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Proximitizing altermagnets with conventional superconductors

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read A metallic altermagnet on a conventional s-wave superconductor picks up a mixed singlet/triplet superconducting order with eight Dirac nodes and a spin-current dynamo, provided Rashba coupling sits at the interface.

desk verdict Solid proximity-effect paper: correct symmetry argument, consistent effective theory, and numerics; the nodal claim is real but its generality is a bit oversold. read the letter →

arxiv 2509.03774 v1 pith:CJJC2YYY submitted 2025-09-03 cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el

Niclas Heinsdorf , Marcel Franz This is my paper
classification cond-mat.supr-concond-mat.mtrl-scicond-mat.str-el
keywords altermagnetismproximityeffectspin-tripletsuperconductivityRashbaspin-orbitcouplingnodalsuperconductorpersistentspincurrents-waveheterostructure
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

Altermagnets are magnetic metals whose spin-split bands make ordinary spin-singlet Cooper pairing unlikely, and none has yet been found to superconduct on its own. This paper asks whether superconductivity can be injected into a thin altermagnet film by placing it on a conventional s-wave superconductor, and what the induced state would be. It answers that, with Rashba spin-orbit coupling at the interface, the proximity effect creates a mixed singlet/triplet superconducting state: singlet pairing dominates near the Brillouin-zone diagonals, equal-spin p-wave triplet pairing dominates elsewhere, and the two regions are separated by eight Dirac nodal points (gapless points in the quasiparticle spectrum). The triplet component has the Jz = 0 structure p↑−/p↓+ and makes the bilayer a spin-current source: a charge supercurrent along the zone diagonal drives a pure spin supercurrent perpendicular to it. This matters because it offers a practical experimental route to the predicted topological and spintronic superconducting phases of altermagnets, with concrete low-temperature signatures and candidate heterostructures.

What carries the argument

The central object is the two-layer Bogoliubov–de Gennes Hamiltonian of Eq. (8), coupling a d-wave altermagnet (Eq. 4) to an s-wave superconductor with Rashba spin-orbit coupling (Eq. 3) through spin- and momentum-conserving tunneling (Eq. 5), together with its second-order effective theory (Eqs. 9–11) obtained by integrating out the superconductor. The load-bearing identity is the Jz = Sz + Lz = 0 selection rule: among the four degenerate equal-spin triplet channels of the altermagnet, p↑− and p↓+ transform trivially under the fourfold rotations of the square lattice and therefore couple linearly to a singlet s-wave order parameter once inversion is broken. The effective pairing matrix Σk h

What would settle it

Measure the low-temperature specific heat and superfluid density of a clean Al/Rb1−δV2Te2O bilayer with a phase gradient along (1,1). The paper predicts cv ~ T², δρs^e ~ T, and a pure spin supercurrent perpendicular to the gradient; observing exponentially activated behavior and no spin supercurrent in the altermagnet layer would falsify the central claim. A simpler control is to remove or invert the interface Rashba symmetry: the nodal triplet state should vanish.

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Extended reading notes

Core claim

Contrary to the expectation that the spin-split Fermi surface of an altermagnet cannot accept spin-singlet Cooper pairs, the paper establishes that a thin metallic altermagnet proximitized by a conventional s-wave superconductor acquires a superconducting state with a mixed singlet/triplet order parameter. The key is inversion breaking at the interface, modeled as Rashba spin-orbit coupling: it permits the s-wave singlet order to couple linearly to the Jz = 0 equal-spin triplet channels p↑− and p↓+. In the induced pairing matrix, the singlet component sk gaps the Fermi surface only where the altermagnetic splitting is small (near the zone diagonals), while the triplet component pk gaps the r

Load-bearing premise

The load-bearing premise is that the superconductor/altermagnet interface has a non-negligible Rashba spin-orbit coupling and passes electrons coherently without flipping spin or momentum; if that coupling is absent, only singlet pairing is induced and the nodal triplet state and spin-current effect do not occur.

Editorial extensions

If this is right

  • The predicted mixed singlet/triplet state can be searched for immediately in standard superconductor/altermagnet bilayers, without waiting for an intrinsically superconducting altermagnet; the paper proposes specific low-mismatch material pairs.
  • The 8 Dirac nodal points per Brillouin zone give distinctive low-temperature thermodynamics: electronic specific heat cv ~ T² and superfluid density δρs^e ~ T, plus flat band edge modes analogous to cuprates.
  • The bilayer is a persistent spin-current generator: a charge supercurrent along the zone diagonal produces a pure spin supercurrent perpendicular to it, with spin superfluid density up to a few percent of the charge superfluid density.
  • Removing or suppressing the interface Rashba spin-orbit coupling eliminates the triplet, the nodes, and the spin current, leaving only singlet pairing that gaps the altermagnet near the zone diagonals; hence the Rashba term is a switch for the whole effect.
  • The same nodal quasiparticles imply a T² specific heat and T-linear penetration-depth shift that distinguish this proximity state from a fully gapped conventional proximity superconductor.

Reading between the lines

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

  • I infer that the Jz = 0 selection rule is not specific to d-wave altermagnets: any compensated magnet with momentum-dependent spin splitting whose leading triplet channels contain Jz = 0 components should show the same proximity-induced triplet order, so the mechanism likely generalizes beyond the square-lattice model.
  • I infer that the nodal positions and the singlet/triplet balance are tunable through the interface Rashba strength and the tunneling amplitude; an electrically gated heterostructure could therefore sweep the system between mostly singlet, nodal, and triplet-dominated regimes in a single device, a knob the paper does not explore.
  • I infer that a fully gapped variant could be reached by using an altermagnet with spin-up and spin-down Fermi pockets centered at X and Y points, as the paper notes; such a state would be a natural platform for probing chiral or helical edge modes and Majorana zero modes in vortices.
  • I infer that allowing the superconducting substrate gap to respond self-consistently would renormalize the pair-breaking suppression of the charge superfluid density seen at intermediate tunneling, and could change the saturation value of the spin superfluid density; a self-consistent calculation would test the robustness of the few-percent estimate.
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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 / 5 minor

Summary. The paper argues that a thin-film metallic altermagnet (ALM) placed on a conventional s-wave superconductor acquires a proximity-induced superconducting state whose order parameter is a mixture of spin-singlet and spin-triplet components, provided Rashba spin-orbit coupling is present at the interface. The singlet component dominates near the Brillouin-zone diagonals, the triplet p↑− ⊗ p↓+ component dominates elsewhere, and the two regions are separated by Dirac nodal points. For the minimal d-wave ALM model the authors find eight nodes per BZ, leading to cv ∼ T^2 and δρ_s^e ∼ T, and they demonstrate a pure spin supercurrent for a phase gradient along the zone diagonal. The claims are supported by a symmetry analysis of the Ginzburg-Landau coupling, a second-order effective theory obtained by integrating out the superconductor, and numerical diagonalization of the full 8×8 BdG Hamiltonian. A table of candidate heterostructures with low lattice mismatch is also provided.

Significance. If established, the result is significant: it gives a concrete microscopic route to triplet pairing and nodal superconductivity starting from a conventional s-wave superconductor, and it proposes a device-oriented spin-current dynamo in a proximitized heterostructure. The symmetry argument connecting Jz = 0 equal-spin p-wave channels to a linear coupling with ψ0 is correct and well explained. The paper also gains credibility from the fact that the effective theory (Eqs. 9–11) and the full numerical solution agree, including the g-dependence of the nodal positions (Fig. 2c vs. Eq. 18), and from the explicit candidate materials list. The main weakness is that the central claim of generic nodality is demonstrated for a single parameter set, and the authors' own End Matter analysis shows that the nodes disappear when the singlet component dominates everywhere. Since the proposed experimental fingerprints (T^2 specific heat, T-linear superfluid-density suppression, and part of the spin-current response) all rely on the nodal structure, this regime question is load-bearing and needs to be addressed before the generic claims can be accepted.

major comments (3)
  1. [Conclusion and Abstract; End Matter, Eq. (18)] The abstract and conclusions state that the resulting superconductor is 'generically nodal with 8 Dirac nodes per BZ.' The supporting analysis, however, establishes this only for the specific parameter set used in Fig. 2, namely (η0, λR, Δ0, μ′) = (0.2, 0.1, 0.4, −3.05), with g up to 0.3. The node condition derived in Eq. (18) is |s_k| = sqrt(η_k^2 + |p_k|^2) on the Fermi surface ξ′_k = 0. Since |s_k| > |p_k|, this requires a sufficiently large altermagnetic splitting relative to the induced singlet gap. For smaller η0, or for larger g where s_k ∼ g^2 grows, the inequality |s_k| > |η_k| can hold everywhere on the Fermi surface, in which case, as the End Matter itself notes, the singlet component opens a full gap and the nodes disappear. The claim of generic nodality is therefore not justified without a phase diagram over (η0, g, λR) or at least a parameter-regime discussion. This is a ma
  2. [Figs. 2(d)–3 and Conclusions] The paper's advertised experimental signatures—cv(T) ∼ T^2, δρ_s^e(T) ∼ T, and the spin-current dynamo with js ≃ (η0/t)je—are all computed in the nodal regime. In the fully gapped regime that occurs for weak altermagnetic splitting or strong coupling, cv(T) becomes activated, δρ_s^e(T) becomes exponentially small, and the low-temperature spin-current response changes qualitatively. The paper should either state clearly that these predictions apply only in the nodal regime, or map out the regime boundaries. As it stands, the Conclusions overgeneralize the numerical results shown in Figs. 2 and 3.
  3. [End Matter, Eq. (17)] The inequality E^2_{k−} ≤ ξ′^2_k + (|s_k| − sqrt(η_k^2 + |p_k|^2))^2 is used to locate the nodes. This gives a sufficient condition for the right-hand side to vanish (ξ′_k = 0 and |s_k| = sqrt(η_k^2 + |p_k|^2)), but the paper does not show that these are necessary conditions for E_k− = 0 in the full model. The numerical agreement shown in Fig. 2(c) for one g-trajectory is encouraging, but a demonstration that the nodes are exactly at these points—or at least a statement of the approximation under which they are—would strengthen the derivation. Without this, the count of '8 Dirac nodes per BZ' remains partially numerical rather than fully analytic.
minor comments (5)
  1. [Eq. (11)] The notation Σk for the pairing matrix and its later decomposition in Eq. (13) into sk and pk is clear, but the text should state explicitly that pk in Eq. (13) is not the same as the momentum k but the triplet component; the notation is potentially confusing and should be flagged or renamed.
  2. [Fig. 2(c)] The horizontal axis of Fig. 2(c) is labeled kα, but the text says the gap is plotted as a function of the angle α. This is likely a typo or a missing definition of kα as a radial distance; please clarify. Also, the different curve styles for different g values are mentioned in the caption but the legend is not visible in the text; this should be fixed.
  3. [Table I] The table includes a hexagonal symmetry entry (Nb4Se8/FeBr3), but the text notes that spin-current dynamo effects are forbidden in hexagonal crystal symmetry. It would be helpful to state in the table caption that this candidate is included only to demonstrate low lattice mismatch, not for the spin-current application.
  4. [Introduction, Ref. [13]] The sentence 'Ref. [13] studied proximitized altermagnets and found numerous interesting topological phases' is slightly vague; a brief specification of what Ref. [13] found (e.g., Majorana modes) would help the reader see the distinction between that work and the present one.
  5. [Eq. (8) and general notation] The 8×8 Hamiltonian in Eq. (8) is written schematically with V = τ_z g. Since V is momentum-independent, this is fine, but it would be useful for reproducibility to state the full BdG basis and the sign conventions for the triplet components explicitly in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all predictions follow from the stated microscopic model by direct derivation and numerical diagonalization.

full rationale

The paper's central derivation is self-contained. Starting from the microscopic model in Eqs. (3)-(5), the authors derive the effective proximity-induced pairing Sigma_k in Eq. (11) via a second-order unitary transformation, then obtain the exact eigenvalue expression Eq. (14) in the End Matter. The nodal condition follows algebraically from Eq. (14): setting the right-hand side of inequality (17) to zero gives xi'_k = 0 and |s_k| = sqrt(eta_k^2 + |p_k|^2), leading to Eq. (18). This is a mathematical consequence of the model, not an input assumption. All spectral, thermodynamic, and superfluid-density results (Figs. 2-3) are computed by direct numerical diagonalization of the full 8x8 Hamiltonian Eq. (8), with no parameter fitted to the predicted quantities. Self-citations to Refs. [7,9,33] are contextual rather than load-bearing: the triplet structure is independently reproduced by the microscopic expression in Eq. (11), and the spin-current dynamo is re-derived from the bilayer Hamiltonian rather than imported. The candidate heterostructures in Table I use external crystallographic data. The only substantive caveat is whether the 'generically nodal' claim persists across the full parameter range (e.g., weak eta_0 or strong g), but that is a robustness concern, not circularity.

Assumptions & free parameters 5 free parameters · 7 assumptions · 1 invented entities

The central claim rests on standard modeling assumptions (single-band tight-binding, d-wave altermagnetic splitting, interface Rashba, coherent tunneling, rigid Delta_0) and standard tools (BdG + second-order perturbation). Five model parameters are chosen by hand for convenience and are not fitted to any experimental data; the qualitative claims (nodal structure, T^2 specific heat, spin dynamo) are structure-driven rather than parameter-driven, which keeps the circularity burden low.

free parameters (5)
  • eta_0 (altermagnetic splitting strength) = 0.2 (chosen model value, not fitted)
    Sets the spin splitting eta_k = 2 eta_0 (cos kx - cos ky) in Eq. 4; controls where singlet vs triplet gap wins and hence node position.
  • lambda_R (interface Rashba SOC) = 0.1 (chosen model value, not fitted)
    Required ingredient: converts singlet pairs to triplet (Eq. 11 off-diagonal); the interesting state vanishes as lambda_R goes to 0.
  • Delta_0 (s-wave gap of substrate) = 0.4 (chosen model value, not fitted)
    Rigid pair amplitude injected into the altermagnet; sets the overall scale of s_k and p_k.
  • g (interlayer tunneling) = swept 0 to 0.35
    Controls induced gap magnitude and node separation (nodes move as g^2, Eq. 18); central coupling of the study.
  • t', mu, mu' (band parameters) = 1.0, -2.80, -3.05
    Choose the Fermi surface geometry of the two layers; qualitative results are structure-driven, not tuned to these values.
assumptions (7)
  • standard math BdG/Nambu formalism and second-order unitary transformation (Ref. 19) used in Eqs. 9-11.
    Standard condensed matter toolset; no new mathematics claimed.
  • domain assumption Single-band tight-binding description of both layers (Eqs. 3-5); orbital details neglected.
    The minimal model is the basis of all claims; real materials may need multi-orbital treatment.
  • domain assumption d-wave altermagnetic splitting eta_k = 2 eta_0 (cos kx - cos ky) (Eq. 4).
    C4-symmetric d-wave altermagnet; the 8-node structure depends on this form.
  • domain assumption Rashba SOC at the SC surface/interface (Eq. 3), allowed by inversion breaking.
    The load-bearing premise of the mechanism: as lambda_R goes to 0 only singlet pairing is induced and the state gaps only near the zone diagonals where |s_k| > |eta_k| (End Matter); consequently triplet-dominated regions, nodes, and the spin dynamo disappear.
  • domain assumption Coherent spin- and momentum-conserving tunneling V = tau_z g (Eq. 5).
    Spin-flip or momentum-changing tunneling is excluded, which could alter the conversion efficiency.
  • domain assumption Rigid Delta_0 in the substrate; induced pairing not computed self-consistently.
    Standard in minimal proximity modeling; back-reaction is only partially captured in the rho_s^e pair-breaking discussion.
  • domain assumption Leading channels are the equal-spin triplet channels p_up+/-, p_down+/- from Refs. [6,7,9].
    Inherited from intrinsic superconducting altermagnet studies; the proximity analysis assumes these are the channels that can be induced.
invented entities (1)
  • none
    purpose: n/a
    No new particles, fields, or conserved quantities are introduced; the triplet component is an induced consequence of the standard model, not a new entity.

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Cite this review

Pith. "Pith review of Proximitizing altermagnets with conventional superconductors." pith.science (2026). https://pith.science/paper/CJJC2YYY

@misc{pith2026250903774,
  author       = {Pith},
  title        = {Pith review of: Proximitizing altermagnets with conventional superconductors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CJJC2YYY}},
  note         = {Machine review of arXiv:2509.03774}
}
read the original abstract

Recent theoretical work highlighted unique properties of superconducting altermagnets, including the wealth of topologically non-trivial phases as well as their potential uses in spintronic applications. Given that no intrinsically superconducting altermagnets have yet been discovered, we study here the possibility of superconducting order induced by proximity effect from a conventional s-wave superconductor. Through symmetry analysis and microscopic modeling we find that interesting superconducting phases can indeed be proximity-induced in a thin altermagnetic film provided that weak Rashba spin-orbit coupling is present at the interface. Surprisingly, the resulting superconductor is generically nodal with a mixed singlet/triplet order parameter and, importantly for applications, capable of generating spin-polarized persistent current. We propose a set of candidate heterostructures with low lattice mismatch suitable to probe these effects experimentally.

Figures

Figures reproduced from arXiv: 2509.03774 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Sketch of the proposed setup: Altermagnetic [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Charge and spin superfluid densities of the combined [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Reference graph

Works this paper leans on

35 extracted references · 31 canonical work pages · cited by 9 Pith papers

  1. [1]

    Antiferromagnetism in ruo 2 as d-wave pomeranchuk instability,

    Kyo-Hoon Ahn, Atsushi Hariki, Kwan-Woo Lee, and Jan Kuneˇ s, “Antiferromagnetism in ruo 2 as d-wave pomeranchuk instability,” Physical Review B 99, 184432 (2019)

    work page 2019

  2. [2]

    Panels (a,b) show the spectral function A(k, ω) = −Tr′Im(ω + iδ − Hk)−1 of electrons in the altermagnet layer where Tr ′ indicates trace over the 4 elements per- 4 Out[]= 0.0 0.2 0.4 0.6 0.8 1.0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.00.20.40.60.81.00.00 0.05 0.10 0.15 0.20 0.00.20.40.60.81.00.000 0.001 0.002 0.003...

    work page

  3. [3]

    Momentum-dependent spin splitting by collinear anti- ferromagnetic ordering,

    Satoru Hayami, Yuki Yanagi, and Hiroaki Kusunose, “Momentum-dependent spin splitting by collinear anti- ferromagnetic ordering,” journal of the physical society of japan 88, 123702 (2019)

    work page 2019

  4. [4]

    Beyond conventional ferromagnetism and antiferromag- netism: A phase with nonrelativistic spin and crystal rotation symmetry,

    Libor ˇSmejkal, Jairo Sinova, and Tomas Jungwirth, “Beyond conventional ferromagnetism and antiferromag- netism: A phase with nonrelativistic spin and crystal rotation symmetry,” Phys. Rev. X 12, 031042 (2022)

    work page 2022

  5. [5]

    Emerging research landscape of altermagnetism,

    Libor ˇSmejkal, Jairo Sinova, and Tomas Jungwirth, “Emerging research landscape of altermagnetism,” Phys. Rev. X 12, 040501 (2022)

    work page 2022

  6. [6]

    Editorial: Altermagnetism—a new punch line of fundamental magnetism,

    Igor Mazin (The PRX Editors), “Editorial: Altermagnetism—a new punch line of fundamental magnetism,” Phys. Rev. X 12, 040002 (2022)

    work page 2022

  7. [7]

    Topological superconductivity in two-dimensional altermagnetic metals,

    Di Zhu, Zheng-Yang Zhuang, Zhigang Wu, and Zhongbo Yan, “Topological superconductivity in two-dimensional altermagnetic metals,” Phys. Rev. B 108, 184505 (2023)

    work page 2023

  8. [8]

    Probing topological degeneracy on a torus using superconducting altermag- nets,

    Tsz Fung Heung and Marcel Franz, “Probing topological degeneracy on a torus using superconducting altermag- nets,” Phys. Rev. B 111, 205145 (2025)

    work page 2025

Show all 35 references
  1. [9]

    Ex- otic superconducting states in altermagnets,

    Kirill Parshukov and Andreas P. Schnyder, “Ex- otic superconducting states in altermagnets,” (2025), arXiv:2507.10700 [cond-mat.supr-con]

    2025 arXiv

  2. [10]

    Persistent spin currents in superconducting altermagnets,

    Kyle Monkman, Joan Weng, Niclas Heinsdorf, Al- berto Nocera, and Marcel Franz, “Persistent spin currents in superconducting altermagnets,” (2025), arXiv:2507.22139 [cond-mat.supr-con]

    2025 arXiv

  3. [11]

    Fulde-ferrell-larkin-ovchinnikov state induced by anti- ferromagnetic order in κ-type organic conductors,

    Shuntaro Sumita, Makoto Naka, and Hitoshi Seo, “Fulde-ferrell-larkin-ovchinnikov state induced by anti- ferromagnetic order in κ-type organic conductors,” Phys. Rev. Res. 5, 043171 (2023)

    2023

  4. [12]

    Zero-field finite-momentum and field-induced supercon- ductivity in altermagnets,

    Debmalya Chakraborty and Annica M. Black-Schaffer, “Zero-field finite-momentum and field-induced supercon- ductivity in altermagnets,” (2024), arXiv:2309.14427 [cond-mat.supr-con]

    2024 arXiv

  5. [13]

    Paired states of fermions in two dimensions with breaking of parity and time- reversal symmetries and the fractional quantum hall ef- fect,

    N. Read and Dmitry Green, “Paired states of fermions in two dimensions with breaking of parity and time- reversal symmetries and the fractional quantum hall ef- fect,” Phys. Rev. B 61, 10267–10297 (2000)

    2000

  6. [14]

    Altermagnetic routes to majorana modes in zero net magnetization,

    Sayed Ali Akbar Ghorashi, Taylor L. Hughes, and Jen- nifer Cano, “Altermagnetic routes to majorana modes in zero net magnetization,” Phys. Rev. Lett. 133, 106601 (2024)

    2024

  7. [15]

    Pairing symmetry in cuprate superconductors,

    C. C. Tsuei and J. R. Kirtley, “Pairing symmetry in cuprate superconductors,” Rev. Mod. Phys.72, 969–1016 (2000)

    2000

  8. [16]

    Magnetic field de- pendence of the density of states of yba 2cu3o6.95 as de- termined from the specific heat,

    K. A. Moler, D. J. Baar, J. S. Urbach, Ruixing Liang, W. N. Hardy, and A. Kapitulnik, “Magnetic field de- pendence of the density of states of yba 2cu3o6.95 as de- termined from the specific heat,” Phys. Rev. Lett. 73, 2744–2747 (1994)

    1994

  9. [17]

    Inter- pretation of the temperature dependence of the electro- magnetic penetration depth in yba2cu3o7−δ,

    James Annett, Nigel Goldenfeld, and S. R. Renn, “Inter- pretation of the temperature dependence of the electro- magnetic penetration depth in yba2cu3o7−δ,” Phys. Rev. B 43, 2778–2782 (1991)

    1991

  10. [18]

    Precision measurements of the tem- perature dependence of λ in yba 2cu3o6.95: Strong evi- dence for nodes in the gap function,

    W. N. Hardy, D. A. Bonn, D. C. Morgan, Ruixing Liang, and Kuan Zhang, “Precision measurements of the tem- perature dependence of λ in yba 2cu3o6.95: Strong evi- dence for nodes in the gap function,” Phys. Rev. Lett. 70, 3999–4002 (1993)

    1993

  11. [19]

    Minimal models for al- termagnetism,

    Merc` e Roig, Andreas Kreisel, Yue Yu, Brian M. Ander- sen, and Daniel F. Agterberg, “Minimal models for al- termagnetism,” Phys. Rev. B 110, 144412 (2024)

    2024

  12. [20]

    Spin-orbit gap of graphene: First- principles calculations,

    Yugui Yao, Fei Ye, Xiao-Liang Qi, Shou-Cheng Zhang, and Zhong Fang, “Spin-orbit gap of graphene: First- principles calculations,” Phys. Rev. B 75, 041401 (2007)

    2007

  13. [21]

    Commentary: The Ma- terials Project: A materials genome approach to accel- erating materials innovation,

    Anubhav Jain, Shyue Ping Ong, Geoffroy Hautier, Wei Chen, William Davidson Richards, Stephen Dacek, Shreyas Cholia, Dan Gunter, David Skinner, Gerbrand Ceder, and Kristin A. Persson, “Commentary: The Ma- terials Project: A materials genome approach to accel- erating materials ...

    2013

  14. [22]

    The computational 2d materi- als database: high-throughput modeling and discovery of atomically thin crystals,

    Sten Haastrup, Mikkel Strange, Mohnish Pandey, Thorsten Deilmann, Per S Schmidt, Nicki F Hinsche, Morten N Gjerding, Daniele Torelli, Peter M Larsen, An- ders C Riis-Jensen, et al., “The computational 2d materi- als database: high-throughput modeling and discovery of atomicall...

    2018

  15. [23]

    Recent progress of the computational 2d materials database (c2db),

    Morten Niklas Gjerding, Alireza Taghizadeh, Asbjørn 6 Rasmussen, Sajid Ali, Fabian Bertoldo, Thorsten Deilmann, Nikolaj Rørbæk Knøsgaard, Mads Kruse, Ask Hjorth Larsen, Simone Manti, et al. , “Recent progress of the computational 2d materials database (c2db),” 2D Materials 8, ...

    2021

  16. [24]

    Weak metal-metal transition in the vanadium oxytelluride rb 1- δ v 2 te 2 o,

    Abduweli Ablimit, Yun-Lei Sun, Hao Jiang, Si-Qi Wu, Ya-Bin Liu, and Guang-Han Cao, “Weak metal-metal transition in the vanadium oxytelluride rb 1- δ v 2 te 2 o,” Physical Review B 97, 214517 (2018)

    2018

  17. [25]

    Two- dimensional altermagnets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects,

    Joachim Sødequist and Thomas Olsen, “Two- dimensional altermagnets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects,” Applied Physics Letters 124 (2024)

    2024

  18. [26]

    Pre- diction of double-weyl points in the iron-based supercon- ductor ca k fe 4 as 4,

    Niclas Heinsdorf, Morten H Christensen, Mikel Iraola, Shang-Shun Zhang, Fan Yang, Turan Birol, Cristian D Batista, Roser Valent ´ ı, and Rafael M Fernandes, “Pre- diction of double-weyl points in the iron-based supercon- ductor ca k fe 4 as 4,” Physical Review B 104, 075101 (2021)

    2021

  19. [27]

    The electronic structures, magnetic transition and fermi surface instability of room-temperature altermag- net kv2se2o,

    Yuanji Xu, Huiyuan Zhang, Maoyuan Feng, and Fuyang Tian, “The electronic structures, magnetic transition and fermi surface instability of room-temperature altermag- net kv2se2o,” (2025), arXiv:2506.20968 [cond-mat.str-el]

    2025

  20. [28]

    Altermagnetic behavior in oso 2: Parallels with ruo 2,

    Parul R Raghuvanshi, Tom Berlijn, David S Parker, Shaofei Wang, Michael E Manley, Rapha¨ el P Hermann, Lucas Lindsay, and Valentino R Cooper, “Altermagnetic behavior in oso 2: Parallels with ruo 2,” Physical Review Materials 9, 034407 (2025)

    2025

  21. [29]

    Pre- diction of unconventional magnetism in doped fesb2,

    Igor I Mazin, Klaus Koepernik, Michelle D Johannes, Rafael Gonz´ alez-Hern´ andez, and LiborˇSmejkal, “Pre- diction of unconventional magnetism in doped fesb2,” Proceedings of the National Academy of Sciences 118, e2108924118 (2021)

    2021

  22. [30]

    Superconductivity in or- thorhombic nbs,

    Bin-Bin Ruan, Jun-Kun Yi, Le-Wei Chen, Menghu Zhou, Yun-Qing Shi, Qing-Song Yang, Ya-Dong Gu, Gen- Fu Chen, and Zhi-An Ren, “Superconductivity in or- thorhombic nbs,” Physical Review B 108, 174517 (2023)

    2023

  23. [31]

    Topological relation be- tween bulk gap nodes and surface bound states: Appli- cation to iron-based superconductors,

    Fa Wang and Dung-Hai Lee, “Topological relation be- tween bulk gap nodes and surface bound states: Appli- cation to iron-based superconductors,” Phys. Rev. B 86, 094512 (2012)

    2012

  24. [32]

    Crystal- symmetry-paired spin-valley locking in a layered room- temperature antiferromagnet,

    Fayuan Zhang, Xingkai Cheng, Zhouyi Yin, Changchao Liu, Liwei Deng, Yuxi Qiao, Zheng Shi, Shuxuan Zhang, Junhao Lin, Zhengtai Liu, Mao Ye, Yaobo Huang, Xiangyu Meng, Cheng Zhang, Taichi Okuda, Kenya Shimada, Shengtao Cui, Yue Zhao, Guang-Han Cao, Shan Qiao, Junwei Liu, and Cha...

    2024

  25. [33]

    Spin-triplet superconductivity from quantum-geometry- induced ferromagnetic fluctuation,

    Taisei Kitamura, Akito Daido, and Youichi Yanase, “Spin-triplet superconductivity from quantum-geometry- induced ferromagnetic fluctuation,” Physical Review Let- ters 132, 036001 (2024)

    2024

  26. [34]

    Altermagnetic instabilities from quan- tum geometry,

    Niclas Heinsdorf, “Altermagnetic instabilities from quan- tum geometry,” Phys. Rev. B 111, 174407 (2025)

    2025

  27. [35]

    Manipulation of the large rashba spin split- ting in polar two-dimensional transition-metal dichalco- genides,

    Qun-Fang Yao, Jia Cai, Wen-Yi Tong, Shi-Jing Gong, Ji-Qing Wang, Xiangang Wan, Chun-Gang Duan, and JH Chu, “Manipulation of the large rashba spin split- ting in polar two-dimensional transition-metal dichalco- genides,” Physical review B 95, 165401 (2017). 1 End Matter Spectru...

    2017

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Reviewed August 5, 2026 · model on record in the stance chip above.