Pith. sign in

REVIEW 3 major objections 4 minor 91 references

A 45-degree twist of FeSe on a cuprate creates a Lieb lattice that splits electron bands without any net magnetization, opening a route to study altermagnetism alongside high-temperature superconductivity.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 09:23 UTC pith:3AJYYS4B

load-bearing objection A well-executed theory proposal for altermagnetism in FeSe/cuprate heterostructures, but its flagship mechanism leans on a checkerboard magnetic order that remains a working hypothesis. the 3 major comments →

arxiv 2607.27331 v1 pith:3AJYYS4B submitted 2026-07-29 cond-mat.str-el cond-mat.supr-con

Altermagnetism from a Cu-Fe Lieb Lattice in FeSe/Cuprate Heterostructures

Ying Li , Augustin Davignon , Peng Rao , Runhan Li , Maia G. Vergniory , Roser Valent\'i , Johannes Knolle This is my paper
classification cond-mat.str-el cond-mat.supr-con
keywords altermagnetismLieb latticeFeSecuprate heterostructuresd-wave spin splittingproximity effecthigh-temperature superconductivitydensity functional theory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper proposes that stacking a monolayer of FeSe on a cuprate superconductor, rotated by 45 degrees, arranges the copper and iron atoms into an effective Lieb lattice. In that lattice, two independent mechanisms — copper-iron hybridization and a substrate-induced inequivalence of the selenium sites — produce altermagnetic d-wave spin splitting: spin-up and spin-down bands split in momentum space while the net magnetization stays zero. Density functional theory calculations on FeSe/Bi-2201 predict splittings of 15–25 meV. If correct, this gives a realistic platform to study altermagnetism side by side with high-temperature superconductivity, since both layers are potential superconductors.

Core claim

The authors claim that 45°-twisted FeSe/cuprate heterostructures form a nearly ideal CuFe2 Lieb lattice, and that this lattice hosts altermagnetism through two cooperating routes. The first uses checkerboard antiferromagnetic order on the Fe sites together with finite Cu–Fe interlayer hopping t0 to generate a d-wave spin splitting. The second uses the substrate to break the equivalence of the two Se atoms, making the next-nearest-neighbor Fe–Fe hoppings alternate (t ± δt), which alone splits the bands. DFT for FeSe/Bi2Sr2CuO6 confirms both routes, with splittings of 15 meV in the BiO2-cleaved structure and 25 meV when the CuO2 plane is exposed, and the splitting is carried mainly by the Fe d

What carries the argument

The central object is the effective CuFe2 Lieb lattice — a square lattice with extra atoms on the bonds, realized by the 45° twist because the Cu–Cu distance in the cuprate is close to √2 times the Fe–Fe distance in FeSe. Two parameters carry the argument: t0, the Cu–Fe interlayer hopping, and δt, the substrate-induced difference between the two next-nearest-neighbor Fe–Fe hoppings. Combined with checkerboard antiferromagnetic order on Fe, these parameters generate a momentum-dependent sign-reversing (d-wave) spin splitting. The spin conductivity tensor, with σ_xy = σ_yx as the only non-zero components, provides the transport fingerprint.

Load-bearing premise

The central mechanism assumes the iron sites in FeSe order in a checkerboard antiferromagnetic pattern, a state the paper adopts as a working hypothesis because different density functionals disagree; if the real material orders in a stripe pattern instead, the Lieb-lattice route collapses and only the weaker substrate-induced splitting remains.

What would settle it

Measure the magnetic ground state of the FeSe layer inside the actual heterostructure (e.g., spin-polarized scanning tunneling microscopy or neutron diffraction); observing stripe rather than checkerboard antiferromagnetic order would invalidate the primary mechanism. Alternatively, a spin- and angle-resolved photoemission scan along Γ–M+ versus Γ–M− that finds no sign-reversing spin splitting would falsify the altermagnetic claim outright.

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

Share X Bluesky LinkedIn Reddit HN

If this is right

  • FeSe/cuprate heterostructures become a tunable platform for altermagnetism in the parent compounds of high-Tc superconductors.
  • The altermagnetic order in FeSe is transferred to the CuO2 layer by proximity, so the cuprate layer also develops spin splitting.
  • Because both layers can be superconducting with distinct pairing symmetries, the platform may host coexistence of altermagnetism and superconductivity, enabling mixed singlet-triplet pairing, persistent spin currents, and non-reciprocal Josephson transport.
  • Band splittings scale with interlayer coupling: shortening the Fe–Cu distance raises the splitting from 15 to 25 meV, offering a practical design lever.
  • The predicted spin conductivity has a distinctive off-diagonal-only tensor, giving a measurable transport signature that could be detected experimentally.

Where Pith is reading between the lines

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

  • If the checkerboard magnetic order is fragile, the Lieb-lattice mechanism becomes inactive; the substrate-induced route may still produce a weaker splitting, so spin-resolved experiments comparing structures with and without Cu could identify which mechanism dominates.
  • The near-√2 lattice matching that enables the twist suggests a wider family of iron-chalcogenide/cuprate pairs with similar lattice ratios could be screened systematically for altermagnetism, not just FeSe on Bi-2201.
  • Because the sign of the Se-site distortion controls the relative order of spin-up and spin-down bands, strain engineering or substrate choice could flip the altermagnetic texture, potentially enabling switchable spintronic devices.
  • The 15–25 meV splittings are comparable to typical superconducting gap scales, so the interplay between altermagnetic splitting and Cooper pairing may be directly accessible in tunneling or photoemission experiments — an inference beyond the paper's explicit claims.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This paper proposes that a 45°-twisted FeSe/cuprate heterostructure forms an effective CuFe2 Lieb lattice and supports altermagnetism through two mechanisms: (i) Cu-Fe interlayer hybridization t0 within a checkerboard antiferromagnetic Fe layer, and (ii) substrate-induced Fe-Fe next-nearest-neighbor hopping inequivalence δt. A ten-band mean-field tight-binding model is used to show that both parameters generate d-wave spin splitting, and DFT GGA+U calculations on FeSe/Bi-2201 report 15–25 meV band splittings. The paper also computes the spin conductivity tensor and discusses proximity-induced splitting on the CuO2 layer. The central caveat, acknowledged by the authors, is the dependence on checkerboard Fe magnetic order; r2SCAN calculations favor stripe order, and the paper adopts the checkerboard state as a working hypothesis.

Significance. If the checkerboard order is realized in the heterostructure, the paper provides a convincing and generic mechanism for altermagnetism in a potentially superconducting platform, with clear falsifiable predictions (spin-split bands, spin conductivity anisotropy, proximity-induced splitting). The model is fully specified and the parameter scan in Fig. 2(a) is a legitimate generic demonstration, not circular. The paper is also commendably transparent about the magnetic ground-state ambiguity. The main limitation is that the DFT 'confirmation' is conditional on the same assumption used to build the model, so the claim is not independent. Nevertheless, the proposal is timely and the methodology is appropriate for a first proposal.

major comments (3)
  1. [First-principles Realization] The central prediction relies on the checkerboard antiferromagnetic order on Fe sites, which the authors adopt as a working hypothesis. The text states 'The checkerboard state is a key ingredient for both AM routes' and acknowledges that r2SCAN stabilizes a stripe state. Both the model Eqs. (1)-(3) and the DFT calculations in Fig. 3 impose this order. Consequently, the 15-25 meV splittings in Fig. 3(c,d) do not constitute independent evidence for the mechanism; they establish internal consistency conditional on the assumed order. If the true ground state is stripe, neither mechanism as formulated is expected to yield the predicted d-wave splitting. The authors should either provide a more definitive determination of the magnetic ground state for the specific heterostructure (e.g., DFT+DMFT or a quantum spin model with realistic J1-J2-J3-K parameters) or explicitly reframe the central cla
  2. [Supplemental Material, FeSe/Bi2Sr2CaCu2O8 heterostructure] There is an apparent inconsistency about r2SCAN. The main text uses the r2SCAN preference for stripe order to justify the checkerboard working hypothesis, yet the SM reports that an r2SCAN calculation for FeSe/Bi-2212 'still captures the spin splitting near the Fermi level' using the same magnetic configurations as the FeSe/Bi-2201 system. If the calculation was constrained to checkerboard order, then it does not test the ground-state issue; if it was unconstrained and the stripe state still shows the splitting, the assertion that stripe order destroys both AM routes is untenable. The authors need to clarify the magnetic state used in this r2SCAN calculation and, if the stripe state does exhibit splitting, reconcile it with the main-text claim.
  3. [Fig. 2(d) and footnote [66]] The 'realistic' parameters t0=0.02 eV and δt=0.02 eV are extracted from the same DFT calculation (structure B) whose band splittings are cited as confirmation. This closes the confirmation loop through the model and does not provide an independent test of the mechanism. The generic demonstration in Fig. 2(a) is independent because t0 and δt are scanned as free parameters, but the panel meant to represent the material is not. The authors should explicitly state this limitation and, where possible, derive the parameters from a different source (e.g., a separate functional or experiment).
minor comments (4)
  1. [Fig. 2 caption] The caption refers to 'the Kpoint' (dotted green lines). The band paths in panels (b-d) are M+-Γ-M-, so the high-symmetry point should likely be labeled 'M' or 'k point'. Please correct.
  2. [Supplemental Material, isolated FeSe monolayer] The main text reports δl=-0.002 for the heterostructure, while the SM states that 'we adopted a dimensionless distortion parameter δl=-0.02' for the isolated FeSe monolayer. Please clarify the relationship between these values and why a factor of 10 larger distortion is used in the SM.
  3. [Supplemental Material, refined parameters] In the sentence 'with t1 = 0.1 eV, t2 = -0.35 eV, t3 = 0.22, and t4 = 0.11 eV', the units for t3 and t4 are missing.
  4. [Spin conductivity] The notation σ is used both for the spin index in h(k,σ) and for the spin-polarization direction in σ^a_bc. Using a different symbol (e.g., s for the spin index in the Hamiltonian) would avoid confusion.

Circularity Check

0 steps flagged

No significant circularity: the derivation is a conditional model/DFT consistency study, not a by-construction reduction.

full rationale

The paper's derivation chain is: (i) a generic tight-binding model with free parameters t0 and δt shows d-wave spin splitting under checkerboard AFM order; (ii) DFT on FeSe/Bi-2201 yields a checkerboard state and band splitting; (iii) Wannier-derived t0 and δt are inserted into the model to show consistency. Step (iii) is not circular: the target quantity (the 15–25 meV DFT splitting) is not used to fit t0 or δt; those parameters come from independent Wannier/projection hoppings, and the model uses Raghu rather than DFT-derived Fe-Fe hoppings. The d-wave splitting is a calculated consequence of the Hamiltonian, not identical to an input. The one load-bearing assumption—checkerboard Fe order—is explicitly flagged: 'we adopt the checkerboard state as a working hypothesis', and the paper says it does 'not attempt to resolve the ground-state controversy'. The motivation cites a J1-J2-J3-K study [77] with an overlapping author (Valentí), but it is corroborated by external STM [78] and by the paper's own GGA+U result, and the assumption is presented as a hypothesis rather than as a derived theorem. Reference [61] establishing the substrate-induced FeSe AM route is external. Thus no step reduces, by construction or by self-citation, to its own input.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 0 invented entities

Central claim rests on the checkerboard magnetic order, the geometric Lieb-lattice matching, and the effective models/DFT functionals. The two control parameters t0 and delta_t are extracted partly from the same DFT used for validation, and the ground-state assumption is the largest unverified input.

free parameters (2)
  • t0 (Cu-Fe interlayer hopping) = 0.02 eV (from DFT ratio; used in Fig. 2d)
    Central control parameter for the Lieb-lattice AM mechanism. Value obtained by multiplying the DFT-derived (t0/t2) ratio by the model t2 = -1.3 eV.
  • delta_t (next-nearest-neighbor Fe-Fe hopping asymmetry) = 0.02 eV (from DFT ratio; used in Fig. 2d)
    Central control parameter for the substrate-inequivalence mechanism. Set equal for both diagonals (delta_t3 = delta_t4 = delta_t); value obtained from DFT-derived (delta_t/t2) ratio.
axioms (6)
  • ad hoc to paper Checkerboard antiferromagnetic order on Fe sites is the relevant magnetic ground state of monolayer FeSe in the heterostructure.
    Stated as a working hypothesis because GGA+U gives checkerboard while r2SCAN gives stripe order. The first AM mechanism (Lieb-lattice route) requires this order.
  • domain assumption The Cu–Cu distance in the cuprate layer and the Fe–Fe distance in FeSe satisfy d_CuCu ≈ √2 × d_FeFe, so a 45° twist produces a close-to-ideal Lieb lattice.
    Geometric condition motivating the heterostructure design; real materials deviate slightly from the ideal ratio.
  • domain assumption The two-orbital (Fe dxz, dyz) model captures the low-energy FeSe physics and the Cu dx2-y2 orbital captures cuprate physics.
    Standard minimal model following Raghu et al.; the authors compare with five-orbital DFT-derived parameters in the SM.
  • domain assumption Mean-field treatment of the Hubbard interaction is sufficient to capture the magnetic order and band splitting.
    UCu=4 eV, UFe=3 eV treated at Hartree level; correlations beyond mean-field are neglected.
  • domain assumption GGA+U with U_Cu = 8 eV and U_Fe = 0 eV provides a reliable description of the heterostructure electronic structure.
    Choice motivated by prior cuprate and FeSe studies; the authors note functional sensitivity (r2SCAN gives stripe order).
  • domain assumption The substrate-induced strain enters only via the next-nearest-neighbor Fe-Fe hopping asymmetry δt3 = δt4 = δt.
    Model simplification; other strain effects (on-site energies, nearest-neighbor hoppings) are neglected.

pith-pipeline@v1.3.0-daily-deepseek · 17981 in / 12146 out tokens · 105601 ms · 2026-08-01T09:23:39.858805+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of Altermagnetism from a Cu-Fe Lieb Lattice in FeSe/Cuprate Heterostructures." pith.science (2026). https://pith.science/paper/3AJYYS4B

@misc{pith2026260727331,
  author       = {Pith},
  title        = {Pith review of: Altermagnetism from a Cu-Fe Lieb Lattice in FeSe/Cuprate Heterostructures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3AJYYS4B}},
  note         = {Machine review of arXiv:2607.27331}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Realizing altermagnetism in high-$T_c$ cuprate-based systems would provide a direct route for studying spin-split electronic bands in the absence of net magnetization and investigate their interplay with unconventional superconductivity. Here, we propose that FeSe/cuprate heterostructures offer such a platform, where a 45$^\circ$ twist of Cu and Fe layers creates an effective CuFe$_2$ Lieb lattice in which Fe magnetic order and Cu-Fe hybridization through the ligands induces altermagnetic $d$-wave spin splitting. A minimal tight-binding model shows that this mechanism is generic. Furthermore, a substrate-induced inequivalence of the two Se sites in FeSe provides a second route in which altermagnetism originates in the Fe layer and is transferred to the cuprate layer by proximity. Density functional theory calculations for FeSe/Bi$_2$Sr$_2$CuO$_6$ heterostructures confirm the viability of both mechanisms and reveal ways to enhance the spin splitting. These results establish superconducting cuprate/transition metal chalcogenide heterostructures as a promising setting for engineering altermagnetism and studying its coupling to unconventional superconductivity.

Figures

Figures reproduced from arXiv: 2607.27331 by Augustin Davignon, Johannes Knolle, Maia G. Vergniory, Peng Rao, Roser Valent\'i, Runhan Li, Ying Li.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Side view of FeSe/Cu in the FeSe/cuprate het [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Mean-field results of Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (c)], consistent with the model predictions. To probe the impact of stronger Cu-Fe coupling in the Lieb lattice, we designed structure B [ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Color plots of the transversal component of the spin [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

91 extracted references · 10 linked inside Pith

  1. [1]

    ˇSmejkal, R

    L. ˇSmejkal, R. Gonz´ alez-Hern´ andez, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv.6, eaaz8809 (2020)

    2020

  2. [2]

    I. I. Mazin, K. Koepernik, M. D. Johannes, R. Gonz´ alez- Hern´ andez, and L.ˇSmejkal, Prediction of unconventional magnetism in doped FeSb 2, Proceedings of the National Academy of Sciences118, e2108924118 (2021)

    2021

  3. [3]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging re- search landscape of altermagnetism, Phys. Rev. X12, 040501 (2022)

    2022

  4. [4]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X12, 031042 (2022)

    2022

  5. [5]

    ˇSmejkal, A

    L. ˇSmejkal, A. B. Hellenes, R. Gonz´ alez-Hern´ andez, J. Sinova, and T. Jungwirth, Giant and tunneling mag- netoresistance in unconventional collinear antiferromag- nets with nonrelativistic spin-momentum coupling, Phys. Rev. X12, 011028 (2022)

    2022

  6. [6]

    Jungwirth, J

    T. Jungwirth, J. Sinova, R. M. Fernandes, Q. Liu, H. Watanabe, S. Murakami, S. Nakatsuji, and L.ˇSmejkal, Symmetry, microscopy and spectroscopy signatures of al- termagnetism, Nature649, 837 (2026)

    2026

  7. [7]

    L. Bai, W. Feng, S. Liu, L. ˇSmejkal, Y. Mokrousov, and Y. Yao, Altermagnetism: Exploring new frontiers in mag- netism and spintronics, Adv. Funct. Mater.34, 2409327 (2024)

    2024

  8. [8]

    C. Song, H. Bai, Z. Zhou, L. Han, H. Reichlova, J. H. Dil, J. Liu, X. Chen, and F. Pan, Altermagnets as a new class of functional materials, Nat. Rev. Mater.10, 473 (2025)

    2025

  9. [9]

    Mazin, Altermagnetism then and now, Physics17, 4 (2024)

    I. Mazin, Altermagnetism then and now, Physics17, 4 (2024)

    2024

  10. [10]

    K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneˇ s, Antifer- romagnetism in RuO 2 as d-wave pomeranchuk instabil- ity, Phys. Rev. B99, 184432 (2019)

    2019

  11. [11]

    Hayami, Y

    S. Hayami, Y. Yanagi, and H. Kusunose, Momentum- dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn.88, 123702 (2019)

    2019

  12. [12]

    L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-zantiferromagnets, Phys. Rev. B 102, 014422 (2020)

    2020

  13. [13]

    H.-Y. Ma, M. Hu, N. Li, J. Liu, W. Yao, J.-F. Jia, and J. Liu, Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current, Nat. Commun.12, 2846 (2021). 6

    2021

  14. [14]

    V. Leeb, A. Mook, L. ˇSmejkal, and J. Knolle, Sponta- neous formation of altermagnetism from orbital ordering, Phys. Rev. Lett.132, 236701 (2024)

    2024

  15. [15]

    P. Das, V. Leeb, J. Knolle, and M. Knap, Realizing al- termagnetism in Fermi-Hubbard models with ultracold atoms, Phys. Rev. Lett.132, 263402 (2024)

    2024

  16. [16]

    M. Roig, A. Kreisel, Y. Yu, B. M. Andersen, and D. F. Agterberg, Minimal models for altermagnetism, Phys. Rev. B110, 144412 (2024)

    2024

  17. [17]

    Ferrari and R

    F. Ferrari and R. Valent ´ ı, Altermagnetism on the shastry- sutherland lattice, Phys. Rev. B110, 205140 (2024)

    2024

  18. [18]

    Zeng and Y.-J

    S. Zeng and Y.-J. Zhao, Bilayer stackingA-type al- termagnet: A general approach to generating two- dimensional altermagnetism, Phys. Rev. B110, 174410 (2024)

    2024

  19. [19]

    Kaushal, A

    N. Kaushal, A. S. Patri, and M. Franz, Spontaneous altermagnetism in multi-orbital correlated electron sys- tems, arXiv:2602.23522 (2026)

    arXiv 2026

  20. [20]

    O. J. Amin, A. Dal Din, E. Golias, Y. Niu, A. Zakharov, S. C. Fromage, C. J. B. Fields, S. L. Heywood, R. B. Cousins, F. Maccherozzi, andet al., Nanoscale imaging and control of altermagnetism in MnTe, Nature636, 348 (2024)

    2024

  21. [21]

    Reimers, L

    S. Reimers, L. Odenbreit, L. ˇSmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. Jaeschke Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, and et al., Direct observation of altermagnetic band splitting in CrSb thin films, Nat. Commun.15, 2116 (2024)

    2024

  22. [22]

    G. Yang, Z. Li, S. Yang, J. Li, H. Zheng, W. Zhu, Z. Pan, Y. Xu, S. Cao, W. Zhao, andet al., Three-dimensional mapping of the altermagnetic spin splitting in CrSb, Nat. Commun.16, 1442 (2025)

    2025

  23. [23]

    Z. Zhou, X. Cheng, M. Hu, R. Chu, H. Bai, L. Han, J. Liu, F. Pan, and C. Song, Manipulation of the al- termagnetic order in CrSb via crystal symmetry, Nature 638, 645 (2025)

    2025

  24. [24]

    Q. Cui, C. Liu, A. Delin, and K. Wang, Data- driven discovery of unconventional antiferromagnets, arXiv:2606.00409 (2026)

    Pith/arXiv arXiv 2026

  25. [25]

    Chakraborty, R

    A. Chakraborty, R. Gonz´ alez Hern´ andez, L.ˇSmejkal, and J. Sinova, Strain-induced phase transition from antiferro- magnet to altermagnet, Phys. Rev. B109, 144421 (2024)

    2024

  26. [26]

    Khodas, S

    M. Khodas, S. Mu, I. I. Mazin, and K. D. Belashchenko, Tuning of altermagnetism by strain, Phys. Rev. B113, 104422 (2026)

    2026

  27. [27]

    d’Ornellas, V

    P. d’Ornellas, V. Leeb, A. G. Grushin, and J. Knolle, Altermagnetism without crystal symmetry, Phys. Rev. B 113, 024426 (2026)

    2026

  28. [28]

    Y. Chen, Q. Huang, Y. Wu, X. Yan, and S.-H. Wei, Iden- tifying and designing altermagnetic crystals in real space, arXiv:2605.27151 (2026)

    Pith/arXiv arXiv 2026

  29. [29]

    Z.-F. Gao, S. Qu, B. Zeng, Y. Liu, J.-R. Wen, H. Sun, P.- J. Guo, and Z.-Y. Lu, AI-accelerated discovery of alter- magnetic materials, National Science Review12, nwaf066 (2025)

    2025

  30. [30]

    Y. Li, V. Leeb, K. Wohlfeld, R. Valent ´ ı, and J. Knolle, Exploringd-wave magnetism in cuprates from oxygen moments, Phys. Rev. B112, 125139 (2025)

    2025

  31. [31]

    D¨ urrnagel, H

    M. D¨ urrnagel, H. Hohmann, A. Maity, J. Seufert, M. Klett, L. Klebl, and R. Thomale, Altermagnetic phase transition in a Lieb metal, Phys. Rev. Lett.135, 036502 (2025)

    2025

  32. [32]

    Kaushal and M

    N. Kaushal and M. Franz, Altermagnetism in modified Lieb lattice hubbard model, Phys. Rev. Lett.135, 156502 (2025)

    2025

  33. [33]

    Zhang, X

    F. Zhang, X. Cheng, Z. Yin, C. Liu, L. Deng, Y. Qiao, Z. Shi, S. Zhang, J. Lin, Z. Liu, andet al., Crystal- symmetry-paired spin–valley locking in a layered room- temperature metallic altermagnet candidate, Nat. Phys. 21, 760 (2025)

    2025

  34. [34]

    Jiang, M

    B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, andet al., A metallic room-temperature d-wave altermagnet, Nat. Phy.21, 754 (2025)

    2025

  35. [35]

    Garcia-Gassull, A

    L. Garcia-Gassull, A. Razpopov, P. P. Stavropoulos, I. I. Mazin, and R. Valent ´ ı, Microscopic origin of the mag- netic interactions and their experimental signatures in altermagnetic La2O3Mn2Se2, npj Spintronics4, 9 (2026)

    2026

  36. [36]

    C.-C. Wei, X. Li, S. Hatt, X. Huai, J. Liu, B. Singh, K.-M. Kim, R. M. Fernandes, P. Cardon, L. Zhao, and et al., La 2O3Mn2Se2: A correlated insulating layered d- wave altermagnet, Phys. Rev. Mater.9, 024402 (2025)

    2025

  37. [37]

    Zhang, P

    X. Zhang, P. Jiang, L.-Y. Xu, L. Wang, L. Liu, H.-M. Huang, T. Cao, and Y.-L. Li, Giant spin splitting and anisotropic spin polarization in 2D altermagnet Cr 2O, Nano Letters25, 16547 (2025)

    2025

  38. [38]

    S.-D. Guo, Q. Luo, S.-H. Zhang, and P. Jiang, Exter- nal field induced transition from altermagnetic metal to fully compensated ferrimagnetic metal in monolayer Cr2O, Phys. Rev. B113, 064408 (2026)

    2026

  39. [39]

    Ta¸ skıran, S

    T. Ta¸ skıran, S. Ershadrad, B. Sanyal, and C. S ¸ahin, Novel 2D altermagnetic vanadium oxide with a buckled Lieb structure, arXiv:2606.08637 (2026)

    Pith/arXiv arXiv 2026

  40. [40]

    Liu, J.-T

    M. Liu, J.-T. Sun, and S. Meng, Uncompensated linear dichroism of magneto-optical kerr effect in a 2D altermag- net, Advanced Functional Materials36, e21111 (2026)

    2026

  41. [41]

    Monkman, J

    K. Monkman, J. Weng, N. Heinsdorf, A. Nocera, Y. Bar- las, and M. Franz, Persistent spin currents in supercon- ducting altermagnets, Phys. Rev. X16, 011057 (2026)

    2026

  42. [42]

    J. A. Ouassou, A. Brataas, and J. Linder, dc Joseph- son effect in altermagnets, Phys. Rev. Lett.131, 076003 (2023)

    2023

  43. [43]

    M. H. Fischer and E.-A. Kim, Mean-field analysis of intra-unit-cell order in the Emery model of the CuO 2 plane, Phys. Rev. B84, 144502 (2011)

    2011

  44. [44]

    Park and R

    C. Park and R. L. Snyder, Structures of high-temperature cuprate superconductors, Journal of the American Ce- ramic Society78, 3171 (1995)

    1995

  45. [45]

    S. Tan, Y. Zhang, M. Xia, Z. Ye, F. Chen, X. Xie, R. Peng, D. Xu, Q. Fan, H. Xu, andet al., Interface- induced superconductivity and strain-dependent spin density waves in FeSe/SrTiO3 thin films, Nat. Mater.12, 634 (2013)

    2013

  46. [46]

    H. Wang, Y. Zhu, Z. Bai, Z. Wang, S. Hu, H.-Y. Xie, X. Hu, J. Cui, M. Huang, J. Chen, andet al., Prominent Josephson tunneling between twisted single copper oxide planes of Bi 2Sr2−xLaxCuO6+y, Nat. Commun.14, 5201 (2023)

    2023

  47. [47]

    Y. Yu, L. Ma, P. Cai, R. Zhong, C. Ye, J. Shen, G. D. Gu, X. H. Chen, and Y. Zhang, High-temperature su- perconductivity in monolayer Bi2Sr2CaCu2O8+δ, Nature 575, 156 (2019)

    2019

  48. [48]

    O. Can, T. Tummuru, R. P. Day, I. Elfimov, A. Damas- celli, and M. Franz, High-temperature topological super- conductivity in twisted double-layer copper oxides, Nat. Phys.17, 519 (2021)

    2021

  49. [49]

    Margalit, B

    G. Margalit, B. Yan, M. Franz, and Y. Oreg, Chiral ma- jorana modes via proximity to a twisted cuprate bilayer, 7 Phys. Rev. B106, 205424 (2022)

    2022

  50. [50]

    Tummuru, S

    T. Tummuru, S. Plugge, and M. Franz, Josephson effects in twisted cuprate bilayers, Phys. Rev. B105, 064501 (2022)

    2022

  51. [51]

    J. Lee, W. Lee, G.-Y. Kim, Y.-B. Choi, J. Park, S. Jang, G. Gu, S.-Y. Choi, G. Y. Cho, G.-H. Lee, and H.-J. Lee, Twisted van der waals Josephson junction based on a high-Tc superconductor, Nano Letters21, 10469 (2021)

    2021

  52. [52]

    S. Y. F. Zhao, N. Poccia, and X. Cui, Emergent inter- facial superconductivity between twisted cuprate super- conductors, arXiv:2108.13455 (2021)

    Pith/arXiv arXiv 2021

  53. [53]

    Y. Zhu, M. Liao, Q. Zhang, H.-Y. Xie, F. Meng, Y. Liu, Z. Bai, S. Ji, J. Zhang, K. Jiang, R. Zhong, J. Schnee- loch, G. Gu, L. Gu, X. Ma, D. Zhang, and Q.-K. Xue, Presence ofs-wave pairing in Josephson junctions made of twisted ultrathin Bi2Sr2CaCu2O8+δ flakes, Phys. Rev. X11, 031011 (2021)

    2021

  54. [54]

    Q. Li, Y. N. Tsay, M. Suenaga, R. A. Klemm, G. D. Gu, and N. Koshizuka, Bi 2Sr2CaCu2O8+δ bicrystalc- axis twist Josephson junctions: A new phase-sensitive test of order parameter symmetry, Phys. Rev. Lett.83, 4160 (1999)

    1999

  55. [55]

    Takano, T

    Y. Takano, T. Hatano, A. Fukuyo, A. Ishii, M. Ohmori, S. Arisawa, K. Togano, and M. Tachiki, d-like symmetry of the order parameter and intrinsic Josephson effects in Bi2Sr2CaCu2O8+δ cross-whisker junctions, Phys. Rev. B 65, 140513 (R) (2002)

    2002

  56. [56]

    Y. I. Latyshev, A. P. Orlov, A. M. Nikitina, P. Monceau, and R. A. Klemm,c-axis transport in naturally grown Bi2Sr2CaCu2O8+δ cross-whisker junctions, Phys. Rev. B 70, 094517 (2004)

    2004

  57. [57]

    Huang and J

    D. Huang and J. E. Hoffman, Monolayer FeSe on SrTiO3, Annu. Rev. of Condens. Matter Phys.8, 311 (2017)

    2017

  58. [58]

    Y. Xu, H. Rong, Q. Wang, D. Wu, Y. Hu, Y. Cai, Q. Gao, H. Yan, C. Li, C. Yin, andet al., Spectroscopic evi- dence of superconductivity pairing at 83 K in single-layer FeSe/SrTiO3 films, Nat. Commun.12, 2840 (2021)

    2021

  59. [59]

    Ge, Z.-L

    J.-F. Ge, Z.-L. Liu, C. Liu, C.-L. Gao, D. Qian, Q.-K. Xue, Y. Liu, and J.-F. Jia, Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3, Nat. Mater. 14, 285 (2015)

    2015

  60. [60]

    S. He, J. He, W. Zhang, L. Zhao, D. Liu, X. Liu, D. Mou, Y.-B. Ou, Q.-Y. Wang, Z. Li, andet al., Phase diagram and electronic indication of high-temperature supercon- ductivity at 65 K in single-layer FeSe films, Nat. Mater. 12, 605 (2013)

    2013

  61. [61]

    Mazin, R

    I. Mazin, R. Gonz´ alez-Hern´ andez, and L. ˇSmejkal, In- duced monolayer altermagnetism in MnP(S,Se) 3 and FeSe, arXiv:2309.02355 (2023)

    Pith/arXiv arXiv 2023

  62. [62]

    Raghu, X.-L

    S. Raghu, X.-L. Qi, C.-X. Liu, D. J. Scalapino, and S.-C. Zhang, Minimal two-band model of the superconducting iron oxypnictides, Phys. Rev. B77, 220503 (2008)

    2008

  63. [63]

    Sheshadri, D

    K. Sheshadri, D. Malterre, A. Fujimori, and A. Chainani, Connecting the one-band and three-band Hubbard mod- els of cuprates via spectroscopy and scattering experi- ments, Physical Review B107, 085125 (2023)

    2023

  64. [64]

    Lanat` a, H

    N. Lanat` a, H. U. R. Strand, G. Giovannetti, B. Hells- ing, L. de’ Medici, and M. Capone, Orbital selectivity in Hund’s metals: The iron chalcogenides, Phys. Rev. B87, 045122 (2012)

    2012

  65. [65]

    M. D. Watson, S. Backes, A. A. Haghighirad, M. Hoesch, T. K. Kim, A. I. Coldea, and R. Valent ´ ı, Formation of Hubbard-like bands as a fingerprint of strong electron- electron interactions in FeSe, Phys. Rev. B95, 081106 (2017)

    2017

  66. [66]

    3 (b), we de- termine the ratios (t 0/t2)DFT and (δt/t 2)DFT

    From the DFT results for structure B in Fig. 3 (b), we de- termine the ratios (t 0/t2)DFT and (δt/t 2)DFT. Multiply- ing these ratios by the modelt2 =−1.3 eV givest 0 = 0.02 eV andδt= 0.02 eV, which are used in Fig. 2 (d)

  67. [67]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci.6, 15 (1996)

    1996

  68. [68]

    Hafner,Ab-initiosimulations of materials using V ASP: Density-functional theory and beyond, J

    J. Hafner,Ab-initiosimulations of materials using V ASP: Density-functional theory and beyond, J. Com- put. Chem.29, 2044 (2008)

    2044

  69. [69]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    1996

  70. [70]

    V. I. Anisimov, J. Zaanen, and O. K. Andersen, Band theory and Mott insulators: HubbardUinstead of Stoner I, Phys. Rev. B44, 943 (1991)

    1991

  71. [71]

    A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Or- bital ordering in Mott-Hubbard insulators, Phys. Rev. B 52, R5467 (1995)

    1995

  72. [72]

    V. I. Anisimov, F. Aryasetiawan, and A. I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+U method, J. Phys.: Condens. Matter9, 767 (1997)

    1997

  73. [73]

    Yamada and T

    T. Yamada and T. Tohyama, Multipolar nematic state of nonmagnetic FeSe based on DFT +U, Phys. Rev. B 104, L161110 (2021)

    2021

  74. [74]

    K. Liu, M. Gao, Z.-Y. Lu, and T. Xiang, First-principles study of FeSe epitaxial films on SrTiO 3, Chin. Phys. B 24, 117402 (2015)

    2015

  75. [75]

    Wang and F

    S. Wang and F. Wang, Magnetic interactions in fese studied by first principle calculations, arXiv:1510.05476 (2015)

    Pith/arXiv arXiv 2015

  76. [76]

    L. A. Myers, N. L. E. Hew, S.-L. Shang, and Z.-K. Liu, Stripe antiferromagnetic ground-state configuration of FeSe revealed by density functional theory, Phys. Rev. B111, L121109 (2025)

    2025

  77. [77]

    J. K. Glasbrenner, I. I. Mazin, H. O. Jeschke, P. J. Hirschfeld, R. M. Fernandes, and R. Valent ´ ı, Effect of magnetic frustration on nematicity and superconductiv- ity in iron chalcogenides, Nat. Phys.11, 953 (2015)

    2015

  78. [78]

    S. Qiao, P. Zhang, H. Ding, S. Zhang, L. Liang, Z. Zhang, X. Long, X. Chen, J. Lu, and J. Wu, Fingerprint of checkerboard antiferromagnetic order in FeSe monolayer due to magnetic-electric correlation, Materials Today41, 44 (2020)

    2020

  79. [79]

    Z. Zhu, R. Huang, X. Chen, Z. Cui, X. Duan, J. Zhang, I. ˇZuti´ c, and T. Zhou, Altermagnetic proximity effect, Phys. Rev. Lett.136, 186702 (2026)

    2026

  80. [80]

    Gonz´ alez-Hern´ andez, L.ˇSmejkal, K

    R. Gonz´ alez-Hern´ andez, L.ˇSmejkal, K. V´ yborn´ y, Y. Ya- hagi, J. Sinova, T. Jungwirth, and J. ˇZelezn´ y, Ef- ficient electrical spin splitter based on nonrelativis- tic collinear antiferromagnetism, Phys. Rev. Lett.126, 127701 (2021)

    2021

Showing first 80 references.