pith. machine review for the scientific record. sign in

arxiv: 2604.20312 · v1 · submitted 2026-04-22 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

Recognition: unknown

Perfect spin nonreciprocity in gated superconducting altermagnetic heterostructures

Pei-Hao Fu , Jun-Feng Liu , Luca Chirolli , Jorge Cayao
Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:12 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall
keywords superconducting altermagnetsspin nonreciprocitygated heterostructuresmomentum-selective transportnonlocal spin currentssuperconducting spintronics
0
0 comments X

The pith

Gating a normal region in superconducting altermagnet junctions produces perfect nonreciprocal spin-polarized currents.

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

The paper examines a heterostructure consisting of a superconducting altermagnet connected to a metallic reservoir through a gated finite normal region. It shows that this setup creates a filter selecting specific transverse momentum channels that align with the momentum-dependent spin-split states of the altermagnet. The resulting directionally selective transport produces perfectly nonreciprocal spin-polarized currents, both locally and nonlocally. These currents also appear in charge flow, exhibit tunable polarity through gate voltage and region length, and depend sensitively on the strength of the altermagnetic field.

Core claim

The central claim is that the interplay between altermagnetism and a selective filter of transverse momentum channels, realized by gating a finite normal region, enables perfect nonreciprocal spin-polarized currents in both local and nonlocal configurations, with nearly perfect quality factors that can be tuned electrically and used to distinguish altermagnet types.

What carries the argument

The selective filter of transverse momentum channels created by gating the finite normal region, which directionally selects transport channels that match the momentum-dependent spin-split superconducting altermagnetic states.

If this is right

  • Local spin currents display nonreciprocity with tunable polarity controlled by gate voltage.
  • Nonlocal spin currents reach nearly perfect quality factors adjustable by the length of the gated region.
  • Charge currents develop nonreciprocal behavior that can also achieve perfect quality factors.
  • All currents vary with the altermagnetic field strength, providing a way to identify the type of altermagnetism present.

Where Pith is reading between the lines

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

  • The same gating approach might be tested in nonsuperconducting altermagnetic junctions to isolate the role of superconductivity in the nonreciprocity.
  • Varying the gate voltage could switch the device between reciprocal and nonreciprocal regimes on demand.
  • The momentum-filter mechanism suggests possible extensions to other momentum-dependent order parameters beyond altermagnetism.

Load-bearing premise

The gated normal region functions as an ideal selective filter that transmits only the momentum channels aligned with the altermagnet's spin-split states while blocking others.

What would settle it

Measuring the spin current for forward and reverse bias under fixed gate voltage and finding identical magnitudes instead of direction-dependent differences would falsify the perfect nonreciprocity.

Figures

Figures reproduced from arXiv: 2604.20312 by Jorge Cayao, Jun-Feng Liu, Luca Chirolli, Pei-Hao Fu.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a), where we attach a normal metallic lead (NR) on the right side of the superconducting AM of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We consider a superconducting altermagnet heterostructure and demonstrate that the interplay between altermagnetism and a selective filter of transverse momentum channels enables perfect nonreciprocal spin-polarized currents. We demonstrate that this nonreciprocity manifests in both local and nonlocal spin currents, signalling the emergence of directionally selective local and nonlocal spin behaviors. We show that the selective filter of transverse momentum channels is realized by gating a finite normal region between the superconducting altermagnet and the metallic reservoir, which then directionally selects transport channels that match the momentum-dependent spin-split superconducting altermagnetic states, allowing for nonreciprocal spin-polarized currents. We discover that the local and nonlocal spin nonreciprocity features a highly tunable polarity and nearly perfect quality factors, respectively, which is achieved by means of gate voltages and by varying the length of the finite region. Moreover, we find that local and nonlocal charge currents also develop a nonreciprocal behavior, whose quality factors can also reach perfect values. In all cases, the spin and charge currents are sensitive to variations of the altermagnetic field, a functional dependence that can be exploited to identify the type of altermagnetism. Our findings put forward an electrically controllable route towards nonreciprocal superconducting spintronic devices based on altermagnets.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript considers a heterostructure consisting of a superconducting altermagnet, a gated finite-length normal region, and a metallic reservoir. It claims that gating induces a selective filter for transverse momentum channels whose transmission matches the momentum-dependent spin-split states of the altermagnet, producing perfect (or near-perfect) nonreciprocity in both local and nonlocal spin-polarized currents. The polarity and quality factors are stated to be tunable by gate voltage and normal-region length; nonreciprocity is also reported for charge currents, and all currents are sensitive to the altermagnetic field strength and symmetry, offering a route to identify altermagnet type.

Significance. If the central claim of electrically tunable perfect spin nonreciprocity holds under realistic conditions, the work would be significant for superconducting spintronics. Altermagnets are a timely platform because they combine spin splitting with zero net magnetization; combining them with gating to achieve directional selectivity could enable compact nonreciprocal devices. The emphasis on both local and nonlocal transport and on falsifiable dependence on altermagnetic parameters strengthens the potential impact.

major comments (2)
  1. [Model and Results sections (specific equations for the gate potential and BdG scattering matrix not cited in abstract)] The claim of perfect nonreciprocity (abstract and main text) rests on the assumption that the gated normal region acts as an ideal transverse-momentum filter. The skeptic note and the absence of any discussion of smoothed gate potentials or finite interface transparency raise the question whether the quality factor remains unity once the step-like potential is replaced by a continuous barrier; this is load-bearing for the 'perfect' qualifier.
  2. [Numerical or scattering formalism] It is unclear from the provided abstract and description whether the calculations include evanescent modes or interface scattering that would mix channels and degrade the reported nonreciprocity; a concrete check against a smoothed potential or finite transparency should be added to support the central claim.
minor comments (2)
  1. [Abstract] The abstract repeatedly uses 'demonstrate' and 'discover' without referencing specific figures or equations; the main text should tie each claim to explicit results.
  2. [Introduction or Model] Notation for the altermagnetic field strength and the gate-induced potential should be defined consistently when first introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We appreciate the positive assessment of the potential significance for superconducting spintronics. We address the major comments point by point below.

read point-by-point responses

  1. Referee: The claim of perfect nonreciprocity (abstract and main text) rests on the assumption that the gated normal region acts as an ideal transverse-momentum filter. The skeptic note and the absence of any discussion of smoothed gate potentials or finite interface transparency raise the question whether the quality factor remains unity once the step-like potential is replaced by a continuous barrier; this is load-bearing for the 'perfect' qualifier.

    Authors: We acknowledge that the reported perfect (or near-perfect) nonreciprocity is obtained within the idealized step-like gate potential model detailed in the Model section, where the gate potential and BdG scattering matrix are explicitly defined. The abstract emphasizes the ideal-case result while the main text qualifies some quality factors as 'nearly perfect.' We agree that robustness to smoothed potentials and finite transparency is important for the 'perfect' claim and will add explicit numerical checks and discussion of continuous barriers in the revised manuscript. revision: yes

  2. Referee: It is unclear from the provided abstract and description whether the calculations include evanescent modes or interface scattering that would mix channels and degrade the reported nonreciprocity; a concrete check against a smoothed potential or finite transparency should be added to support the central claim.

    Authors: The calculations employ the full Bogoliubov-de Gennes scattering-matrix formalism, which incorporates evanescent modes via wavefunction solutions in each region and interface scattering through boundary matching. To clarify this and directly address the concern, we will include additional calculations with smoothed gate potentials and reduced interface transparency in a revised version, quantifying their effect on the nonreciprocity quality factors. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper computes nonreciprocal spin and charge currents by solving the Bogoliubov-de Gennes equations on a heterostructure consisting of a superconducting altermagnet, a gated normal segment, and a metallic reservoir. The gated region is introduced as an explicit model input (step-like potential, tunable length and voltage) whose transmission properties are calculated from scattering states; the resulting directionally selective matching to altermagnetic spin-split bands and the emergence of perfect quality factors are direct numerical/analytical outputs of that scattering problem. No parameters are fitted to the nonreciprocity itself, no self-citations supply load-bearing uniqueness theorems, and no definitions are circular. The derivation therefore remains independent of the claimed perfect nonreciprocity.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; full paper likely introduces additional model parameters such as altermagnetic exchange strength and superconducting gap. The listed items are inferred directly from the abstract description.

free parameters (2)
  • gate voltage
    Used to tune the transverse-momentum filter and to achieve nearly perfect quality factors for local and nonlocal nonreciprocity.
  • length of finite normal region
    Varied to reach perfect quality factors for spin and charge nonreciprocity.
axioms (2)
  • domain assumption Altermagnetic order produces momentum-dependent spin splitting that survives in the superconducting state.
    Invoked when stating that transport channels must match the spin-split altermagnetic states.
  • domain assumption A finite normal region can be gated to act as a selective transverse-momentum filter.
    Central to the mechanism that enables directional selection of channels.

pith-pipeline@v0.9.0 · 5543 in / 1539 out tokens · 74597 ms · 2026-05-09T23:12:10.459341+00:00 · methodology

discussion (0)

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

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Spin-polarized Josephson current induced by inhomogeneous altermagnetic interlayers

    cond-mat.supr-con 2026-05 unverdicted novelty 7.0

    An inhomogeneous altermagnetic interlayer in a Josephson junction induces a net spin-polarized Josephson current at π misorientation of Néel vectors, enhancing the critical current while suppressing 0-π transitions.

  2. Spin-polarized Josephson current induced by inhomogeneous altermagnetic interlayers

    cond-mat.supr-con 2026-05 unverdicted novelty 7.0

    An inhomogeneous altermagnetic interlayer in a Josephson junction produces enhanced critical current and spin-polarized supercurrent at π misorientation of Néel vectors through cancellation of pair-breaking oscillations.

Reference graph

Works this paper leans on

115 extracted references · 23 canonical work pages · cited by 1 Pith paper · 4 internal anchors

  1. [1]

    Fukaya, B

    Y. Fukaya, B. Lu, K. Yada, Y. Tanaka, and J. Cayao, Superconducting phenomena in systems with unconven- tional magnets, J. Phys.: Condens. Matter37, 313003 12 (2025)

    2025

  2. [2]

    Z. Liu, H. Hu, and X.-J. Liu, Altermagnetism and superconductivity: A short historical review, arXiv , 2510.09170 (2025)

    work page arXiv 2025

  3. [3]

    Brando, D

    M. Brando, D. Belitz, F. M. Grosche, and T. R. Kirk- patrick, Metallic quantum ferromagnets, Rev. Mod. Phys.88, 025006 (2016)

    2016

  4. [4]

    Huang, P

    P. Huang, P. Zhang, S. Xu, H. Wang, X. Zhang, and H. Zhang, Recent advances in two-dimensional ferro- magnetism: materials synthesis, physical properties and device applications, Nanoscale12, 2309 (2020)

    2020

  5. [5]

    Hirohata, D

    A. Hirohata, D. C. Lloyd, T. Kubota, T. Seki, K. Takanashi, H. Sukegawa, Z. Wen, S. Mitani, and H. Koizumi, Antiferromagnetic films and their applica- tions, IEEE Access11, 117443 (2023)

    2023

  6. [6]

    Y. Noda, K. Ohno, and S. Nakamura, Momentum- dependent band spin splitting in semiconducting MnO2: a density functional calculation, Phys. Chem. Chem. Phys.18, 13294 (2016)

    2016

  7. [7]

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

    2019

  8. [8]

    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

  9. [9]

    K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneˇ s, Anti- ferromagnetism in RuO2 asd-wave Pomeranchuk insta- bility, Phys. Rev. B99, 184432 (2019)

    2019

  10. [10]

    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. B102, 014422 (2020)

    2020

  11. [11]

    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

  12. [12]

    M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Mo- tome, and H. Seo, Anomalous Hall effect inκ-type organic antiferromagnets, Phys. Rev. B102, 075112 (2020)

    2020

  13. [13]

    L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, Prediction of low-Zcollinear and noncollinear antifer- romagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling, Phys. Rev. Mater.5, 014409 (2021)

    2021

  14. [16]

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

    I. Mazin, Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys. Rev. X12, 040002 (2022)

    2022

  15. [17]

    Zhang, L.-H

    S.-B. Zhang, L.-H. Hu, and T. Neupert, Finite- momentum Cooper pairing in proximitized altermag- nets, Nat. Commun.15, 1801 (2024)

    2024

  16. [18]

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

    2023

  17. [19]

    G. Z. Yang, Z.-T. Sun, Y.-M. Xie, and K. Law, Topological altermagnetic Josephson junctions, arXiv:2502.20283 (2025)

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  18. [20]

    B. Lu, K. Maeda, H. Ito, K. Yada, and Y. Tanaka,φ Josephson junction induced by altermagnetism, Phys. Rev. Lett.133, 226002 (2024)

    2024

  19. [21]

    Cheng and Q.-F

    Q. Cheng and Q.-F. Sun, Orientation- dependent Josephson effect in spin-singlet superconductor/altermagnet/spin-triplet supercon- ductor junctions, Phys. Rev. B109, 024517 (2024)

    2024

  20. [22]

    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 unconventional mag- nets, Phys. Rev. B111, 064502 (2025)

    2025

  21. [23]

    Sun, S.-B

    H.-P. Sun, S.-B. Zhang, C.-A. Li, and B. Trauzettel, Tunable second harmonic in altermagnetic Josephson junctions, Phys. Rev. B111, 165406 (2025)

    2025

  22. [24]

    W. Zhao, Y. Fukaya, P. Burset, J. Cayao, Y. Tanaka, and B. Lu, Orientation-dependent transport in junc- tions formed byd-wave altermagnets andd-wave su- perconductors, Phys. Rev. B111, 184515 (2025)

    2025

  23. [25]

    Alipourzadeh and Y

    M. Alipourzadeh and Y. Hajati, Andreev bound states and supercurrent in an unconventional superconductor- altermagnet Josephson junction, Phys. Rev. B111, 214515 (2025)

    2025

  24. [26]

    A. Pal, D. Mondal, T. Nag, and A. Saha, Josephson current signature of Floquet Majorana and topological accidental zero modes in altermagnet heterostructures, Phys. Rev. B112, L201408 (2025)

    2025

  25. [27]

    Maeda, Y

    K. Maeda, Y. Fukaya, K. Yada, B. Lu, Y. Tanaka, and J. Cayao, Classification of pair symmetries in supercon- ductors with unconventional magnetism, Phys. Rev. B 111, 144508 (2025)

    2025

  26. [28]

    Chakraborty and A

    D. Chakraborty and A. M. Black-Schaffer, Con- straints on superconducting pairing in altermagnets, arXiv:2408.03999 (2024)

    work page arXiv 2024

  27. [29]

    Khodas, S

    M. Khodas, S. Mu, I. I. Mazin, and K. D. Belashchenko, Tuning of altermagnetism by strain, arXiv:2506.06257 (2025)

    work page arXiv 2025

  28. [30]

    Feng and Z

    X. Feng and Z. Zhang, Superconducting order parame- ters in spin space groups: Methodology and application, Phys. Rev. B111, 054520 (2025)

    2025

  29. [31]

    Parshukov and A

    K. Parshukov and A. P. Schnyder, Exotic superconduct- ing states in altermagnets, arXiv:2507.10700 (2025)

    work page arXiv 2025

  30. [32]

    I. I. Mazin, Notes on altermagnetism and superconduc- tivity, AAPPS Bull.35, 18 (2025)

    2025

  31. [33]

    P.-H. Fu, S. Mondal, J.-F. Liu, and J. Cayao, Light- induced Floquet spin-triplet Cooper pairs in unconven- tional magnets, SciPost Phys.20, 059 (2026)

    2026

  32. [34]

    P.-H. Fu, S. Mondal, J.-F. Liu, Y. Tanaka, and J. Cayao, Floquet engineering spin triplet states in unconventional magnets, Phys. Rev. Lett.136, 066703 (2026)

    2026

  33. [35]

    Yokoyama, Floquet engineering triplet superconduc- tivity in superconductors with spin-orbit coupling or al- termagnetism, Phys

    T. Yokoyama, Floquet engineering triplet superconduc- tivity in superconductors with spin-orbit coupling or al- termagnetism, Phys. Rev. B112, 024512 (2025)

    2025

  34. [36]

    Mukasa and Y

    K. Mukasa and Y. Masaki, Finite-momentum su- perconductivity in two-dimensional altermagnets with a Rashba-type spin-orbit coupling, arXiv:2409.08972 (2025)

    work page arXiv 2025

  35. [37]

    Heinsdorf and M

    N. Heinsdorf and M. Franz, Proximitizing altermagnets with conventional superconductors, arXiv:2509.03774 (2025)

    work page arXiv 2025

  36. [38]

    Monkman, J

    K. Monkman, J. Weng, N. Heinsdorf, A. Nocera, and M. Franz, Persistent spin currents in superconducting altermagnets, arXiv:2507.22139 (2025)

    work page arXiv 2025

  37. [39]

    Cheng, Y

    Q. Cheng, Y. Mao, and Q.-F. Sun, Field-free Josephson diode effect in altermagnet/normal metal/altermagnet 13 junctions, Phys. Rev. B110, 014518 (2024)

    2024

  38. [40]

    Sim and J

    G. Sim and J. Knolle, Pair density waves and super- current diode effect in altermagnets, Phys. Rev. B112, L020502 (2025)

    2025

  39. [41]

    Banerjee and M

    S. Banerjee and M. S. Scheurer, Altermagnetic super- conducting diode effect, Phys. Rev. B110, 024503 (2024)

    2024

  40. [42]

    Jiang, H.-L

    Y. Jiang, H.-L. Liu, and J. Wang, Josephson diode effect in altermagnet-baseds-wave superconductor junction, Chinese Phys. B34, 107803 (2025)

    2025

  41. [43]

    Chakraborty and A

    D. Chakraborty and A. M. Black-Schaffer, Perfect su- perconducting diode effect in altermagnets, Phys. Rev. Lett.135, 026001 (2025)

    2025

  42. [44]

    Sharma and M

    L. Sharma and M. Thakurathi, Tunable Josephson diode effect in singlet superconductor-altermagnet- triplet superconductor junctions, Phys. Rev. B112, 104506 (2025)

    2025

  43. [45]

    Debnath, A

    D. Debnath, A. Saha, and P. Dutta, Spin-polarization and diode effect in thermoelectric current through altermagnet-based superconductor heterostructures, arXiv:2509.12198 (2025)

    work page arXiv 2025

  44. [46]

    S. V. S. Sai Ruthvik and T. Nag, Field-free diode effects in one-dimensional superconductor: a complex inter- play between Fulde-Ferrell pairing and altermagnetism, arXiv:2512.01415 (2025)

    work page arXiv 2025

  45. [47]

    Sharma, B

    L. Sharma, B. Ghimire, and M. Thakurathi,p- wave magnet driven field-free Josephson diode effect, arXiv:2602.16677 (2026)

    work page arXiv 2026

  46. [48]

    Debnath, A

    D. Debnath, A. Saha, and P. Dutta, Spin polar- ization and diode effect in thermoelectric current through altermagnet-based superconductor heterostruc- tures, Phys. Rev. B113, 104508 (2026)

    2026

  47. [49]

    V. D. Esin, D. Y. Kazmin, Y. S. Barash, A. V. Timo- nina, N. N. Kolesnikov, and E. V. Deviatov, Josephson diode and spin-valve effects on the surface of altermag- net CrSb, arXiv:2602.08766 (2026)

    work page arXiv 2026

  48. [50]

    Mondal and J

    S. Mondal and J. Cayao, Spin-polarized andreev molecules and anomalous nonlocal Josephson effects in altermagnetic junctions, arXiv:2603.04954 (2026)

    work page arXiv 2026

  49. [51]

    & Levchenko, A

    D. Shaffer and A. Levchenko, Theories of superconduct- ing diode effects, arXiv:2510.25864 (2025)

    work page arXiv 2025

  50. [52]

    Nagaosa and Y

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

    2024

  51. [53]

    Tokura and N

    Y. Tokura and N. Nagaosa, Nonreciprocal responses from non-centrosymmetric quantum materials, Nat. Commun.9, 3740 (2018)

    2018

  52. [54]

    Nadeem, M

    M. Nadeem, M. Fuhrer, and X. Wang, The supercon- ducting diode effect, Nat. Rev. Phys.5, 558 (2023)

    2023

  53. [55]

    Wakatsuki, Y

    R. Wakatsuki, Y. Saito, S. Hoshino, Y. M. Itahashi, T. Ideue, M. Ezawa, Y. Iwasa, and N. Nagaosa, Nonre- ciprocal charge transport in noncentrosymmetric super- conductors, Sci. Adv.3, e1602390 (2017)

    2017

  54. [56]

    A. I. Braginski, Superconductor electronics: Status and outlook, J. Supercond. Nov. Magn.32, 23 (2019)

    2019

  55. [57]

    Kochan and C

    D. Kochan and C. Strunk, Low-loss electronics with su- perconducting diodes: Superconducting devices, Nat. Electron.8, 380 (2025)

    2025

  56. [58]

    A. I. Buzdin, Proximity effects in superconductor- ferromagnet heterostructures, Rev. Mod. Phys.77, 935 (2005)

    2005

  57. [59]

    Cayao, C

    J. Cayao, C. Triola, and A. M. Black-Schaffer, Odd- frequency superconducting pairing in one-dimensional systems, Eur. Phys. J. Special Topics229, 545 (2020)

    2020

  58. [60]

    Tanaka, S

    Y. Tanaka, S. Tamura, and J. Cayao, Theory of Ma- jorana zero modes in unconventional superconductors, Prog. Theor. Exp. Phys.2024, 08C105 (2024)

    2024

  59. [61]

    ˇSmejkal, J

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

    2022

  60. [62]

    ˇSmejkal, J

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

    2022

  61. [63]

    Giazotto and F

    F. Giazotto and F. Taddei, Superconductors as spin sources for spintronics, Phys. Rev. B77, 132501 (2008)

    2008

  62. [64]

    Strambini, V

    E. Strambini, V. N. Golovach, G. De Simoni, J. S. Moodera, F. S. Bergeret, and F. Giazotto, Supercon- ducting spintronic tunnel diode, Nat. Commun.13, 2431 (2022)

    2022

  63. [65]

    C. I. L. de Araujo, P. Virtanen, M. Spies, C. Gonz´ alez- Orellana, S. Kerschbaumer, M. Ilyn, C. Rogero, T. T. Heikkil¨ a, F. Giazotto, and E. Strambini, Superconduct- ing spintronic heat engine, Nat. Commun.15, 4823 (2024)

    2024

  64. [66]

    Giazotto, P

    F. Giazotto, P. Solinas, A. Braggio, and F. S. Bergeret, Ferromagnetic-insulator-based superconducting junc- tions as sensitive electron thermometers, Phys. Rev. Appl.4, 044016 (2015)

    2015

  65. [67]

    Z. Geng, A. Hijano, S. Ili´ c, M. Ilyn, I. J. Maasilta, A. Monfardini, M. Spies, E. Strambini, P. Virta- nen, M. Calvo, C. Gonz´ alez-Orell´ ana, A. P. Helenius, S. Khorshidian, C. I. L. de Araujo, F. Levy-Bertrand, C. Rogero, F. Giazotto, F. S. Bergeret, and T. T. Heikkil¨ a, Superconductor-ferromagnet hybrids for non- reciprocal electronics and detector...

    2023

  66. [68]

    A. V. Putilov, S. V. Mironov, and A. I. Buzdin, Nonre- ciprocal electron transport in finite-size superconduc- tor/ferromagnet bilayers with strong spin-orbit cou- pling, Phys. Rev. B109, 014510 (2024)

    2024

  67. [69]

    Dom´ ınguez, J

    F. Dom´ ınguez, J. Cayao, P. San-Jose, R. Aguado, A. L. Yeyati, and E. Prada, Zero-energy pinning from inter- actions in majorana nanowires, npj Quantum Mater.2, 13 (2017)

    2017

  68. [70]

    A. E. Antipov, A. Bargerbos, G. W. Winkler, B. Bauer, E. Rossi, and R. M. Lutchyn, Effects of gate-induced electric fields on semiconductor Majorana nanowires, Phys. Rev. X8, 031041 (2018)

    2018

  69. [71]

    B. D. Woods, T. D. Stanescu, and S. Das Sarma, Effec- tive theory approach to the Schr¨ odinger-Poisson prob- lem in semiconductor Majorana devices, Phys. Rev. B 98, 035428 (2018)

    2018

  70. [72]

    A. E. G. Mikkelsen, P. Kotetes, P. Krogstrup, and K. Flensberg, Hybridization at superconductor- semiconductor interfaces, Phys. Rev. X8, 031040 (2018)

    2018

  71. [73]

    G. W. Winkler, A. E. Antipov, B. van Heck, A. A. Soluyanov, L. I. Glazman, M. Wimmer, and R. M. Lutchyn, Unified numerical approach to topological semiconductor-superconductor heterostructures, Phys. Rev. B99, 245408 (2019)

    2019

  72. [74]

    C.-X. Liu, S. Schuwalow, Y. Liu, K. Vilkelis, A. L. R. Manesco, P. Krogstrup, and M. Wimmer, Electronic properties of InAs/EuS/Al hybrid nanowires, Phys. Rev. B104, 014516 (2021)

    2021

  73. [75]

    G. B. Lesovik, A. L. Fauch´ ere, and G. Blatter, Non- linearity in normal-metal–superconductor transport: 14 Scattering-matrix approach, Phys. Rev. B55, 3146 (1997)

    1997

  74. [76]

    Melo, C.-X

    A. Melo, C.-X. Liu, P. Ro˙ zek, T. O. Rosdahl, and M. Wimmer, Conductance asymmetries in mesoscopic superconducting devices due to finite bias, SciPost Phys. 10, 037 (2021)

    2021

  75. [77]

    Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2005)

    S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2005)

    2005

  76. [78]

    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. B25, 4515 (1982)

    1982

  77. [79]

    M. P. Lopez Sancho, J. M. Lopez Sancho, and J. Ru- bio, A nonorthogonal-basis calculation of the spectral density of surface states for the (100) and (110) faces of tungsten, J. Phys. F: Met. Phys.15, 851 (1985)

    1985

  78. [80]

    M. P. Lopez Sancho, J. M. Lopez Sancho, and J. Rubio, Quick iterative scheme for the calculation of transfer matrices: Application to Mo (100), J. Phys. F: Met. Phys.14, 1205 (1984)

    1984

  79. [81]

    M. P. Lopez Sancho, J. M. Lopez Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, J. Phys. F: Met. Phys.15, 851 (1985)

    1985

  80. [82]

    M. P. Anantram, M. S. Lundstrom, and D. E. Nikonov, Modeling of nanoscale devices, Proc. IEEE96, 1511 (2008)

    2008

Showing first 80 references.