arxiv: 2604.12695 · v1 · submitted 2026-04-14 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

Recognition: unknown

Robust realization of spin-polarized specular Andreev reflection in V₂O-based altermagnets

Yutaro Nagae , Andreas P. Schnyder , Satoshi Ikegaya

Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:07 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall

keywords altermagnetsAndreev reflectionspin polarizationV2OCooper pair splittingnonlocal conductancequasi-one-dimensional Fermi surfacessuperconductor junctions

0 comments

The pith

V2O-based altermagnets produce robust spin-polarized specular Andreev reflection at junctions with conventional superconductors.

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

The authors examine charge transport in a superconductor-altermagnet junction where the altermagnet has spin-split quasi-one-dimensional Fermi surfaces. They employ a six-orbital model that includes both vanadium and oxygen sites to calculate the scattering processes under multiple boundary conditions. The calculations show that specular Andreev reflection arises reliably and carries a definite spin polarization. This outcome matters because it offers a route to split Cooper pairs into spin-resolved electrons, a step toward sources of energy-entangled pairs. The work also describes a multiterminal geometry in which nonlocal conductance signals can confirm the polarized reflection.

Core claim

Calculations performed under various boundary conditions demonstrate the robust emergence of specular Andreev reflection with a distinctive spin polarization in a junction between a conventional superconductor and a V2O-based altermagnet exhibiting spin-split quasi-one-dimensional Fermi surfaces. An efficient multiterminal setup is proposed to detect this reflection through nonlocal conductance measurements, establishing V2O-based altermagnets as a platform for spin-resolved Cooper pair splitting essential for generating energy-entangled electron pairs.

What carries the argument

A microscopically motivated six-orbital model that incorporates sublattice degrees of freedom on both V and O sites; this model encodes the altermagnet's spin-split quasi-one-dimensional Fermi surfaces and permits explicit scattering calculations across different interface conditions.

Load-bearing premise

The six-orbital model correctly reproduces the altermagnet's spin-split quasi-one-dimensional Fermi surfaces and the relevant boundary conditions at the junction.

What would settle it

Observation of only retro Andreev reflection or absence of spin polarization in the reflected current for a superconductor-V2O altermagnet junction would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.12695 by Andreas P. Schnyder, Satoshi Ikegaya, Yutaro Nagae.

**Figure 2.** Figure 2: FIG. 2. (a) Schematic illustration of the multiterminal set [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a)–(d) FSs of the altermagnet tilted by 45 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a), (b) Nonlocal differential conductances [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Nonlocal differential conductance [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. (a), (b) Schematic illustrations of scattering proc [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

read the original abstract

We theoretically investigate charge transport in a junction between a conventional superconductor and a V$_2$O-based altermagnet exhibiting distinctive spin-split quasi-one-dimensional Fermi surfaces. The altermagnet is described by a microscopically motivated six-orbital model that incorporates sublattice degrees of freedom associated with both V and O sites. Based on calculations performed under various boundary conditions, we demonstrate the robust emergence of specular Andreev reflection with a distinctive spin polarization. Furthermore, we propose an efficient multiterminal setup to detect this specular Andreev reflection through nonlocal conductance measurements. Our results establish V$_2$O-based altermagnets as a promising platform for realizing spin-resolved Cooper pair splitting, which is essential for generating energy-entangled electron pairs.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note private letter to a colleague

The paper offers a model-based prediction of robust spin-polarized specular Andreev reflection in V2O altermagnets with a detection proposal, though the six-orbital model's accuracy remains unverified against first-principles data.

read the letter

The one or two things to know: this paper calculates spin-polarized specular Andreev reflection in a junction with a V2O-based altermagnet using a six-orbital model, and it holds up under different boundary conditions. They also give a multiterminal geometry for detecting it with nonlocal conductance. The new element is the focus on V2O systems with their distinctive spin-split quasi-one-dimensional Fermi surfaces, modeled with both V and O sublattice degrees of freedom. The work does a solid job within its framework by showing the spin polarization of the reflected holes is robust and by linking it to a practical measurement scheme for energy-entangled pairs. This builds on prior altermagnet and Andreev physics but pins it to a specific material class. Where it is softer is in the lack of external benchmarks for the model. The Hamiltonian is called microscopically motivated, yet the paper does not compare its Fermi surfaces or spin splitting to DFT results or other tight-binding versions. As noted in the stress test, if the parameters do not accurately reflect the real band velocities or interface hybridization, the reported spin polarization and the conductance signature could be model-specific rather than material-specific. All the boundary condition checks stay inside this single description, which limits how convincing the robustness claim is without more checks. This is aimed at condensed matter physicists working on altermagnets, topological superconductivity, or spintronic devices. Someone looking for theoretical suggestions on platforms for spin-resolved Cooper pair splitting would find it worthwhile. The thinking is clear and the proposal is testable, so it deserves a serious referee who can push on the numerics and model choices. I would recommend putting it through peer review.

Referee Report

1 major / 1 minor

Summary. The manuscript theoretically investigates charge transport in a junction between a conventional superconductor and a V₂O-based altermagnet with distinctive spin-split quasi-one-dimensional Fermi surfaces. The altermagnet is modeled by a microscopically motivated six-orbital Hamiltonian incorporating sublattice degrees of freedom for both V and O sites. Numerical calculations under various boundary conditions are used to demonstrate the robust emergence of specular Andreev reflection carrying distinctive spin polarization. The authors further propose a multiterminal setup to detect this process via nonlocal conductance measurements and position V₂O-based altermagnets as a platform for spin-resolved Cooper pair splitting.

Significance. If the six-orbital model faithfully reproduces the altermagnet's spin-split Fermi surfaces, orbital character, and interface scattering, the work would identify a concrete materials platform for realizing spin-polarized specular Andreev reflection and spin-resolved Cooper pair splitting. This has clear relevance to spintronics and to proposals for generating energy-entangled electron pairs. The internal consistency checks across multiple boundary conditions constitute a positive feature of the numerical approach.

major comments (1)

[six-orbital model construction and parameter choice] The central claim that spin-polarized specular Andreev reflection emerges robustly depends on the quantitative accuracy of the six-orbital model's spin splitting, band velocities, and orbital projections at the superconductor interface. No comparison is presented to DFT-derived bands, ARPES data, or alternative tight-binding parametrizations that would confirm these quantities; if the effective parameters deviate from the real material (e.g., due to unaccounted hybridization or strain), the reported spin polarization and the proposed nonlocal conductance signature can disappear or reverse.

minor comments (1)

[Abstract] The abstract and introduction would benefit from a brief statement of the specific spin polarization direction (e.g., relative to the altermagnetic Néel vector) observed in the specular Andreev channel.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major concern below and have revised the manuscript to strengthen the presentation of the model and its limitations.

read point-by-point responses

Referee: [six-orbital model construction and parameter choice] The central claim that spin-polarized specular Andreev reflection emerges robustly depends on the quantitative accuracy of the six-orbital model's spin splitting, band velocities, and orbital projections at the superconductor interface. No comparison is presented to DFT-derived bands, ARPES data, or alternative tight-binding parametrizations that would confirm these quantities; if the effective parameters deviate from the real material (e.g., due to unaccounted hybridization or strain), the reported spin polarization and the proposed nonlocal conductance signature can disappear or reverse.

Authors: We acknowledge that the manuscript does not include direct comparisons of the six-orbital model to DFT band structures, ARPES data, or alternative parametrizations. The model is constructed from microscopic considerations of the V2O lattice, incorporating sublattice degrees of freedom for V and O sites to reproduce the characteristic spin-split quasi-one-dimensional Fermi surfaces of altermagnets, with parameters selected to match known orbital characters from prior literature on related compounds. The robustness of spin-polarized specular Andreev reflection is shown through explicit calculations under multiple boundary conditions, which test sensitivity to interface details and parameter variations. To address the referee's point, we have added a new subsection in the revised manuscript that discusses the model's relation to available DFT results for V2O-based systems, highlights the key features it captures, and explicitly notes the possible effects of unaccounted hybridization or strain as limitations that could affect quantitative predictions in real devices. This revision clarifies the scope of our claims without altering the core theoretical results. revision: partial

Circularity Check

0 steps flagged

No circularity: numerical transport calculations from independent model Hamiltonian

full rationale

The paper applies standard Bogoliubov-de Gennes scattering theory to a fixed six-orbital tight-binding Hamiltonian for the V2O altermagnet, computing Andreev reflection probabilities and nonlocal conductances for several boundary conditions. No parameter is fitted to the target Andreev or conductance observables, no self-referential definition equates the claimed spin-polarized specular reflection to an input, and no uniqueness theorem or ansatz from prior self-citations is invoked to force the result. The multiterminal detection proposal follows directly from the computed conductances without circular reduction. The central claims therefore remain independent of the model inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the six-orbital model for the altermagnet and on the numerical treatment of boundary conditions; no explicit free parameters or invented entities are stated in the abstract.

axioms (1)

domain assumption The six-orbital model accurately describes the V2O-based altermagnet including sublattice degrees of freedom for V and O sites.
Invoked to generate the spin-split quasi-one-dimensional Fermi surfaces used in the transport calculations.

pith-pipeline@v0.9.0 · 5438 in / 1243 out tokens · 33392 ms · 2026-05-10T14:07:29.784877+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

63 extracted references · 5 canonical work pages · 1 internal anchor

[1]

5t1, m 2 = 0

5t1, ε 2 = − 0. 5t1, m 2 = 0 . 7t1, and t3 = 0 . 4t1, which are used to generate Fig. 1(c). Note that the FSs obtained from HAM well reproduce those observed in experiments and ﬁrst-principles calculations of KV 2Se2O [43]. B. Multiterminal setup In this paper, we study the transport properties of a multiterminal setup consisting of three normal metal lea...
[2]

5t1 for α = px, p y, p z, while ¯tJN(S),α = δtJN(S),α = 0 for the other orbitals. Figure 5(d) shows the results when the hopping integrals exhibit a signiﬁcant imbal- ance between the normal-metal–altermagnet interfaces and the altermagnet–superconductor interface, where we set ¯tJN,α = 0 . 7t1 and δtJN,α = 0 . 5t1 while ¯tJS,α = 0 . 3t1 and δtJS,α = 0 . ...
[3]

A. F. Andreev, Thermal conductivity of the intermedi- ate state of superconductors, Sov. Phys. JETP 46, 1823 (1964)

1964
[4]

Deutscher and D

G. Deutscher and D. Feinberg, Coupling superconducting-ferromagnetic poing contact by Andreev reﬂections, Appl. Phys. Lett. 76, 487 (2000)

2000
[5]

Recher, E

P. Recher, E. V. Sukhorukov, and D. Loss, Andreev tun- neling, Coulomb blockade, and resonant transport of non- local spin-entangled electrons, Phys. Rev. B 63, 165314 (2001)

2001
[6]

C. W. J. Beenakker, Specular Andreev reﬂection in graphen, Phys. Rev. Lett. 97, 067007 (2006)

2006
[7]

G. B. Lesovik, T. Martin, and G. Blatter, Electronic entanglement in the vicinity of a superconductor, Eur. Phys. J. B 24, 287 (2001)

2001
[8]

N. M. Chtchelkatchev, G. Blatter, G. B. Lesovik, and T. Martin, Bell inequalities and entanglement in solid-state devices, Phys. Rev. B 66, 161320(R) (2002)

2002
[9]

Hofstteter, S

L. Hofstteter, S. Csonka, J. Nygøard, and C. Sch¨ onenberger, Cooper pair splitter realized in a two-quantum-dot Y-junction, Nature 461, 960-963 (2009)

2009
[10]

Hofstetter, S

L. Hofstetter, S. Csonka, A. Baumgartner, G. F¨ ul¨ op, S. d’Hollosy, J. Nygøard, and C. Sch¨ onenberger, Finite- Bias Cooper Pair Splitting, Phys. Rev. Lett. 107, 136801 (2011)

2011
[11]

Schindele, A

J. Schindele, A. Baumgartner, and C. Sch¨ onenberger, Near-Unity Cooper Pair Splitting Eﬃciency, Phys. Rev. 11 Lett. 109, 157002 (2012)

2012
[12]

A. Das, Y. Ronen, M. Heiblum, D. Mahalu, A. V. Kre- tinin, and H. Shtrikman, High-eﬃciency Cooper pair splitting demonstrated by two-partivle conductance res- onance and positive noise cross-corelation, Nat. Comm. 3, 1165 (2012)

2012
[13]

F¨ ul¨ op, S

G. F¨ ul¨ op, S. d’Hollosy, A. Baumgartner, P. Makk, V. A. Guzenko, M. H. Madsen, J. Nygøard, C. Sch¨ onenberger, and S. Csonka, Local electrical tuning of the nonlocal signals in a Cooper pair splitter, Phys. Rev. B 90, 235412 (2014)

2014
[14]

F¨ ul¨ op, F

G. F¨ ul¨ op, F. Dom ´ ınguez, S. d’Hollosy, A. Baumgartner, P. Makk, M. H. Madsen, V. A. Guzenko, J. Nygøard, C. Schn¨ onenberger, A. L. Yeyati, and S. Csonka, Mag- netic Field Tuning and Quantum Interference in a Cooper Pair Splitter, Phys. Rev. Lett. 115, 227003 (2015)

2015
[15]

S. Baba, C. J¨ unger, S. Matsuo, A. Baumgartner, Y. Sato, H. Kamata, K. Li, S. Jeppesen, L. Samuelson, H. Q. Xu, C. Sch¨ onenberger, and S. Tarucha, Cooper-pair splitting in two parallel InAs nanowires, New J. Phys. 20, 063012 (2018)

2018
[16]

G. Wang, T. Dvir, G. P. Mazur, C. -X. Liu, N. van Loo, S. L. D. ten Haaf, A. Bordin, S. Gazibegovic, G. Badawy, E. P. A. M. Bakkers, M. Wimmer, and L. P. Kouwen- hoven, Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires, Nature 612, 448-453 (2022)

2022
[17]

Bordoloi, V

A. Bordoloi, V. Zannier, L. Sorba, C. Sch¨ onenberger, and A. Baumgartner, Spin cross-correlation experiments in an electron entangler, Nature 612, 454-458 (2022)

2022
[18]

de Jong, C

D. de Jong, C. G. Prosko, L. Han, F. K. Malinowski, Y. Liu, L. P. Kouwenhoven and W. Pfaﬀ, Controllable Single Cooper Pair Splitting in Hybrid Quantum Dot Systems, Phys. Rev. Lett. 131, 157001 (2023). Phys. Rev. Lett. 108, 106603 (2012)

2023
[19]

W. Chen, L. Jiang, R. Shen, L. Sheng, B. G. Wang, and D. Y. Xing, Specular Andreev reﬂection in inversion- symmetric Weyl semimetals, Europhys. Lett. 103, 27006 (2013)

2013
[20]

Majidi and R

L. Majidi and R. Asgari, Specular Andreev reﬂection in thin ﬁlms of topological insulators, Phys. Rev. B 93, 195404 (2016)

2016
[21]

Hou and Q.-F

Z. Hou and Q.-F. Sun, Double Andreev reﬂections in type-II Weyl semimetal-superconductor junctions, Phys. Rev. B 96, 155305 (2017)

2017
[22]

Cheng, Z

Q. Cheng, Z. Hou, and Q.-F. Sun, Double Andreev reﬂections and double normal reﬂections in nodal-line semimetal-superconductor junctions, Phys. Rev. B 101, 094508 (2020)

2020
[23]

Nagae, A

Y. Nagae, A. P. Schnyder, and S. Ikegaya, Spin-polarize d specular Andreev reﬂections in altermagnets, Phys. Rev. B 111, L100507 (2025)

2025
[24]

M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Mo- tome, and H. Seo, Spin current generation in organic an- tiferromagnets, Nat. Commun., 10, 4305 (2019)

2019
[25]

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
[26]

Hayami, Y

S. Hayami, Y. Yanagi, and H. Kusunose, Bottom-up de- sign of spin-split and reshaped electronic band structures in antiferromagnets without spin-orbit coupling: Proce- dure on the basis of augmented multipoles, Phys. Rev. B 102, 144441 (2020)

2020
[27]

M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Mo- tome, and H. Seo, Anomalous Hall eﬀect in κ-type organic antiferromagnets, Phys. Rev. B 102, 075112 (2020)

2020
[28]

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
[29]

M. Naka, Y. Motome, H. Seo, Perovskite as a spin current generator, Phys. Rev. B 103, 125114 (2021)

2021
[30]

I. I. Mazin, K. Koepernik, M. D. Johannes, and L. ˇSmejkal, Prediction of unconventional magnetism in doped FeSb 2, Proc. Natl. Acad. Sci. U. S. A. 118, e2108924118 (2021)

2021
[31]

Seo, and M

H. Seo, and M. Naka, Antiferromagnetic State in κ-type Molecular Conductors: Spin Splitting and Mott Gap, J. Phys. Soc. Jpn. 90, 064713 (2021)

2021
[32]

ˇSmejkal, J

L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond Con- ventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry, Phys. Rev. X 12, 031042 (2022)

2022
[33]

ˇSmejkal, J

L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging Re- search Landscape of Altermagnetism, Phys. Rev. X 12, 040501 (2022)

2022
[34]

C. Sun, A. Brataas, and J. Linder, Andreev reﬂection in altermagnets, Phys. Rev. B 108, 054511 (2023)

2023
[35]

C. W. J. Beenakker, and T. Vakhtel, Phase-shifted An- dreev levels in an altermagnet Josephson junction, Phys. Rev. B 108, 075425 (2023)

2023
[36]

Papaj, Andreev reﬂection at the altermagnet- superconductor interface, Phys

M. Papaj, Andreev reﬂection at the altermagnet- superconductor interface, Phys. Rev. B 108, L060508 (2023)

2023
[37]

H. G. Giil, B. Brekke, J. Linder, and A. Brataas, Qua- siclassical theory of superconducting spin-splitter eﬀec ts and spin-ﬁltering via altermagnets, Phys. Rev. B 110, L140506 (2024)

2024
[38]

D. Y. Kazmin, V. D. Esin, Y. S¿ Barash, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, Andreev reﬂection for MnTe altermagnet candidate, Physica B: Condensed Matter 696, 416602 (2025)

2025
[39]

Fukaya, K

Y. Fukaya, K. Maeda, K. Yada, J. Cayao, Y. Tanaka, and B. Lu, Josephson eﬀect and odd-frequency pairing in superconducting junctions with unvonventional magnets, Phys. Rev. B 111, 064502 (2025)

2025
[40]

Fukaya, B

Y. Fukaya, B. Lu, K. Yada, Y. Tanaka, and J. Cayao, Superconducting phenomena in systems with unconven- tional magnets, J. Phys.: Condens. Matter 37, 313003 (2025)

2025
[41]

I. V. Bobkova, P. J. Hirschfeld, and Yu. S. Barash, Spin- Dependent Quasiparticle Reﬂection and Bound States at Interfaces with Itinerant Antiferromagnets, Phys. Rev. Lett. 94, 037005 (2005)

2005
[42]

B. M. Andersen, I. V. Bobkova, P. J. Hirschfeld, and Y. S. Barash, Bound states at the interface between an- tiferromagnets and superconductors, Phys. Rev. B 72, 184510 (2005)

2005
[43]

B. M. Andersen, I. V. Bobkova, P. J. Hirschfeld, and Y. S. Barash, Bound states at the interface between an- tiferromagnets and superconductors, Phys. Rev. B 72, 184510 (2005). 0– π Transitions in Josephson Junctions with Antiferromagnetic Interlayers, Phys. Rev. Lett. 96, 117005(2006)

2005
[44]

G. A. Bobkov, I. V. Bobkova, A. M. Bobkov, and A. Kamra, N´ eel proximity eﬀect at antiferromag- net/superconductor interfaces, Phys. Rev. B 106, 144512 (2022). 12

2022
[45]

Jiang, M

B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, Y, -J. Sun, Y. Huang, X. Zheng, Y. Peng, L. He, S. Li, J. Luo, Z. Li, G. Chen, H. Weng, and T. Qian, A metallic room-temperature d-wave altermagnet, Nat. Phys. 21, 754-759 (2025)

2025
[46]

Zhang, X

F. Zhang, X. Cheng, Z. Yin, C. Liu, L. Deng, Y. Qiao, Z. Shi, S. Zhang, J. Lin, Z. Liu, M. Yeo, Y. Huang, X. Meng, C. Zhang, T. Okuda, K. Shimada, S. Cui, Y. Zhao, G. -H. Cao, S. Qiao, J. Liu, and C. Chen, Crystal-symmetry- paired spin–valley locking in a layered room-temperature metallic altermagnet candidate, Nat. Phys. 21, 760-767 (2025)

2025
[47]

J. Lai, T. Yu, P. Liu, L. Liu, C. Xing, X. -Q. Chen, and Y. Sun, d-wave Flat Fermi Surface in Altermagnets Enables Maximum Charge-to-Spin Conversion, Phys. Rev. Lett. 135, 256702 (2025)

2025
[48]

C. -C. Liu, J. Li, J. -Y. Liu, J. -Y. Lu, H. -X. Li, Y. Liu, and G. -H. Cao, Physical properties and ﬁrst-principles calculations of an altermagnet candidate Cs 1− δ V2Te2O, Phys. Rev. B 112, 224439 (2025)

2025
[49]

Zhang, E

W. Zhang, E. Zhu, Z. Li, and H. Lv, Strain-tunable spin- valley locking and the inﬂuence of spin-orbit coupling in the two-dimensional altermagnet V 2Te2O, Phys. Rev. B 112, 144427 (2025)

2025
[50]

Z. Wang, S. Yu, X. Cheng, X. Xiao, W. Ma, F. Quan, H. Song, K. Zhang, Y. Zhang, Y. Ma, W. Liu, P. Yadav, X. Shi, Z. Wang, Q. Niu, Y. Gao, B. Xiang, J. Liu, Z. Wang, and X. Chen, Atomic-scale spin sensing of a 2D d- wave altermagnet via helical tunneling, arXiv:2512.23290 (2025)

work page arXiv 2025
[51]

D. Fu, L. Yang, K. Xiao, Y. Wang, Z. Wang, Y. Yao, Q. -K. Xue, and W. Li, Atomic-scale visualization of d-wave altermagnetism, arXiv:2512.24114 (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[52]

Q. Hu, X. Cheng, Q. Duan, Y. Hu, B. Jiang, Y. Xiao, Y. Li, M. Pan, L. Deng, C. Liu, G. Cao, Z. Liu, M. Ye, S. Qiao, Z. Liu, Z. Sun, A. Gao, Y. Huang, R. Zhong, J. Liu, B. Lv, and H. Ding, Observation of spin-valley locked nodal lines in a quasi-2D altermagnet, arXiv:2601.02883 (2026)

work page arXiv 2026
[53]

Cheng, Y

X. Cheng, Y. Gao, J. Pengand, and J. Liu, Realitic tight-binding model for V 2Se2O-family altermagnets, arXiv:2602.09465 (2026)

work page arXiv 2026
[54]

Brekke, A

B. Brekke, A. Brataas, and A. Sudbø, Two-dimensional altermagnets: Superconductivity in a minimal micro- scopic model, Phys. Rev. B, 108, 224421 (2023)

2023
[55]

J. Bai, B. Ruan, Q. Dong, L. Zhang, Q. Liu, J. Cheng, P. Liu, C. Li, Y. Sun, Y. Huang, Z. Ren, and G. Chen, Absense of long-range order in the vanadium oxychalco- genide KV 2Se2O with nontrivial band topology, Phys. Rev. B, 110, 165151 (2024)

2024
[56]

G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Tran- sition from metallic to tunneling regimes in supercon- ducting microconstrictions: Excess current, charge im- balance, and supercurrent conversion, Phys. Rev. B 25, 4515 (1982)

1982
[57]

M. P. Anantram, and S. Datta, Current ﬂuctuations in mesoscopic systems with Andreev scattering, Phys. Rev. B 53, 16390 (1996)

1996
[58]

P. A. Lee, and D. S. Fisher, Anderson Localization in Two dimensions,Phys. Rev. Lett. 47, 882 (1981)

1981
[59]

Ando, Quantum point contacts in magnetic ﬁelds, Phys

T. Ando, Quantum point contacts in magnetic ﬁelds, Phys. Rev. B 44, 8017 (1991)

1991
[60]

R. A. Jalabert, H. U. Baranger, and A. D. Stone, Con- ductance ﬂuctuations in the ballistic regime: A probe of quantum chaos?, Phys. Rev. Lett. 65, 2442 (1990)

1990
[61]

Y. Sun, Y. Huang, J. Cheng, S. Zhang, Z. Li, H. Luo, X. Ma, W. Yang, J. Yang, D. Chen, K. Sun, M. Gut- mann, S. C. Capelli, F. Shen, J. Hao, L. He, G. Chen, and S. Li, Antiferromagnetic structure of KV 2Se2O: A neu- tron diﬀraction study, Phys. Rev. B 112, 184416 (2025)

2025
[62]

Lange, R

C. Lange, R. Jaeschke-Ubiergo, A. Chakraborty, X. H. Verbeek, L. ˇSmejkal, J. Sinova, and A. Moo, Emergent altermagnetism at surfaces of antiferromag- nets: full symmetry classiﬁcation and material identi- ﬁcation, arXiv:2602.08773 (2026)

work page arXiv 2026
[63]

https://github.com/nagaephysics0204- ops/datasets V2OAM