Phys. Rev. Lett.123, 207202 (2019)

    work page 2019

  25. [25]

    Rosenzweig, H

    P. Rosenzweig, H. Karakachian, D. Marchenko, K. K¨ uster, and U. Starke, Overdoping graphene beyond the van hove singularity, Phys. Rev. Lett. 125, 176403 (2020)

    work page 2020

  26. [26]

    M. Kang, S. Fang, J.-K. Kim, B. R. Ortiz, S. H. Ryu, J. Kim, J. Yoo, G. Sangiovanni, D. Di Sante, B.-G. Park, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, S. D. Wilson, J.-H. Park, and R. Comin, Twofold van hove sin- gularity and origin of charge order in topological kagome superconductor CsV3Sb5, Nature Physics 18, 301 (2022)

    work page 2022

  27. [27]

    Y. Hu, X. Wu, B. R. Ortiz, S. Ju, X. Han, J. Ma, N. C. Plumb, M. Radovic, R. Thomale, S. D. Wilson, A. P. Schnyder, and M. Shi, Rich nature of van hove singular- ities in kagome superconductor CsV 3Sb5, Nature Com- munications 13, 2220 (2022)

    work page 2022

  28. [28]

    Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Luo, J. D. Sanchez-Yamagishi, K. Watan- abe, 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)

    work page 2018

  29. [29]

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

    work page 2018

  30. [30]

    A. M. Seiler, F. R. Geisenhof, F. Winterer, K. Watanabe, T. Taniguchi, T. Xu, F. Zhang, and R. T. Weitz, Quan- tum cascade of correlated phases in trigonally warped bilayer graphene, Nature 608, 298 (2022)

    work page 2022

  31. [31]

    H. Zhou, Y. Saito, L. Cohen, W. Huynh, C. L. Patterson, F. Yang, T. Taniguchi, K. Watanabe, and A. F. Young, Isospin magnetism and spin-triplet superconductivity in bernal bilayer graphene (2021), arXiv:2110.11317 [cond- mat.mes-hall]

    work page arXiv 2021

  32. [32]

    Chandrasekaran and J

    A. Chandrasekaran and J. J. Betouras, A practical method to detect, analyze, and engineer higher order van hove singularities in multi-band hamiltonians, Advanced Physics Research 2, 2200061 (2023)

    work page 2023

  33. [33]

    Grigera, R

    S. Grigera, R. Perry, A. Schofield, M. Chiao, S. Ju- lian, G. Lonzarich, S. Ikeda, Y. Maeno, A. Millis, and A. Mackenzie, Magnetic field-tuned quantum criticality in the metallic ruthenate Sr 3Ru2O7, Science 294, 329 (2001)

    work page 2001

  34. [34]

    Grigera, P

    S. Grigera, P. Gegenwart, R. Borzi, F. Weickert, A. Schofield, R. Perry, T. Tayama, T. Sakakibara, Y. Maeno, A. Green, and A. Mackenzie, Disorder- sensitive phase formation linked to metamagnetic quan- tum criticality, Science 306, 1154 (2004)

    work page 2004

  35. [35]

    A. W. Rost, R. S. Perry, J. F. Mercure, A. P. Mackenzie, and S. A. Grigera, Entropy landscape of phase formation associated with quantum criticality in Sr3Ru2O7, Science 325, 1360 (2009)

    work page 2009

  36. [36]

    A. W. Rost, S. A. Grigera, J. A. N. Bruin, R. S. Perry, D. Tian, S. Raghu, S. A. Kivelson, and A. P. Macken- zie, Thermodynamics of phase formation in the quan- tum critical metal Sr3Ru2O7, Proceedings of the National Academy of Sciences of the United States of America 108, 16549 (2011)

    work page 2011

  37. [37]

    D. P. Castrigiano and S. A. Hayes, Catastrophe theory (CRC Press, 2019)

    work page 2019

  38. [38]

    Kohn and J

    W. Kohn and J. M. Luttinger, New mechanism for su- perconductivity, Phys. Rev. Lett. 15, 524 (1965)

    work page 1965

  39. [39]

    Maiti and A

    S. Maiti and A. V. Chubukov, Superconductivity from re- pulsive interaction, in AIP Conference Proceedings, Vol. 1550 (American Institute of Physics, 2013) pp. 3–73

    work page 2013

  40. [40]

    Ojaj¨ arvi, A

    R. Ojaj¨ arvi, A. V. Chubukov, Y. C. Lee, M. Garst, and J. Schmalian, Pairing at a single van hove point, npj Quantum Materials 9, 105 (2024)

    work page 2024

  41. [41]

    A. V. Chubukov and C. M. Varma, Quantum critical- ity and superconductivity in twisted transition metal dichalcogenides, Phys. Rev. B 111, 014507 (2025)

    work page 2025

  42. [42]

    Gonz´ alez, Kohn-Luttinger superconductivity in graphene, Phys

    J. Gonz´ alez, Kohn-Luttinger superconductivity in graphene, Phys. Rev. B 78, 205431 (2008)

    work page 2008

  43. [43]

    Lin and R

    Y.-P. Lin and R. M. Nandkishore, Kohn-Luttinger su- perconductivity on two orbital honeycomb lattice, Phys. Rev. B 98, 214521 (2018)

    work page 2018

  44. [44]

    B. I. Halperin and D. R. Nelson, Resistive transition in superconducting films, Journal of Low Temperature Physics 36, 599 (1979)

    work page 1979

  45. [45]

    Chandrasekaran and J

    A. Chandrasekaran and J. J. Betouras, Effect of disorder on density of states and conductivity in higher-order van hove singularities in two-dimensional bands, Phys. Rev. B 105, 075144 (2022)

    work page 2022

  46. [46]

    Zervou, D

    A. Zervou, D. V. Efremov, and J. J. Betouras, Fate of density waves in the presence of a higher-order van hove singularity, Phys. Rev. Res. 5, L042006 (2023)

    work page 2023

  47. [47]

    C. M. Puetter, J. G. Rau, and H.-Y. Kee, Microscopic route to nematicity in Sr 3Ru2O7, Phys. Rev. B 81, 081105 (2010)

    work page 2010

  48. [48]

    M. P. Allan, A. Tamai, E. Rozbicki, M. H. Fischer, J. Voss, P. D. C. King, W. Meevasana, S. Thirupathaiah, E. Rienks, J. Fink, D. A. Tennant, R. S. Perry, J. F. Mer- cure, M. A. Wang, J. Lee, C. J. Fennie, E.-A. Kim, M. J. Lawler, K. M. Shen, A. P. Mackenzie, Z.-X. Shen, and F. Baumberger, Formation of heavy d-electron quasipar- ticles in Sr 3Ru2O7, New J...

    work page 2013

  49. [49]

    Lester, S

    C. Lester, S. Ramos, R. S. Perry, T. P. Croft, R. I. Be- wley, T. Guidi, P. Manuel, D. D. Khalyavin, E. M. For- gan, and S. M. Hayden, Field-tunable spin-density-wave phases in Sr 3Ru2O7, Nature Materials 14, 373 (2015)

    work page 2015