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REVIEW 3 major objections 4 minor 97 references

Quantum geometric magnetic monopole and two-phase superconductivity in CeRh$_2$As$_2$

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Pith's one-line read The Dirac point at the $M$ point of CeRh$_2$As$_2$ produces quantum-geometric magnetic-monopole fluctuations that select spin-triplet $B_{1u}$ and $B_{2g}$ pairing states, explaining the material's two-phase diagram.

desk verdict A realistic 12-orbital model with solid RPA/FLEX numerics gives leading B1u/B2g pairing in CeRh2As2, but the quantum-geometry causal claim is asserted rather than demonstrated. read the letter →

arxiv 2510.24289 v1 pith:AWO5OCNJ submitted 2025-10-28 cond-mat.supr-con cond-mat.str-el

Kosuke Nogaki , Youichi Yanase This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords quantumgeometrymetricmagneticmonopolefluctuationspin-tripletsuperconductivityDirac-AndersonmodelCeRh2As2heavy-fermionsuperconductorlinearizedEliashbergequation
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 sets out to explain the two superconducting phases of CeRh$_2$As$_2$ from a single microscopic model rather than from a fitted pairing interaction. The authors build a two-dimensional 12-orbital Dirac-Anderson model whose bands reproduce the measured angle-resolved photoemission spectra and DFT+$U$ calculations, including a heavy $f$-electron Dirac point at the $M$ point. They show that the quantum metric of that Dirac point suppresses finite-momentum magnetic fluctuations and makes a ferroic magnetic-monopole fluctuation dominate, and they solve the linearized Eliashberg equation to find that spin-triplet $B_{1u}$ and $B_{2g}$ superconducting instabilities then become leading. If correct, this connects the geometric structure of the wave functions to the pairing symmetry of a real heavy-fermion superconductor and explains why the even- and odd-parity states are nearly degenerate in the pressure-tuned phase diagram.

What carries the argument

The central object is the quantum metric, the real part of the quantum geometric tensor, which measures how strongly Bloch wave functions change between neighboring momenta. Large values of the metric near the $M$-point Dirac point suppress magnetic fluctuations at finite $\mathbf{q}$ and push them toward $\mathbf{q}=0$, which in the sublattice-resolved basis appears as a ferroic magnetic-monopole fluctuation ($s_z\otimes\sigma_z$). This fluctuation enters the linearized Eliashberg equation through the particle-particle vertex and favors the $B_{1u}$ and $B_{2g}$ spin-triplet channels whose gap functions sit on the Dirac Fermi surface and near the Brillouin-zone edge, where inter-sublattice hopping is inefficient and the even/odd parity eigenvalues stay nearly degenerate. The RPA-versus-FLEX comparison then tests how much of the geometric mechanism survives the self-energy renormalization.

What would settle it

Compute the quantum metric $g_{\mu\nu}(\mathbf{k})$ for the 12-orbital Dirac-Anderson model and compare the integrated metric in the $M$-point Dirac region with the rest of the Brillouin zone; then artificially gap the Dirac point while preserving the Fermi surfaces and check whether the ferroic magnetic-monopole peak at $\mathbf{q}=0$ survives. If the peak does not track the Dirac-region metric, the quantum-geometric attribution fails.

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Extended reading notes

Core claim

The central claim is that the $M$-point Dirac point, through its quantum metric, controls both the magnetic and superconducting responses in CeRh$_2$As$_2$. In the Dirac-Anderson model, the magnetic-monopole susceptibility $s_z\otimes\sigma_z$ has its largest peak at $\mathbf{q}=0$, and the paper attributes this ferroic fluctuation to the quantum-geometric suppression of finite-$\mathbf{q}$ fluctuations inherited from the Dirac band. Solving the linearized Eliashberg equation near the multipole quantum critical point ($\alpha\simeq0.985$) gives leading eigenvalues $\lambda_{B_{1u}}=1.0314$ and $\lambda_{B_{2g}}=1.0306$, with spin-triplet gap functions concentrated on the small Fermi surface that surrounds the $M$ point. A comparison of the random-phase and fluctuation-exchange approximations shows that self-energy corrections weaken the geometric effect, partially restoring antiferromagnetic fluctuations and making the even-parity $B_{2g}$ channel competitive; the paper uses this to interpret the ambient-pressure and high-pressure behavior of CeRh$_2$As$_2$.

Load-bearing premise

The load-bearing premise is that the quantum-geometric suppression of finite-$\mathbf{q}$ magnetic fluctuations, which has an analytic foundation only in SU(2)-symmetric models, carries over to the spin-orbit coupled 12-orbital Dirac-Anderson model; the argument relies on that analogy without directly computing the quantum metric or testing a model without the Dirac point.

Editorial extensions

If this is right

  • At Stoner factors near the multipole instability, the odd-parity $B_{1u}$ and even-parity $B_{2g}$ states are the leading superconducting channels and have nearly equal eigenvalues.
  • The $B_{1u}$ gap function is concentrated on the small Fermi surface derived from the Dirac point, so the same band feature drives the magnetic fluctuations and the pairing amplitude.
  • Self-energy corrections in the FLEX approximation reduce the quantum-geometric suppression of finite-$\mathbf{q}$ fluctuations and the magnetic anisotropy, yielding coexisting ferroic magnetic-monopole and antiferromagnetic fluctuations.
  • With the renormalized fluctuations, the even-parity $B_{2g}$ state should win at zero field, consistent with the observation that the low-field phase is even-parity in CeRh$_2$As$_2$.
  • Under pressure the renormalization effects weaken, so the nearly degenerate even- and odd-parity eigenvalues of the $B_{2g}$ and $B_{1u}$ states become the relevant description, matching the pressure-induced merging of the two transition temperatures.

Reading between the lines

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

  • If the paper is right, directly computing the quantum metric $g_{\mu\nu}(\mathbf{k})$ of the 12-orbital model should show that the $M$-point Dirac band dominates the integrated metric; this calculation can also predict how strongly the ferroic monopole peak responds to band-structure changes.
  • If the geometric mechanism is generic, other heavy-fermion compounds with a heavy Dirac point near $E_F$ and local inversion-symmetry breaking should also show near-degenerate even/odd-parity superconducting channels, and the model's band-structure criteria could be used to screen candidates.
  • The predicted renormalization of the quantum metric by Hubbard interactions implies a concrete pressure signature: the antiferromagnetic spectral weight already visible in neutron scattering should grow relative to the $\mathbf{q}=0$ monopole response as pressure weakens correlation renormalization.
  • A full $H$-$T$ phase-boundary calculation from the model would turn the identification of $B_{2g}$ and $B_{1u}$ with the two phases into a quantitative prediction of field-angle dependence and transition field, which existing experiments could test.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper constructs a two-dimensional 12-orbital Dirac-Anderson model for the locally noncentrosymmetric heavy-fermion superconductor CeRh2As2, with tight-binding parameters chosen to reproduce the ARPES and DFT+U band structure, including the van Hove singularities and an f-electron Dirac point at the M point. Using RPA and FLEX approximations, the authors compute multipole susceptibilities and find a dominant ferroic magnetic-monopole fluctuation (odd-parity longitudinal magnetic fluctuation, s_z ⊗ σ_z). Solving the linearized Eliashberg equation, they report that for large Hubbard U the B1u and B2g representations, both spin-triplet dominated, have nearly degenerate leading eigenvalues, which they connect to the field- and pressure-induced two-phase superconducting behavior of CeRh2As2. A comparison of RPA and FLEX is used to argue that strong correlations weaken the quantum-geometric suppression of finite-q fluctuations, restoring antiferromagnetic fluctuations consistent with neutron scattering, and that pressure suppresses this renormalization to recover the RPA-like near degeneracy.

Significance. If the central causal claim holds, the paper would provide a material-specific mechanism linking the quantum metric of a Dirac point to ferroic magnetic-monopole fluctuations and to spin-triplet pairing in a heavy-fermion superconductor, offering a unified explanation of the two superconducting phases in CeRh2As2. The numerical study is substantial: the model Hamiltonian and parameters are explicit (Appendix A), the calculations use a dense 1024×1024 momentum mesh, and the RPA/FLEX/Eliashberg machinery is standard and internally consistent. The authors also merit credit for stating clearly where their analytic support ends, noting that the quantum-geometry argument is proven only in SU(2)-symmetric limits. However, the central mechanism as stated in the title and abstract — that quantum geometry of the Dirac point causes the monopole fluctuations and the leading spin-triplet instabilities — is not directly demonstrated by the calculations, which do not compute the quantum metric and do not isolate the Dirac point's role from conventional density-of-states or nesting effects.

major comments (3)
  1. [Section III, paragraph beginning 'Let us discuss the origin...'] The assertion that quantum geometry drives the ferroic magnetic-monopole fluctuations is not established. The text explicitly concedes that an analytic expression is available only for SU(2)-symmetric cases [72,76] and then asserts that 'quantum geometry should play a pivotal role in the spin-orbit coupled Dirac-Anderson model as well.' The paper computes no quantum metric tensor, does not decompose the susceptibility into geometric and conventional contributions, and performs no control calculation with the M-point Dirac point removed or deformed. Consequently, the abstract's statement that 'quantum geometry strongly favors magnetic-monopole fluctuations because of the Dirac point at the M point' is an extrapolation rather than a result of the calculations. The pronounced q=0 peak in χ_{s_z⊗σ_z}(q) in Fig. 2 could originate from the high density of states of the heavy Dirac band or from Stoner enhancement independent of geometry. To support the causal claim, please compute the quantum metric (or band-resolved geometric tensor) and correlate it with the ferroic susceptibility, or run a model with the Dirac point gapped or shifted and show that the monopole peak and the B1u/B2g eigenvalues are suppressed.
  2. [Section IV, final paragraph] The conclusion that 'the Dirac point plays an essential role in both the magnetic fluctuations and the superconductivity through quantum geometry and the large density of states' conflates two distinct mechanisms. The observation that the B1u gap function is concentrated on the small Dirac Fermi surface (Figs. 3(e-g)) is equally consistent with a conventional density-of-states or Fermi-surface-nesting mechanism, and the text itself lists quantum geometry and the large density of states together without separating them. The eigenvalue hierarchy in Fig. 3(a), where B2g/B1u become leading only for large Stoner factor, does not by itself identify the geometric contribution. To justify the abstract's claim that the spin-triplet states 'originate from the Dirac point' through quantum geometry, the authors should disentangle these contributions, for example by comparing the Eliashberg kernel with and without the geometric tensor or by using a band structure in which the M-point degeneracy is lifted while approximately preserving the density of states.
  3. [Section V, Eq. (7) and surrounding paragraph] The conclusion that 'the Coulomb interaction suppresses the effect of quantum geometry' is inferred from the recovery of antiferroic fluctuations in FLEX and from a citation to Ref. [90] for a flat-band model. No quantum metric or geometry-resolved susceptibility is evaluated in the interacting case. The comparison also uses different parameters: RPA is shown at the Stoner factor α≈0.985, while FLEX is shown for U=0.22 with α≈0.995, so the change in the normalized bare susceptibility χ^0(q)/max χ^0(q) reflects the self-energy dressing of the bands as well as any change in geometric effects. Since this mitigation is a key step in the pressure explanation of the two-phase diagram, the authors should either compute the relevant geometric quantity in the FLEX framework or frame this part as a qualitative proposal rather than a demonstrated result.
minor comments (4)
  1. [Appendix B, below Eq. (B2)] The phrase 'gresed Green function' is a typo for 'dressed Green function'.
  2. [Section II, 'Fermi surface' paragraph] The omission of the small cylindrical Fermi surface around Γ is noted as an expectation that it is unimportant, but no quantitative estimate is given. Because the model is presented as material-specific, a brief estimate of its contribution to the relevant susceptibilities would strengthen the justification.
  3. [Appendix B, Eq. (B10)] The static-limit approximation A(q,0) ≈ [A(q,iπT)+A(q,−iπT)]/2 is introduced without justification; a short explanation or reference for why this holds at the chosen temperature would improve reproducibility.
  4. [Section V, paragraph on pressure] The statement that 'applied pressure is expected to weaken the renormalization effect' is an assumption underlying the comparison with experiments [33,34]; it would be helpful to state explicitly that this is a phenomenological expectation rather than a derived result of the model.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the superconducting eigenvalues and monopole susceptibility are direct numerical outputs of an explicit model; the quantum-geometry mechanism is an interpretive extrapolation, not an input.

full rationale

The numerical derivation chain is not circular. The 12-orbital Dirac-Anderson model (Appendix A) is an explicit tight-binding Hamiltonian, and the multipole susceptibilities and Eliashberg eigenvalues (Eqs. 2-4, Figs. 2-3) are computed from it by RPA/FLEX and linearized Eliashberg equations; no superconducting eigenvalue or pairing symmetry is inserted as an input. The renormalization factors z=0.30 and z~=0.3464 are fixed to normal-state ARPES/DFT+U band features, not to Tc or to the B1u/B2g eigenvalues, so the prediction of these leading instabilities is not statistically forced. The only step that leans on same-group prior work is the interpretation in Sec. III that Dirac-point quantum geometry stabilizes ferroic magnetic-monopole fluctuations, citing Refs. [72,76]. But the paper explicitly states the analytic expression is available only for SU(2)-symmetric cases and then offers the extension as an expectation ('quantum geometry should play a pivotal role'), not as a derivation feeding the numerics. The q=0 monopole peak is computed from the Hamiltonian, not from the cited formula, and no quantum-metric term is put into the Hamiltonian; hence the cited result is independent support with stated assumptions rather than a circular input. The lack of a Dirac-point-free control calculation is a verification/completeness gap for the causal narrative, not a case of a predicted quantity being equivalent by construction to its inputs.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on a heavily parameterized tight-binding model fitted to DFT+U and ARPES data, and on an untested extension of the SU(2) quantum-geometry suppression argument to the spin-orbit coupled model. No new particles or forces are invented.

free parameters (5)
  • renormalization factor z (f-orbital hopping) = 0.30
    Introduced in Sec. II/Appendix A so the van Hove singularity position matches ARPES and DFT+U.
  • renormalization factor ztilde (c-f hybridization) = 0.3464
    Same purpose as z.
  • Tight-binding parameters (Table II) = mu_f=-0.085, mu_d1=0.05, mu_d2=-0.475, t1, t2, t3, alpha, t_perp,1, t_perp,2, t_perp, and other hopping terms
    Fit to DFT+U band structure and ARPES Fermi surface; see Appendix A.
  • Filling per unit cell = 7.5
    Chosen to match the electron count of the material; standard for the model.
  • Hubbard U on Ce-4f = scanned in RPA; U=0.22 in FLEX
    Interaction strength is varied to reach Stoner factor alpha=0.985 (RPA) and alpha~0.995 (FLEX); not fitted to superconducting data.
assumptions (6)
  • ad hoc to paper The SU(2) quantum-geometry result that a large quantum metric suppresses finite-q fluctuations extends to the spin-orbit coupled Dirac-Anderson model.
    Sec. III invokes Refs [72,76] and states 'quantum geometry should play a pivotal role' without computing the metric.
  • domain assumption The M-point Dirac point predicted by DFT+U is a real feature of CeRh2As2 near EF.
    Sec. II: the Dirac-Anderson model is built to reproduce this DFT+U feature; ARPES has not confirmed the Dirac point directly.
  • domain assumption The small Gamma-centered Fermi surface is negligible for magnetism and superconductivity.
    Sec. II: omitted 'because it is expected to be not important for magnetism and superconductivity'.
  • standard math The augmented multipole classification, including the s_z⊗sigma_z 'magnetic monopole' label, is valid for this model.
    Sec. III uses the multipole basis of Refs [78-80]; standard group-theoretical classification.
  • domain assumption RPA/FLEX and linearized Eliashberg theory are adequate for the pairing instability analysis.
    Standard approximations in the field, as stated in Secs. IV and Appendix B.
  • ad hoc to paper Applied pressure weakens the self-energy renormalization, making RPA more realistic.
    Sec. V: 'Applied pressure is expected to weaken the renormalization effect'; this is plausible but not calculated.

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Cite this review

Pith. "Pith review of Quantum geometric magnetic monopole and two-phase superconductivity in CeRh$_2$As$_2$." pith.science (2026). https://pith.science/paper/AWO5OCNJ

@misc{pith2026251024289,
  author       = {Pith},
  title        = {Pith review of: Quantum geometric magnetic monopole and two-phase superconductivity in CeRh$_2$As$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AWO5OCNJ}},
  note         = {Machine review of arXiv:2510.24289}
}
abstract

Recent angle-resolved photoemission spectroscopy (ARPES) and density functional theory plus Hubbard $U$ (DFT+$U$) studies revealed that a heavy-fermion superconductor CeRh$_2$As$_2$ exhibits van Hove singularities and the Dirac point near the Fermi level $E_{\mathrm F}$, which are key signatures of strong-correlation effects and quantum geometry. We have constructed a two-dimensional 12-orbital \textit{Dirac-Anderson} model as an effective model for CeRh$_2$As$_2$. The band structure and Fermi-surface topology of the Dirac-Anderson model agree well with the ARPES data and the DFT+$U$ calculations. We show that the quantum geometry strongly favors magnetic-monopole fluctuations because of the Dirac point at the $M$ point. By solving the linearized \'{E}liashberg equation, we demonstrate that the $B_{1u}$ and $B_{2g}$ representations, spin-triplet states originating from the Dirac point, exhibit the leading superconducting instabilities. By comparing the random-phase approximation and the fluctuation-exchange approximation, we further demonstrate that strong-correlation effects mitigate the influence of quantum geometry. The phase diagram of CeRh$_2$As$_2$ under pressure is discussed in connection with the theoretical results.

Figures

Figures reproduced from arXiv: 2510.24289 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Crystalline structure of CeRh [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The momentum dependence of the static multipole suscepti [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Eigenvalues [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison between the RPA and FLEX. Normalized mo [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) The ARPES data (intensity) with DFT+ [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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Works this paper leans on

97 extracted references · 61 canonical work pages

  1. [90]

    Sukhachov, N

    P. Sukhachov, N. H. Aase, K. Mæland, and A. Sudbø, Effect of the hubbard interaction on the quantum metric, Phys. Rev. B 111, 085143 (2025)

    work page 2025

  2. [1]

    Wen,Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, 2007)

    X.-G. Wen,Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, 2007)

    2007

  3. [2]

    Fradkin,Field Theories of Condensed Matter Physics, 2nd ed

    E. Fradkin,Field Theories of Condensed Matter Physics, 2nd ed. (Cambridge University Press, 2013)

    2013

  4. [3]

    R. B. Laughlin, Quantized hall conductivity in two dimensions, Phys. Rev. B23, 5632 (1981)

    1981

  5. [4]

    D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett.49, 405 (1982)

    1982

  6. [5]

    Savary and L

    L. Savary and L. Balents, Quantum spin liquids: a review, Re- ports on Progress in Physics80, 016502 (2016)

    2016

  7. [6]

    Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys.89, 025003 (2017)

    2017

  8. [7]

    Broholm, R

    C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Quantum spin liquids, Science367, eaay0668 (2020)

    2020

Show all 97 references
  1. [8]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Topological insulators and supercon- ductors, Rev. Mod. Phys.83, 1057 (2011)

    2011

  2. [9]

    Tanaka, M

    Y. Tanaka, M. Sato, and N. Nagaosa, Symmetry and topology in superconductors –odd-frequency pairing and edge states–, Journal of the Physical Society of Japan81, 011013 (2012)

    2012

  3. [10]

    Sato and S

    M. Sato and S. Fujimoto, Majorana fermions and topology in superconductors, Journal of the Physical Society of Japan85, 072001 (2016)

    2016

  4. [11]

    Sato and Y

    M. Sato and Y. Ando, Topological superconductors: a review, Reports on Progress in Physics80, 076501 (2017)

    2017

  5. [12]

    A. Y. Kitaev, Unpaired majorana fermions in quantum wires, Physics-Uspekhi44, 131 (2001)

    2001

  6. [13]

    Nayak, S

    C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-abelian anyons and topological quantum computation, Rev. Mod. Phys.80, 1083 (2008)

    2008

  7. [14]

    Moriya and K

    T. Moriya and K. Ueda, Spin fluctuations and high temperature superconductivity, Advances in Physics49, 555 (2000)

    2000

  8. [15]

    Yanase, T

    Y. Yanase, T. Jujo, T. Nomura, H. Ikeda, T. Hotta, and K. Ya- mada, Theory of superconductivity in strongly correlated elec- tron systems, Physics Reports387, 1 (2003)

    2003

  9. [16]

    Aoki, J.-P

    D. Aoki, J.-P. Brison, J. Flouquet, K. Ishida, G. Knebel, Y. Toku- naga, and Y. Yanase, Unconventional superconductivity in ute2, Journal of Physics: Condensed Matter34, 243002 (2022)

    2022

  10. [17]

    M. H. Fischer, F. Loder, and M. Sigrist, Superconductivity and local noncentrosymmetricity in crystal lattices, Phys. Rev. B84, 184533 (2011)

    2011

  11. [18]

    Maruyama, M

    D. Maruyama, M. Sigrist, and Y. Yanase, Locally non- centrosymmetric superconductivity in multilayer systems, Jour- nal of the Physical Society of Japan81, 034702 (2012)

    2012

  12. [19]

    Yoshida, M

    T. Yoshida, M. Sigrist, and Y. Yanase, Pair-density wave states through spin-orbit coupling in multilayer superconductors, Phys. Rev. B86, 134514 (2012)

    2012

  13. [20]

    M. H. Fischer, M. Sigrist, D. F. Agterberg, and Y. Yanase, Su- perconductivity and local inversion-symmetry breaking, Annual Review of Condensed Matter Physics14, 153 (2023)

    2023

  14. [21]

    M ¨ockli, Y

    D. M ¨ockli, Y. Yanase, and M. Sigrist, Orbitally limited pair- density-wave phase of multilayer superconductors, Phys. Rev. B 97, 144508 (2018)

    2018

  15. [22]

    M ¨ockli and A

    D. M ¨ockli and A. Ramires, Superconductivity in disordered locally noncentrosymmetric materials: An application to cerh2as2, Phys. Rev. B104, 134517 (2021)

    2021

  16. [23]

    Maki, The magnetic properties of superconducting alloys

    K. Maki, The magnetic properties of superconducting alloys. ii, Physics Physique Fizika1, 127 (1964)

    1964

  17. [24]

    S. Khim, J. F. Landaeta, J. Banda, N. Bannor, M. Brando, P. M. R. Brydon, D. Hafner, R. K¨ uchler, R. Cardoso-Gil, U. Stockert, A. P. Mackenzie, D. F. Agterberg, C. Geibel, and E. Hassinger, Field-induced transition within the superconduct- ing state of cerh¡sub¿2¡/sub¿as¡sub¿...

    2021

  18. [25]

    Kimura, J

    S.-i. Kimura, J. Sichelschmidt, and S. Khim, Optical study of the electronic structure of locally noncentrosymmetric Cerh2as2, Phys. Rev. B104, 245116 (2021)

    2021

  19. [26]

    Onishi, U

    S. Onishi, U. Stockert, S. Khim, J. Banda, M. Brando, and E. Hassinger, Low-temperature thermal conductivity of the two- phase superconductor cerh2as2, Frontiers in Electronic Materi- alsVolume 2 - 2022, 10.3389/femat.2022.880579 (2022)

    2022

  20. [27]

    Kibune, S

    M. Kibune, S. Kitagawa, K. Kinjo, S. Ogata, M. Manago, 9 T. Taniguchi, K. Ishida, M. Brando, E. Hassinger, H. Rosner, C. Geibel, and S. Khim, Observation of antiferromagnetic order as odd-parity multipoles inside the superconducting phase in CeRh2As2, Phys. Rev. Lett.128, 0570...

    2022

  21. [28]

    Hafner, P

    D. Hafner, P. Khanenko, E.-O. Eljaouhari, R. K¨ uchler, J. Banda, N. Bannor, T. L¨ uhmann, J. F. Landaeta, S. Mishra, I. Sheikin, E. Hassinger, S. Khim, C. Geibel, G. Zwicknagl, and M. Brando, Possible quadrupole density wave in the superconducting kondo lattice cerh2as2, Phys...

    2022

  22. [29]

    Kitagawa, M

    S. Kitagawa, M. Kibune, K. Kinjo, M. Manago, T. Taniguchi, K. Ishida, M. Brando, E. Hassinger, C. Geibel, and S. Khim, Two-dimensional XY-type magnetic properties of locally non- centrosymmetric superconductor CeRh 2As2, Journal of the Physical Society of Japan91, 043702 (2022)

    2022

  23. [30]

    J. F. Landaeta, P. Khanenko, D. C. Cavanagh, C. Geibel, S. Khim, S. Mishra, I. Sheikin, P. M. R. Brydon, D. F. Agter- berg, M. Brando, and E. Hassinger, Field-angle dependence reveals odd-parity superconductivity in cerh 2as2, Phys. Rev. X 12, 031001 (2022)

    2022

  24. [31]

    Mishra, Y

    S. Mishra, Y. Liu, E. D. Bauer, F. Ronning, and S. M. Thomas, Anisotropic magnetotransport properties of the heavy-fermion superconductor cerh2as2, Phys. Rev. B106, L140502 (2022)

    2022

  25. [32]

    Ogata, S

    S. Ogata, S. Kitagawa, K. Kinjo, K. Ishida, M. Brando, E. Has- singer, C. Geibel, and S. Khim, Parity transition of spin-singlet superconductivity using sublattice degrees of freedom, Phys. Rev. Lett.130, 166001 (2023)

    2023

  26. [33]

    Semeniuk, D

    K. Semeniuk, D. Hafner, P. Khanenko, T. L¨ uhmann, J. Banda, J. F. Landaeta, C. Geibel, S. Khim, E. Hassinger, and M. Brando, Decoupling multiphase superconductivity from normal state or- dering in cerh2as2, Phys. Rev. B107, L220504 (2023)

    2023

  27. [34]

    Siddiquee, Z

    H. Siddiquee, Z. Rehfuss, C. Broyles, and S. Ran, Pressure dependence of superconductivity in cerh2as2, Phys. Rev. B108, L020504 (2023)

    2023

  28. [35]

    Ogata, S

    S. Ogata, S. Kitagawa, M. Kibune, K. Ishida, K. Kinjo, M. Brando, C. Geibel, S. Khim, and E. Hassinger, Investigation of the hyperfine coupling constant of locally noncentrosymmet- ric heavy-fermion superconductor CeRh2As2, New Physics: Sae Mulli73, 1115 (2023)

    2023

  29. [36]

    D. S. Christovam, M. Ferreira-Carvalho, A. Marino, M. Sun- dermann, D. Takegami, A. Melendez-Sans, K. D. Tsuei, Z. Hu, S. R¨oßler, M. Valvidares, M. W. Haverkort, Y. Liu, E. D. Bauer, L. H. Tjeng, G. Zwicknagl, and A. Severing, Spectroscopic ev- idence of kondo-induced quasiqu...

    2024

  30. [37]

    Chajewski and D

    G. Chajewski and D. Kaczorowski, Discovery of magnetic phase transitions in heavy-fermion superconductor cerh 2as2, Phys. Rev. Lett.132, 076504 (2024)

    2024

  31. [38]

    X. Chen, L. Wang, J. Ishizuka, R. Zhang, K. Nogaki, Y. Cheng, F. Yang, Z. Chen, F. Zhu, Z. Liu, J. Mei, Y. Yanase, B. Lv, and Y. Huang, Coexistence of near-𝐸𝐹 flat band and van hove singularity in a two-phase superconductor, Phys. Rev. X14, 021048 (2024)

    2024

  32. [39]

    B. Chen, H. Liu, Q.-Y. Wu, C. Zhang, X.-Q. Ye, Y.-Z. Zhao, J.-J. Song, X.-Y. Tian, B.-L. Tan, Z.-T. Liu, M. Ye, Z.-H. Chen, Y.-B. Huang, D.-W. Shen, Y.-H. Yuan, J. He, Y.-X. Duan, and J.-Q. Meng, Exploring possible fermi surface nesting and the nature of heavy quasiparticles i...

    2024

  33. [40]

    Y. Wu, Y. Zhang, S. Ju, Y. Hu, Y. Huang, Y. Zhang, H. Zhang, H. Zheng, G. Yang, E.-O. Eljaouhari, B. Song, N. C. Plumb, F. Steglich, M. Shi, G. Zwicknagl, C. Cao, H. Yuan, and Y. Liu, Fermi surface nesting with heavy quasiparticles in the lo- cally noncentrosymmetric supercond...

    2024

  34. [41]

    Pfeiffer, K

    M. Pfeiffer, K. Semeniuk, J. F. Landaeta, R. Borth, C. Geibel, M. Nicklas, M. Brando, S. Khim, and E. Hassinger, Pressure- tuned quantum criticality in the locally noncentrosymmetric su- perconductor cerh2as2, Phys. Rev. Lett.133, 126506 (2024)

    2024

  35. [42]

    Semeniuk, M

    K. Semeniuk, M. Pfeiffer, J. F. Landaeta, M. Nicklas, C. Geibel, M. Brando, S. Khim, and E. Hassinger, Exposing the odd-parity superconductivity in cerh 2as2 with hydrostatic pressure, Phys. Rev. B110, L100504 (2024)

    2024

  36. [43]

    Ogata, S

    S. Ogata, S. Kitagawa, K. Kinjo, K. Ishida, M. Brando, E. Has- singer, C. Geibel, and S. Khim, Appearance of𝑐-axis magnetic moment in odd-parity antiferromagnetic state in cerh 2as2 re- vealed by 75As-NMR, Phys. Rev. B110, 214509 (2024)

    2024

  37. [44]

    T. Chen, H. Siddiquee, Q. Xu, Z. Rehfuss, S. Gao, C. Ly- gouras, J. Drouin, V. Morano, K. E. Avers, C. J. Schmitt, A. Podlesnyak, J. Paglione, S. Ran, Y. Song, and C. Broholm, Quasi-two-dimensional antiferromagnetic spin fluctuations in the spin-triplet superconductor candidat...

    2024

  38. [45]

    Nogaki, A

    K. Nogaki, A. Daido, J. Ishizuka, and Y. Yanase, Topologi- cal crystalline superconductivity in locally noncentrosymmetric cerh2as2, Phys. Rev. Res.3, L032071 (2021)

    2021

  39. [46]

    Ishizuka, K

    J. Ishizuka, K. Nogaki, M. Sigrist, and Y. Yanase, Correlation- induced fermi surface evolution and topological crystalline superconductivity in CeRh 2As2, Phys. Rev. B110, L140505 (2024)

    2024

  40. [47]

    Nogaki and Y

    K. Nogaki and Y. Yanase, Even-odd parity transition in strongly correlated locally noncentrosymmetric superconductors: Ap- plication to cerh2as2, Phys. Rev. B106, L100504 (2022)

    2022

  41. [48]

    C. Lee, D. F. Agterberg, and P. M. R. Brydon, Unified picture of superconductivity and magnetism in cerh 2as2, Phys. Rev. Lett. 135, 026003 (2025)

    2025

  42. [49]

    Resta, The insulating state of matter: a geometrical theory, Eur

    R. Resta, The insulating state of matter: a geometrical theory, Eur. Phys. J. B79, 121 (2011)

    2011

  43. [50]

    T ¨orm¨a, S

    P. T ¨orm¨a, S. Peotta, and B. A. Bernevig, Superconductivity, su- perfluidity and quantum geometry in twisted multilayer systems, Nature Reviews Physics4, 528 (2022)

    2022

  44. [51]

    Liu, X.-B

    T. Liu, X.-B. Qiang, H.-Z. Lu, and X. C. Xie, Quantum geometry in condensed matter, National Science Review12, nwae334 (2024)

    2024

  45. [52]

    Y. Gao, S. A. Yang, and Q. Niu, Field induced positional shift of bloch electrons and its dynamical implications, Phys. Rev. Lett. 112, 166601 (2014)

    2014

  46. [53]

    Sodemann and L

    I. Sodemann and L. Fu, Quantum nonlinear hall effect induced by berry curvature dipole in time-reversal invariant materials, Phys. Rev. Lett.115, 216806 (2015)

    2015

  47. [54]

    Z. Z. Du, C. M. Wang, H.-Z. Lu, and X. C. Xie, Band signatures for strong nonlinear hall effect in bilayer wte2, Phys. Rev. Lett. 121, 266601 (2018)

    2018

  48. [55]

    Z. Z. Du, C. M. Wang, S. Li, H.-Z. Lu, and X. C. Xie, Disorder- induced nonlinear hall effect with time-reversal symmetry, Na- ture Communications10, 3047 (2019)

    2019

  49. [56]

    Ma, S.-Y

    Q. Ma, S.-Y. Xu, H. Shen, D. MacNeill, V. Fatemi, T.-R. Chang, A. M. Mier Valdivia, S. Wu, Z. Du, C.-H. Hsu, S. Fang, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, E. Kaxiras, H.-Z. Lu, H. Lin, L. Fu, N. Gedik, and P. Jarillo-Herrero, Observa- tion of the nonlinear hall...

    2019

  50. [57]

    N. Wang, D. Kaplan, Z. Zhang, T. Holder, N. Cao, A. Wang, X. Zhou, F. Zhou, Z. Jiang, C. Zhang, S. Ru, H. Cai, K. Watan- abe, T. Taniguchi, B. Yan, and W. Gao, Quantum-metric-induced nonlinear transport in a topological antiferromagnet, Nature621, 487 (2023)

    2023

  51. [58]

    Gao, Y.-F

    A. Gao, Y.-F. Liu, J.-X. Qiu, B. Ghosh, T. V. Trevisan, Y. Onishi, C. Hu, T. Qian, H.-J. Tien, S.-W. Chen, M. Huang, D. B ´erub´e, 10 H. Li, C. Tzschaschel, T. Dinh, Z. Sun, S.-C. Ho, S.-W. Lien, B. Singh, K. Watanabe, T. Taniguchi, D. C. Bell, H. Lin, T.-R. Chang, C. R. Du, A...

    2023

  52. [59]

    J. Han, T. Uchimura, Y. Araki, J.-Y. Yoon, Y. Takeuchi, Y. Ya- mane, S. Kanai, J. Ieda, H. Ohno, and S. Fukami, Room- temperature flexible manipulation of the quantum-metric struc- ture in a topological chiral antiferromagnet, Nature Physics20, 1110 (2024)

    2024

  53. [60]

    Orenstein, J

    J. Orenstein, J. Moore, T. Morimoto, D. Torchinsky, J. Harter, and D. Hsieh, Topology and symmetry of quantum materials via nonlinear optical responses, Annual Review of Condensed Matter Physics12, 247 (2021)

    2021

  54. [61]

    Morimoto, S

    T. Morimoto, S. Kitamura, and N. Nagaosa, Geometric aspects of nonlinear and nonequilibrium phenomena, J. Phys. Soc. Jpn. 92, 072001 (2023)

    2023

  55. [62]

    Nagaosa and Y

    N. Nagaosa and Y. Yanase, Nonreciprocal transport and optical phenomena in quantum materials, Annu. Rev. Condens. Matter Phys.15, 63 (2024)

    2024

  56. [63]

    Peotta and P

    S. Peotta and P. T¨orm¨a, Superfluidity in topologically nontrivial flat bands, Nature Communications6, 8944 (2015)

    2015

  57. [64]

    Julku, S

    A. Julku, S. Peotta, T. I. Vanhala, D.-H. Kim, and P. T ¨orm¨a, Geometric origin of superfluidity in the lieb-lattice flat band, Phys. Rev. Lett.117, 045303 (2016)

    2016

  58. [65]

    Liang, T

    L. Liang, T. I. Vanhala, S. Peotta, T. Siro, A. Harju, and P. T¨orm¨a, Band geometry, berry curvature, and superfluid weight, Phys. Rev. B95, 024515 (2017)

    2017

  59. [66]

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

    2023

  60. [67]

    Tanaka, J

    M. Tanaka, J. ˆI.-J. Wang, T. H. Dinh, D. Rodan-Legrain, S. Zaman, M. Hays, A. Almanakly, B. Kannan, D. K. Kim, B. M. Niedzielski, K. Serniak, M. E. Schwartz, K. Watan- abe, T. Taniguchi, T. P. Orlando, S. Gustavsson, J. A. Grover, P. Jarillo-Herrero, and W. D. Oliver, Superfl...

    2025

  61. [68]

    Banerjee, Z

    A. Banerjee, Z. Hao, M. Kreidel, P. Ledwith, I. Phinney, J. M. Park, A. Zimmerman, M. E. Wesson, K. Watanabe, T. Taniguchi, R. M. Westervelt, A. Yacoby, P. Jarillo-Herrero, P. A. Volkov, A. Vishwanath, K. C. Fong, and P. Kim, Superfluid stiffness of twisted trilayer graphene s...

    2025

  62. [69]

    Tang, J.-W

    E. Tang, J.-W. Mei, and X.-G. Wen, High-temperature fractional quantum hall states, Phys. Rev. Lett.106, 236802 (2011)

    2011

  63. [70]

    K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett.106, 236803 (2011)

    2011

  64. [71]

    Neupert, L

    T. Neupert, L. Santos, C. Chamon, and C. Mudry, Fractional quantum hall states at zero magnetic field, Phys. Rev. Lett.106, 236804 (2011)

    2011

  65. [72]

    Kitamura, A

    T. Kitamura, A. Daido, and Y. Yanase, Spin-triplet supercon- ductivity from quantum-geometry-induced ferromagnetic fluc- tuation, Phys. Rev. Lett.132, 036001 (2024)

    2024

  66. [73]

    Shavit and J

    G. Shavit and J. Alicea, Quantum geometric kohn-luttinger su- perconductivity, Phys. Rev. Lett.134, 176001 (2025)

    2025

  67. [74]

    Jahin and S.-Z

    A. Jahin and S.-Z. Lin, (2025), arXiv:2411.09664 [cond- mat.supr-con]

    2025

  68. [75]

    Heinsdorf, Altermagnetic instabilities from quantum geom- etry, Phys

    N. Heinsdorf, Altermagnetic instabilities from quantum geom- etry, Phys. Rev. B111, 174407 (2025)

    2025

  69. [76]

    Kudo and Y

    K. Kudo and Y. Yanase, Odd-parity magnetism by quantum geometry (2025), arXiv:2505.20907 [cond-mat.str-el]

    2025

  70. [77]

    33, edited by S

    Chapter II - Two Electrons in a Cubic Field, inMultiplets of Transition-Metal Ions in Crystals, Pure and Applied Physics, Vol. 33, edited by S. Sugano, Y. Tanabe, and H. Kamimura (Elsevier, 1970) pp. 38–65

    1970

  71. [78]

    Watanabe and Y

    H. Watanabe and Y. Yanase, Group-theoretical classification of multipole order: Emergent responses and candidate materials, Phys. Rev. B98, 245129 (2018)

    2018

  72. [79]

    Hayami, M

    S. Hayami, M. Yatsushiro, Y. Yanagi, and H. Kusunose, Classi- fication of atomic-scale multipoles under crystallographic point groups and application to linear response tensors, Phys. Rev. B 98, 165110 (2018)

    2018

  73. [80]

    Yatsushiro, H

    M. Yatsushiro, H. Kusunose, and S. Hayami, Multipole classi- fication in 122 magnetic point groups for unified understanding of multiferroic responses and transport phenomena, Phys. Rev. B104, 054412 (2021)

    2021

  74. [81]

    Y. Gao, D. Vanderbilt, and D. Xiao, Microscopic theory of spin toroidization in periodic crystals, Phys. Rev. B97, 134423 (2018)

    2018

  75. [82]

    Shitade, H

    A. Shitade, H. Watanabe, and Y. Yanase, Theory of orbital mag- netic quadrupole moment and magnetoelectric susceptibility, Phys. Rev. B98, 020407 (2018)

    2018

  76. [83]

    Gao and D

    Y. Gao and D. Xiao, Orbital magnetic quadrupole moment and nonlinear anomalous thermoelectric transport, Phys. Rev. B98, 060402 (2018)

    2018

  77. [84]

    Shitade, A

    A. Shitade, A. Daido, and Y. Yanase, Theory of spin magnetic quadrupole moment and temperature-gradient-induced magne- tization, Phys. Rev. B99, 024404 (2019)

    2019

  78. [85]

    Daido, A

    A. Daido, A. Shitade, and Y. Yanase, Thermodynamic approach to electric quadrupole moments, Phys. Rev. B102, 235149 (2020)

    2020

  79. [86]

    Kitamura, J

    T. Kitamura, J. Ishizuka, A. Daido, and Y. Yanase, Thermo- dynamic electric quadrupole moments of nematic phases from first-principles calculations, Phys. Rev. B103, 245114 (2021)

    2021

  80. [87]

    Nogaki and Y

    K. Nogaki and Y. Yanase, Field-induced superconductivity me- diated by odd-parity multipole fluctuation, Phys. Rev. B110, 184501 (2024)

    2024

  81. [88]

    D. C. Cavanagh, T. Shishidou, M. Weinert, P. M. R. Brydon, and D. F. Agterberg, Nonsymmorphic symmetry and field-driven odd-parity pairing in Cerh 2as2, Phys. Rev. B105, L020505 (2022)

    2022

  82. [89]

    H. G. Suh, Y. Yu, T. Shishidou, M. Weinert, P. M. R. Brydon, and D. F. Agterberg, Superconductivity of anomalous pseudospin in nonsymmorphic materials, Phys. Rev. Res.5, 033204 (2023)

    2023

  83. [91]

    Momma and F

    K. Momma and F. Izumi,VESTA3for three-dimensional visual- ization of crystal, volumetric and morphology data, Journal of Applied Crystallography44, 1272 (2011)

    2011

  84. [92]

    Kokalj, Xcrysden—a new program for displaying crystalline structures and electron densities, Journal of Molecular Graphics and Modelling17, 176 (1999)

    A. Kokalj, Xcrysden—a new program for displaying crystalline structures and electron densities, Journal of Molecular Graphics and Modelling17, 176 (1999)

    1999

  85. [93]

    Kawamura, Fermisurfer: Fermi-surface viewer providing multiple representation schemes, Computer Physics Communi- cations239, 197 (2019)

    M. Kawamura, Fermisurfer: Fermi-surface viewer providing multiple representation schemes, Computer Physics Communi- cations239, 197 (2019)

    2019

  86. [94]

    J. M. Luttinger and J. C. Ward, Ground-State Energy of a Many- Fermion System. II, Phys. Rev.118, 1417 (1960)

    1960

  87. [95]

    J. M. Luttinger, Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions, Phys. Rev.119, 1153 (1960)

    1960

  88. [96]

    Baym and L

    G. Baym and L. P. Kadanoff, Conservation Laws and Correlation Functions, Phys. Rev.124, 287 (1961)

    1961

  89. [97]

    Baym, Self-Consistent Approximations in Many-Body Sys- tems, Phys

    G. Baym, Self-Consistent Approximations in Many-Body Sys- tems, Phys. Rev.127, 1391 (1962)

    1962

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