pith. sign in

arxiv: 2511.20424 · v1 · pith:PRTYKTWVnew · submitted 2025-11-25 · ❄️ cond-mat.supr-con · physics.app-ph· physics.ins-det

Planar Josephson junctions for sensors and electronics:Different geometry, new functionality

Pith reviewed 2026-05-17 04:44 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con physics.app-phphysics.ins-det
keywords planar Josephson junctionssuperconducting electronicsmagnetic sensorsterahertz devicesvortex memorysuperconducting diodesminiaturizationmagnetic imaging
0
0 comments X

The pith

Planar Josephson junctions provide enhanced magnetic field sensitivity and enable flexible miniaturization in superconducting electronics.

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

This paper examines how fabricating Josephson junctions in a planar geometry, rather than the traditional overlap stack, changes their properties in useful ways. The author argues that the single-plane layout makes the junctions much more responsive to magnetic fields and better matched for terahertz signals. This geometric shift supports simpler designs for complex circuits and allows components to be made much smaller. Applications discussed include high-resolution magnetic sensors on cantilevers, memory cells based on magnetic vortices, and diodes that can be programmed. A sympathetic reader would see this as opening paths to more compact and sensitive superconducting devices for sensing and computing.

Core claim

The central claim is that the planar geometry of Josephson junctions, formed at the edge of two superconducting films in the same plane instead of vertical overlap, greatly enhances sensitivity to magnetic fields and improves impedance matching for terahertz devices. The two-dimensional structure permits simple and flexible design of electronic components, leading to drastic miniaturization. Recent advances include junction-on-cantilever sensors for super-resolution magnetic imaging, vortex-based memory cells, and programmable superconducting diodes.

What carries the argument

The planar geometry of Josephson junctions, where the weak link is formed laterally between two superconducting films without vertical stacking, which alters the response to magnetic fields and current flow compared to sandwich-type overlap junctions.

If this is right

  • Enhanced magnetic field sensitivity enables junction-on-cantilever sensors for super-resolution magnetic imaging.
  • Improved design flexibility supports vortex-based memory cells in superconducting electronics.
  • Better impedance matching facilitates use in terahertz devices.
  • Two-dimensional structure allows programmable superconducting diodes with new functionalities.
  • Overall, the geometry change enables drastic miniaturization of superconducting components.

Where Pith is reading between the lines

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

  • Integrating planar junctions with existing nanofabrication techniques could accelerate development of hybrid quantum-classical circuits.
  • Testing these junctions in high-frequency circuits might reveal additional benefits for signal processing beyond those described.
  • The emphasis on planar layouts suggests potential compatibility with two-dimensional materials for further performance gains.
  • Future devices might combine sensing and memory functions on the same planar chip more easily than with overlap junctions.

Load-bearing premise

The geometric change from overlap to planar layout produces the claimed enhancements in sensitivity and functionality without being limited by fabrication defects, material interfaces, or other practical constraints.

What would settle it

Fabricating both planar and overlap Josephson junctions from the same materials and measuring no significant difference in their magnetic field sensitivity or impedance matching at terahertz frequencies would challenge the central claims.

Figures

Figures reproduced from arXiv: 2511.20424 by Vladimir M. Krasnov.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) A sketch of geometry difference between overlap and planar Josephson junctions. (b) A sketch of planar junction [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) SEM image (false color) of an array with nine variable-thickness bridge type planar Nb junctions, and with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A sketch (top) and a SEM image (bottom) of a four-terminal Josephson diode with a vortex trap. (b) Magnetic field [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) SEM image (false color) of a [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Josephson junctions are key elements in superconducting electronics. The most common type is the overlap (sandwich-type) junction, formed by vertically stacking two superconducting layers. In contrast, planar junctions are fabricated without overlap, at the edge of two superconducting films within a single plane. This geometric distinction has a significant impact on their physical properties. The planar geometry greatly enhances sensitivity to magnetic fields and improves impedance matching for terahertz (THz) devices. Its two-dimensional structure allows for simple and flexible electronic component design, enabling drastic miniaturization. Here I highlight recent advances in the application of planar junctions for novel technologies, including junction-on-cantilever sensors for super-resolution magnetic imaging, vortex-based memory cells, and programmable superconducting diodes. I will also discuss the general requirements, future perspectives, and key challenges in the evolving field of superconducting electronics.

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 is a perspective article arguing that planar Josephson junctions—fabricated in a single plane at the edge of two superconducting films—offer distinct advantages over conventional overlap (sandwich-type) junctions. It claims that the planar geometry greatly enhances sensitivity to magnetic fields, improves impedance matching for terahertz devices, and enables simple, flexible designs that support drastic miniaturization. The paper reviews recent applications including junction-on-cantilever sensors for super-resolution magnetic imaging, vortex-based memory cells, and programmable superconducting diodes, while outlining general requirements, future perspectives, and key challenges in superconducting electronics.

Significance. If the geometric advantages are borne out by quantitative device performance, the perspective could help steer research toward more compact and sensitive superconducting sensors and electronics, particularly in quantum sensing and THz applications. The synthesis of recent advances in cantilever sensors, vortex memory, and diodes provides a useful overview for the field, though the manuscript itself introduces no new data, derivations, or parameter-free predictions.

major comments (2)
  1. [Abstract / Introduction] Abstract and opening discussion of geometry: the central claim that planar geometry 'greatly enhances sensitivity to magnetic fields' and 'improves impedance matching' is presented without any quantitative comparison (e.g., effective area scaling, critical-current density, or noise spectral density) between planar and overlap devices fabricated from comparable materials. This quantitative gap is load-bearing for the asserted functionality gains.
  2. [Key challenges / Future perspectives] Section on key challenges and future perspectives: fabrication defects, edge roughness, and interface transparency are flagged as challenges, yet no bounds or citations are given on how these factors limit the claimed sensitivity or miniaturization advantages relative to ideal geometry. Without such assessment the extrapolation from geometry to device performance remains untested.
minor comments (2)
  1. [Abstract] The abstract would benefit from one or two concrete citations to the 'recent advances' being highlighted so readers can immediately locate the supporting experimental literature.
  2. [Figures] Figure captions (if present) should explicitly state whether any plotted data are new measurements or reproduced from cited works.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report on our perspective article. The comments correctly identify areas where additional quantitative context and literature grounding would strengthen the presentation. We address each major comment below and indicate the planned revisions.

read point-by-point responses
  1. Referee: [Abstract / Introduction] Abstract and opening discussion of geometry: the central claim that planar geometry 'greatly enhances sensitivity to magnetic fields' and 'improves impedance matching' is presented without any quantitative comparison (e.g., effective area scaling, critical-current density, or noise spectral density) between planar and overlap devices fabricated from comparable materials. This quantitative gap is load-bearing for the asserted functionality gains.

    Authors: We agree that the perspective would benefit from explicit quantitative benchmarks drawn from the literature. While the manuscript synthesizes published experimental results rather than presenting new data, we will revise the introduction and abstract to include a concise comparison of key metrics. This will reference effective area scaling and magnetic sensitivity enhancements reported for planar junction-on-cantilever devices (e.g., from recent super-resolution imaging studies) versus typical overlap junctions, along with impedance-matching advantages in THz contexts supported by cited experimental works. These additions will be framed as summaries of existing measurements rather than new derivations. revision: yes

  2. Referee: [Key challenges / Future perspectives] Section on key challenges and future perspectives: fabrication defects, edge roughness, and interface transparency are flagged as challenges, yet no bounds or citations are given on how these factors limit the claimed sensitivity or miniaturization advantages relative to ideal geometry. Without such assessment the extrapolation from geometry to device performance remains untested.

    Authors: We accept this observation. In the revised manuscript we will expand the challenges section to incorporate additional citations and, where available, quantitative estimates from the literature on how edge roughness and interface transparency affect critical current density and magnetic field sensitivity in planar junctions. We will also note the current scarcity of direct comparative bounds versus ideal geometries as an open issue requiring further experimental work, thereby clarifying the limits of current extrapolations. revision: yes

Circularity Check

0 steps flagged

No circularity: descriptive perspective without derivations or fitted predictions

full rationale

The manuscript is a review-style perspective on planar Josephson junctions that describes geometric differences, application examples, and challenges without any equations, derivations, or quantitative predictions. No load-bearing steps reduce to self-definitions, fitted inputs renamed as predictions, or self-citation chains; claims rest on cited experimental advances and geometric arguments that remain externally verifiable. The text is self-contained as an overview rather than a closed derivation loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract introduces no new mathematical models, free parameters, axioms, or invented physical entities; discussion is limited to geometric distinctions and listed applications.

pith-pipeline@v0.9.0 · 5442 in / 1010 out tokens · 32228 ms · 2026-05-17T04:44:35.997253+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages

  1. [1]

    https://www.iea.org/reports/electricity-2024/executive- summary

  2. [2]

    Weisheng, L. et al. Approaching the quantum limit in two-dimensional semiconductor contacts.Nature613, 274-279 (2023)

  3. [3]

    Cardoso, J. M. P., Coutinho, J. G. F., Diniz, P. C., Em- bedded Computing for High Performance: Efficient Map- ping of Computations Using Customization, Code Trans- formations and Compilation (Morgan Kaufmann Pub- lishers, 2017 Elsevier Inc.)

  4. [4]

    S., Ripple, A

    Holmes, D. S., Ripple, A. L., & Manheimer, M. A. Energy-efficient superconducting computing—Power budgets and requirements.IEEE Trans. Appl. Supercond. 23, 1701610 (2013)

  5. [5]

    IEEE Trans

    Ortlepp, T., and Van Duzer, T., Access time and power dissipation of a model 256-bit single flux quantum RAM. IEEE Trans. Appl. Supercond.24, 1300307 (2014)

  6. [6]

    M., Single Abrikosov vortices as quantized information bits,Nat

    Golod, T., Iovan, A., and Krasnov, V. M., Single Abrikosov vortices as quantized information bits,Nat. Commun.6, 8628 (2015)

  7. [7]

    K., and V

    Likharev, K. K., and V. K. Semenov, RSFQ logic/memory family: A new Josephson-junction tech- nology for sub-terahertz-clock-frequency digital systems. IEEE Transactions on Applied Superconductivity,1(1), 3-28 (1991)

  8. [8]

    K., Superconductor digital electronics: Scal- ability and energy efficiency issues.Low Temperature Physics,42(5), 361-379 (2016)

    Tolpygo, S. K., Superconductor digital electronics: Scal- ability and energy efficiency issues.Low Temperature Physics,42(5), 361-379 (2016)

  9. [9]

    Energy efficiency of adiabatic superconductor logic,Supercond

    Takeuchi, N., Yamanashi, Y., and Yoshikawa, N. Energy efficiency of adiabatic superconductor logic,Supercond. Sci. Technol.28, 015003 (2015)

  10. [10]

    F., Vernik, I

    Kirichenko, A. F., Vernik, I. V., Kamkar, M. Y., Walter, J. Miller, M., Albu, L. R., and Mukhanov, O. A., ERSFQ 8-Bit Parallel Arithmetic Logic Unit.IEEE Trans. Appl. Supercond.,29, 1302407 (2019)

  11. [11]

    V. K. Semenov, Y. A. Polyakov, and S. K. Tolpygo, AC-Biased Shift Registers as Fabrication Process Bench- mark Circuits and Flux Trapping Diagnostic Tool,IEEE Trans. Appl. Supercond.271301409, (2017)

  12. [12]

    S. K. Tolpygo, V. Bolkhovsky, R. Rastogi, S. Zarr, A. L. Day, E. Golden, T. J. Weir, A. Wynn, and L. M. John- son, Advanced Fabrication Processes for Superconduc- tor Electronics: Current Status and New Developments, IEEE Trans. Appl. Supercond.291102513, (2019)

  13. [13]

    I., et al., Beyond Moore’s technologies: oper- ation principles of a superconductor alternative.Beilstein J

    Soloviev, I. I., et al., Beyond Moore’s technologies: oper- ation principles of a superconductor alternative.Beilstein J. Nanotechnol.8, 2689 (2017)

  14. [14]

    M., Word and bit line operation of a 1×1µm 2 supercon- ducting vortex-based memory.Nat

    Golod, T., Morlet-Decarnin, L., and Krasnov, V. M., Word and bit line operation of a 1×1µm 2 supercon- ducting vortex-based memory.Nat. Commun.14, 4926 (2023)

  15. [15]

    S., Srinivasa, S

    Alam, S., Hossain, M. S., Srinivasa, S. R., and Aziz, A., Cryogenic memory technologies.Nat. Electr.6, 185–198 (2023)

  16. [16]

    D., Elsbury, M

    Dresselhaus, P. D., Elsbury, M. M., Olaya, D., Bur- roughs, C. J., and Benz, S. P., 10 Volt Programmable Josephson Voltage Standard Circuits Using NbSi-Barrier Junctions,IEEE Trans. Appl. Supercond.21, 693-696 (2011)

  17. [17]

    planar” may sound confusing for people famil- iar with semiconducting electronics since there “planar

    The term “planar” may sound confusing for people famil- iar with semiconducting electronics since there “planar” junctions are formed along the substrate (as in overlap JJs), while non-planar junctions are expanding in the third (vertical) dimension, as in 3D FinFET. Using simi- lar logics, the term “planar junction” has been sometimes applied to overlap ...

  18. [18]

    K., Superconducting weak links,Rev

    Likharev, K. K., Superconducting weak links,Rev. Mod. Phys.51101-159 (1979)

  19. [19]

    R., Tsuei, C

    Kirtley, J. R., Tsuei, C. C., Rupp, M., Sun, J. Z., Yu- Jahnes, L. S., Gupta, A., Ketchen, M. B., Moler, K. A., and Bhushan, M., Direct Imaging of Integer and Half- Integer Josephson Vortices in High-Tc Grain Boundaries, Phys. Rev. Lett.76, 1336 (1996)

  20. [20]

    A., Rydh, A., Golod, T., Motzkau, H., Klushin, A

    Boris, A. A., Rydh, A., Golod, T., Motzkau, H., Klushin, A. M., and Krasnov, V. M., Evidence for Nonlocal Elec- trodynamics in Planar Josephson Junctions.Phys. Rev. Lett.111, 117002 (2013)

  21. [21]

    M., Bauch, T., Intiso, S., H¨ urfeld, E., Akazaki, T., Takayanagi, H., and Delsing, P., Collapse of Thermal Activation in Moderately Damped Joseph- son Junctions.Phys

    Krasnov, V. M., Bauch, T., Intiso, S., H¨ urfeld, E., Akazaki, T., Takayanagi, H., and Delsing, P., Collapse of Thermal Activation in Moderately Damped Joseph- son Junctions.Phys. Rev. Lett.95, 157002 (2005)

  22. [22]

    Fabian, J

    Baumgartner, C., Fuchs, L., Costa, A., Reinhardt, S., Gronin, S., Gardner, G.C., Lindemann, T., Manfra, M.J., Faria Junior, P.E., Kochan, D. Fabian, J. Paradiso N. & Strunk C. Supercurrent rectification and magnetochi- ral effects in symmetric Josephson junctions.Nat. Nan- otechn.17, 39 (2022)

  23. [23]

    D., Jung, W., Lee, G.-H., Efetov, D

    Walsh, E. D., Jung, W., Lee, G.-H., Efetov, D. K., Wu, B.-I., Huang, K.-F., Ohki, T. A., Taniguchi, T., Watanabe, K., Kim, P., Englund, D., and Fong, K. C., Josephson junction infrared single-photon detector.Sci- ence372, 409–412 (2021)

  24. [24]

    M., de la Barrera, S

    Rodan-Legrain, D., Cao, Y., Park, J. M., de la Barrera, S. C., Randeria, M. T., Watanabe, K., Taniguchi, T., and 10 Jarillo-Herrero, P., Highly tunable junctions and non- local Josephson effect in magic-angle graphene tunnelling devices,Nat. Nanotechn.16, 769 (2021)

  25. [25]

    & Peng, X., Non- reciprocal superconducting NbSe2 antenna.Nat

    Zhang, E., Xu, X., Zou, Y.C., Ai, L., Dong, X., Huang, C., Leng, P., Liu, S., Zhang, Y., Jia, Z. & Peng, X., Non- reciprocal superconducting NbSe2 antenna.Nat. Comm., 11, 5634 (2020)

  26. [26]

    Adv.,11, eadw6925 (2025)

    Kudriashov, A., t al., Non-Majorana origin of anoma- lous current-phase relation and Josephson diode effect in Bi 2Se3/NbSe2 Josephson junctions,Sc. Adv.,11, eadw6925 (2025)

  27. [27]

    W., Booij, W

    Moseley, R. W., Booij, W. E., Tarte, E. J., and Blamire, M. G., Direct writing of low superconductor- normal metal-superconductor junctions using a focused ion beam,Appl. Phys. Lett.75, 262 (1999)

  28. [28]

    M., Ericsson, O., Intiso, S., Delsing, P., Oboznov, V

    Krasnov, V. M., Ericsson, O., Intiso, S., Delsing, P., Oboznov, V. A., Prokofiev, A. S., and Ryazanov, V. V., Planar S–F–S Josephson junctions made by focused ion beam etching.Physica C418, 16-22 (2005)

  29. [29]

    M., Detection of the phase shift from a single Abrikosov vortex.Phys

    Golod, T., Rydh, A., and Krasnov, V. M., Detection of the phase shift from a single Abrikosov vortex.Phys. Rev. Lett.104, 227003 (2010)

  30. [30]

    C., Gallop, J

    Cox, D. C., Gallop, J. C., Hao, L., Focused Ion Beam Processing of Superconducting Junctions and SQUID Based Devices,Nanofabrication1, 53–64 (2014)

  31. [31]

    Reconfigurable Josephson phase shifter

    Golod, T., et al. Reconfigurable Josephson phase shifter. Nano Lett.21, 5240–5246 (2021)

  32. [32]

    Fermin, R., de Wit, B., and Aarts, J., Beyond the effec- tive length: How to analyze magnetic interference pat- terns of thin-film planar Josephson junctions with finite lateral dimensions,Phys. Rev. B107, 064502 (2023)

  33. [33]

    A., Beukers, E., Pleijster, M., Linder, J., Alkemade, P., and Aarts, J., Controlling supercurrents and their spatial distribution in ferromagnets,Nat

    Lahabi, K., Amundsen, M., Ouassou, J. A., Beukers, E., Pleijster, M., Linder, J., Alkemade, P., and Aarts, J., Controlling supercurrents and their spatial distribution in ferromagnets,Nat. Commun.8, 2056 (2017)

  34. [34]

    M., Two mechanisms of Josephson phase shift generation by an Abrikosov vortex.Phys

    Golod, T., Pagliero, A., and Krasnov, V. M., Two mechanisms of Josephson phase shift generation by an Abrikosov vortex.Phys. Rev. B100, 174511 (2019)

  35. [35]

    M., and Krasnov, V

    Golod, T., Kapran, O. M., and Krasnov, V. M., Pla- nar superconductor-ferromagnet-superconductor Joseph- son junctions as scanning-probe sensors,Phys. Rev. Appl. 11, 014062 (2019)

  36. [36]

    and Krasnov, V.M

    Golod, T. and Krasnov, V.M. Demonstration of a super- conducting diode-with-memory, operational at zero mag- netic field with switchable nonreciprocity.Nat. Commun. 13, 3658 (2022)

  37. [37]

    Y., Cattaneo, R., Golod, T., and Kras- nov, V

    Grebenchuk, S. Y., Cattaneo, R., Golod, T., and Kras- nov, V. M., Nonlocal long-range synchronization of pla- nar Josephson-junction arrays,Phys. Rev. Appl.17, 064032 (2022)

  38. [38]

    C., Cho, E., Li, H., Cai, H., and Cybart, S

    LeFebvre, J. C., Cho, E., Li, H., Cai, H., and Cybart, S. A., Flux focused series arrays of long Josephson junctions for high-dynamic range magnetic field sensing,J. Appl. Phys.131, 163902 (2022)

  39. [39]

    Schmid, C., Jozani, A., Kleiner, R., Koelle, D., and Goldobin, E., YBa2Cu3O7 Josephson diode fabricated by focused-helium-ion-beam irradiation,Phys. Rev. Applied 24, 014041 (2025)

  40. [40]

    Direct observation of Josephson vor- tex cores.Nat

    Roditchev, D., et al. Direct observation of Josephson vor- tex cores.Nat. Phys.11, 332 (2015)

  41. [41]

    Y., et al., Observation of interacting Josephson vortex chains by magnetic force microscopy, Phys

    Grebenchuk, S. Y., et al., Observation of interacting Josephson vortex chains by magnetic force microscopy, Phys. Rev. Res.2, 023105 (2020)

  42. [42]

    A., Flaks, M., Zhou, T

    Chen, S., Park, S., Vool, U., Maksimovic, N., Broadway, D. A., Flaks, M., Zhou, T. X., Maletinsky, P., Stern, A., Halperin, B. I., and Yacoby, A., Current induced hidden states in Josephson junctions,Nature Commun.15, 8059 (2024)

  43. [43]

    Barone A., and Paterno, G., Physics and Applications of the Josephson Effect (John Wiley & Sons, New York 1982)

  44. [44]

    G., Dobrovitski, V

    Kogan, V. G., Dobrovitski, V. V., Clem, J. R., Mawatari, Y., and Mints, R. G., Josephson junction in a thin film, Phys. Rev. B63, 144501 (2001)

  45. [45]

    R., Josephson junctions in thin and narrow rect- angular superconducting strips.Phys

    Clem, J. R., Josephson junctions in thin and narrow rect- angular superconducting strips.Phys. Rev. B81, 144515 (2010)

  46. [46]

    A., Demagnetizing Factors of the General El- lipsoid,Phys

    Osborn, J. A., Demagnetizing Factors of the General El- lipsoid,Phys. Rev.67, 351-357 (1945)

  47. [47]

    M., Su- perresolution magnetic imaging by a Josephson junc- tion via holographic reconstruction ofI c(H) modulation, Phys

    Hovhannisyan, R., Golod, T., and Krasnov, V. M., Su- perresolution magnetic imaging by a Josephson junc- tion via holographic reconstruction ofI c(H) modulation, Phys. Rev. Appl.20, 064012 (2023)

  48. [48]

    N., Lisitskii, M

    Gubankov, V. N., Lisitskii, M. P., Serpuchenko, I. L., Sklokin, F. N. and Fistul’, M. V., Influence of trapped Abrikosov vortices on the critical current of the Joseph- son tunnel junction,Supercond. Sci. Technol.5, 168 (1992)

  49. [49]

    K., Thermal depinning of a single superconducting vortex in Nb,Phys

    Sok, J., and Finnemore, D. K., Thermal depinning of a single superconducting vortex in Nb,Phys. Rev. B50, 12770 (1994)

  50. [50]

    Weides, M., Kohlstedt, H., Waser, R., Kemmler, M., Pfeiffer, J., Koelle, D., Kleiner, R., and Goldobin, E., Ferromagnetic 0–πJosephson junctions,Appl. Phys. A 89, 613 (2007)

  51. [51]

    M., Numer- ical Modeling of Vortex-Based Superconducting Memory Cells: Dynamics and Geometrical Optimization.Nan- otechnology14, 1634 (2024)

    Skog, A., Hovhannisyan, R., and Krasnov, V. M., Numer- ical Modeling of Vortex-Based Superconducting Memory Cells: Dynamics and Geometrical Optimization.Nan- otechnology14, 1634 (2024)

  52. [52]

    E., Shiianov, K

    Cattaneo, R., Efimov, A. E., Shiianov, K. I., Kieler, O., and Krasnov, V. M., Cascade switching current detectors based on arrays of Josephson junctions,Nat. Commun. 16, 7927 (2025)

  53. [53]

    A., and Krasnov, V

    Borodianskyi E. A., and Krasnov, V. M., Josephson emission with frequency span 1-11 THz from small Bi2Sr2CaCu2O8+δ mesa structures,Nat. Commun.8, 1742 (2017)

  54. [54]

    Photon.18, 267-275 (2024)

    Miyamoto, M., Kobayashi, R., Kuwano, G., Tsujimoto, M., and Kakeya, I., Wide-band frequency modulation of a terahertz intrinsic Josephson junction emitter of a cuprate superconductor.Nat. Photon.18, 267-275 (2024)

  55. [55]

    O., and Omel’yanchuk, A

    Kulik I. O., and Omel’yanchuk, A. N., Properties of su- perconducting microbridges in the pure limit,Sov. J. Low Temp. Phys.3, 459 (1977). [Zh. Eksp. Teor. Fiz. 73, 1434 (1977)]

  56. [56]

    M., A distributed active patch antenna model of a Josephson oscillator.Beilstein J

    Krasnov, V. M., A distributed active patch antenna model of a Josephson oscillator.Beilstein J. Nanotech- nol.14, 151 (2023)

  57. [57]

    Miller, D., Rice, F., Stern, J

    Karpov, A. Miller, D., Rice, F., Stern, J. A., Bumble, B., Le Duc, H. D., and Zmuidzinas, J., Low Noise 1 THz–1.4 THz Mixers Using Nb/Al-AlN/NbTiN SIS Junctions. IEEE Trans. Appl. Supercond.17, 343 (2007)

  58. [58]

    Ando, Y., Sato, R., Tanaka, M., Takagi, K., Takagi N., and Fujimaki, A., Design and Demonstration of an 8- bit Bit-Serial RSFQ Microprocessor: CORE e4,IEEE Trans. Appl. Supercond.26, 1301205, (2016). 11

  59. [59]

    Electron.E93-C, 440-444 (2010)

    Yamanashi, Y., Kainuma, T., Yoshikawa, N., Kataeva, I., Akaike, H., Fujimaki, A., Tanaka, M., Takagi, N., Naga- sawa, S., and Hidaka, M., 100GHz demonstrations based on the single-flux-quantum cell library for the 10kA/cm2 Nb multi-layer process,IEICE Trans. Electron.E93-C, 440-444 (2010)

  60. [60]

    J., et al., ColdFlux Superconducting EDA and TCAD Tools Project: Overview and Progress,IEEE Trans

    Fourie, C. J., et al., ColdFlux Superconducting EDA and TCAD Tools Project: Overview and Progress,IEEE Trans. Appl. Supercond.29, 1300407 (2019)