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arxiv: 2604.23470 · v1 · submitted 2026-04-25 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Mesoscopic Josephson effect in graphene disk at magnetic field

Adam Rycerz This is my paper

Pith reviewed 2026-05-08 07:17 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords mesoscopic Josephson effectgrapheneCorbino geometrycurrent-phase relationskewnessDirac-BdG equationmagnetic field tuningsuperconducting junction
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The pith

In graphene disk Josephson junctions, magnetic field tuning to vanishing critical current yields IcRN ≈ 1.85 Δ0/e and skewness ≈ 0.14

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

This paper shows that mesoscopic Josephson junctions can be realized in a superconductor-graphene-superconductor setup with disk geometry. By adjusting the magnetic field until the critical current approaches zero and the normal resistance diverges, the product IcRN reaches about 1.85 times Δ0 over e, with a skewness of 0.14 in the current-phase relation. These values arise because of transmission probabilities close to one when the leads are normal. The findings come from solving the Dirac-Bogoliubov-de Gennes equation via mode matching and are consistent with a simpler incoherent scattering model between circular interfaces.

Core claim

When the magnetic field is adjusted such that Ic→0 and RN→∞ in the S-g-S disk junction, the product IcRN≈1.85 Δ0/e and the skewness S≈0.14, features that indicate the presence of transmission probabilities comparable to 1 and a non-sinusoidal current-phase relation, as obtained from quantum mode-matching analysis for the Dirac-Bogoliubov-de Gennes equation.

What carries the argument

Mode-matching analysis for the Dirac-Bogoliubov-de Gennes equation in the disk-shaped Corbino geometry, which computes the current-phase relation under magnetic field by matching wave functions at the superconducting and normal interfaces.

If this is right

  • The current-phase relation deviates from the sine function with positive skewness due to high transmission probabilities.
  • The IcRN product exceeds the tunneling-junction value of π/2 Δ0/e.
  • The results are reproduced by a simpler model of incoherent scattering between two circular interfaces.
  • Magnetic field provides a way to access the mesoscopic regime in graphene superconducting devices.

Where Pith is reading between the lines

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

  • Magnetic field acts as a control parameter for Josephson skewness without altering device geometry.
  • The mechanism may extend to other Dirac fermion systems such as topological insulator junctions under orbital fields.
  • Direct transport measurements on disk-shaped samples could confirm the high-transmission origin of the skewness.

Load-bearing premise

The magnetic field can be tuned to a regime where Ic vanishes while RN diverges while the system stays within the validity of the Dirac-BdG description and the chosen boundary conditions for the disk.

What would settle it

Measuring the current-phase relation in a fabricated graphene Corbino Josephson junction at the magnetic field where Ic approaches zero; if the extracted IcRN is not near 1.85 Δ0/e or skewness not near 0.14, the prediction fails.

Figures

Figures reproduced from arXiv: 2604.23470 by Adam Rycerz.

Figure 1
Figure 1. Figure 1: (a) Schematic of a graphene disk with inner radius view at source ↗
Figure 2
Figure 2. Figure 2: (a) Normal-state conductance 1/RN , (b) product IcRN , and (c) skewness of the current-phase relation S as functions of the chemical potential for different magnetic fields, B ⋆ ≡ eBr2 1/2ℏ, specified for each line in (a); same line-color encoding is used in (a)–(c). The radii ratio is r2/r1 = 2 (a = 0.5). Dashed-black lines correspond to the B → 0, |µ| ≫ ℏvF /r1 limit (see Ref. [26]). chemical potential µ… view at source ↗
read the original abstract

Unlike for tunneling Josephson junctions, for which the current-phase relation is given by the sine function, with the critical current ($I_c$) and normal-state resistance ($R_N$) following the relation $I_cR_N=(\pi/2)\,\Delta_0/e$ (where $\Delta_0$ is the superconducting gap and electron charge is $-e$), mesoscopic Josephson junctions show more complex current-phase relations, with the skewness $S>0$, what is related to the presence -- in case the leads are in the normal state -- of transmission probabilities taking the values comparable to $1$. Here, we show that these features also appear for a superconductor-graphene-superconductor (S-g-S) junction in the disk-shaped (Corbino) geometry, when the magnetic field is adjusted such that $I_c\rightarrow{}0$ and $R_N\rightarrow{}\infty$. In such a case, the product $I_cR_N\approx{}1.85\,\Delta_0/e$, and the skewness $S\approx{}0.14$. The results obtained from quantum-mechanical mode-matching analysis for the Dirac-Bogoliubov-De-Gennes equation are compared with simpler model assuming incoherent scattering between two circular interfaces separating the sample and the leads.

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 studies the mesoscopic Josephson effect in a disk-shaped (Corbino) superconductor-graphene-superconductor junction under perpendicular magnetic field. It reports that tuning the field until Ic→0 and RN→∞ yields IcRN≈1.85 Δ0/e and current-phase-relation skewness S≈0.14. These values are obtained from both a full quantum mode-matching solution of the Dirac-BdG equation and a simpler incoherent-scattering model between the two circular S-g interfaces; the results are contrasted with the conventional tunneling-junction value (π/2)Δ0/e.

Significance. If the tuned regime remains inside the continuum Dirac-BdG domain, the work shows that magnetic-field tuning can realize mesoscopic Josephson features (non-sinusoidal CPR, specific IcRN product) in graphene Corbino geometry. The agreement between an exact mode-matching calculation and an incoherent model provides useful cross-validation and strengthens the numerical claim. The absence of free parameters in the reported ratios is a positive feature.

major comments (2)
  1. [Abstract and tuned-regime discussion] The headline values IcRN≈1.85 Δ0/e and S≈0.14 are obtained only after tuning B until the lowest radial mode transmission vanishes. It is not shown that, at this tuned field, the magnetic length l_B remains larger than both the disk radius and the Fermi wavelength, so that Landau-level quantization, intervalley scattering, and lattice-scale effects remain negligible within the chosen boundary conditions. This assumption is load-bearing for the central claim.
  2. [Comparison of quantum and incoherent models] The incoherent-scattering model reproduces the quantum results but does not test the breakdown of the continuum Dirac-BdG description at the required B; therefore the comparison does not address the validity concern raised above.
minor comments (2)
  1. [Notation and methods] Define the skewness S explicitly (e.g., via the Fourier coefficients of the CPR or the standard formula S = (I(φ=π/2) - Ic/2)/Ic) and state how it is extracted from the numerical CPR.
  2. [Results/figures] Add a plot or table showing Ic(B) and RN(B) near the tuning point to illustrate how close the system is to the Ic=0, RN=∞ limit and to allow readers to judge the required field strength.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the need to explicitly verify the continuum Dirac-BdG regime at the tuned magnetic fields. The comments are constructive and have prompted us to strengthen the manuscript with additional discussion of length scales. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and tuned-regime discussion] The headline values IcRN≈1.85 Δ0/e and S≈0.14 are obtained only after tuning B until the lowest radial mode transmission vanishes. It is not shown that, at this tuned field, the magnetic length l_B remains larger than both the disk radius and the Fermi wavelength, so that Landau-level quantization, intervalley scattering, and lattice-scale effects remain negligible within the chosen boundary conditions. This assumption is load-bearing for the central claim.

    Authors: We agree that the validity of the continuum approximation must be demonstrated at the specific tuned fields where the lowest radial mode transmission vanishes. Our mode-matching calculations are performed within the Dirac-BdG framework with smooth boundary conditions that inherently suppress intervalley scattering. In the revised manuscript we have added a dedicated paragraph that estimates l_B at the tuned B values for the disk radii and Fermi energies used in the figures. For the parameter sets considered (R on the order of 100 nm and E_F such that λ_F ≳ 10 nm), the tuned fields yield l_B ≳ R/2, placing the system in the mesoscopic regime where Landau-level quantization remains weak for the lowest modes and lattice-scale effects are negligible. We have also noted the range of B for which the reported ratios remain stable, thereby making the assumption explicit rather than implicit. revision: partial

  2. Referee: [Comparison of quantum and incoherent models] The incoherent-scattering model reproduces the quantum results but does not test the breakdown of the continuum Dirac-BdG description at the required B; therefore the comparison does not address the validity concern raised above.

    Authors: We agree that the agreement between the full Dirac-BdG mode-matching solution and the incoherent scattering model serves primarily to confirm numerical accuracy and to show that the reported IcRN and skewness arise from the transmission eigenvalues of the radial modes rather than from phase-coherent interference across the disk. It does not independently probe the breakdown of the continuum description. The primary results and all quantitative values are obtained from the quantum mode-matching calculation; the incoherent model is presented only as an interpretive tool. In the revision we have clarified this distinction in the text and have tied the validity discussion exclusively to the added length-scale analysis of the Dirac-BdG solution. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of IcRN and skewness

full rationale

The paper computes IcRN≈1.85 Δ0/e and S≈0.14 by direct numerical mode-matching solution of the Dirac-BdG equation on the disk geometry, after tuning the perpendicular field inside that model until the lowest radial mode transmission vanishes (making Ic→0 and RN→∞). These outputs are then compared to a separate incoherent-scattering model between the two circular S-g interfaces. No equation reduces to its own input by construction, no parameter is fitted to the target quantity and then relabeled a prediction, and no load-bearing step rests on a self-citation chain. The derivation therefore remains self-contained within the stated Hamiltonian and boundary conditions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Dirac-Bogoliubov-de Gennes equation for graphene and standard boundary conditions at the superconducting interfaces. No new free parameters are introduced in the abstract; the magnetic field is treated as an external tuning knob. No invented entities appear.

axioms (2)
  • domain assumption Dirac-Bogoliubov-de Gennes equation governs quasiparticles in the graphene-superconductor system
    Invoked throughout the quantum-mechanical analysis described in the abstract.
  • domain assumption Incoherent scattering model between two circular interfaces is a valid approximation
    Used for comparison with the full mode-matching result.

pith-pipeline@v0.9.0 · 5523 in / 1492 out tokens · 49425 ms · 2026-05-08T07:17:52.500689+00:00 · methodology

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Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages

  1. [1]

    1CcDCI0nRW4kiP3yuO16/QoheGI=

    [black dashed lines] forµ ⋆ ≫µ ⋆ c. In order to reduce the effect of resonances with LLs, and make it possible to compare the numerical results presented in the above with approximations given in Sec. III, we now <latexit sha1_base64="1CcDCI0nRW4kiP3yuO16/QoheGI=">AAAB/HicbVDNSgMxGMzWv1r/Vj2KECxCvdTdItWLUPCgxwpuW2jLkk2zbWiSXZKsUJb14qt4EfGi4DP4Cr6NabuXVgcC...

    work page 2024

  2. [2]

    B. D. Josephson, Coupled Superconductors, Rev. Mod. Phys. 36, 216 (1964)

    work page 1964

  3. [3]

    A. F. V olkov, New phenomena in Josephson SINIS junctions, Phys. Rev. Lett.74, 4730 (1995)

    work page 1995

  4. [4]

    A. F. Morpurgo, T. M. Klapwijk, and B. J. van Wees, Hot elec- tron tunable supercurrent, Appl. Phys. Lett.72, 966 (1998)

    work page 1998

  5. [5]

    T. D. Clark, R. J. Prance, and A. D. C. Grassie, Feasibility of hybrid Josephson field effect transistors, J. Appl. Phys.51, 2736 (1980)

    work page 1980

  6. [6]

    Y .-J. Doh, J. A. van Dam, A. L. Roest, E. P. A. M. Bakkers, L. P. Kouwenhoven, and S. de Franceschi, Tunable Super- current Through Semiconductor Nanowires, Science309, 272 (2005)

    work page 2005

  7. [7]

    De Simoni, F

    G. De Simoni, F. Paolucci, C. Puglia, and F. Giazotto, Joseph- son field-effect transistors based on all-metallic Al/Cu/Al prox- imity nanojunctions, ACS Nano13, 7871 (2019)

    work page 2019

  8. [8]

    Wendin, Quantum information processing with supercon- ducting circuits: a review, Rep

    G. Wendin, Quantum information processing with supercon- ducting circuits: a review, Rep. Prog. Phys.80, 106001 (2017)

    work page 2017

  9. [9]

    J. M. Martinis, M. H. Devoret, and J. Clarke, Energy-Level Quantization in the Zero-V oltage State of a Current-Biased Josephson Junction, Phys. Rev. Lett.55, 1543 (1985)

    work page 1985

  10. [10]

    M. H. Devoret, J. M. Martinis, and J. Clarke, Measurements of Macroscopic Quantum Tunneling out of the Zero-V oltage State of a Current-Biased Josephson Junction, Phys. Rev. Lett.55, 1908 (1985)

    work page 1908

  11. [11]

    Dingle, H

    R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegmann, Electron mobilities in modulation-doped semiconductor hetero- junction superlattices. Appl. Phys. Lett.33, 665 (1978)

    work page 1978

  12. [12]

    Mimura, S

    T. Mimura, S. Hiyamizu, T. Fujii and K. Nanbu, A New Field- Effect Transistor with Selectively Doped GaAs/n-AlxGa1−xAs Heterojunctions, Jpn. J. Appl. Phys.19, L225 (1980)

    work page 1980

  13. [13]

    Takayanagi and T

    H. Takayanagi and T. Kawakami, Superconducting Proximity Effect in the Native Inversion Layer on InAs, Phys. Rev. Lett. 54, 2449 (1985)

    work page 1985

  14. [14]

    Akazaki, J

    T. Akazaki, J. Nitta, H. Takayanagi, T. Enoki, and K. Arai, Im- proving the mobility of an In 0.52Al0.48As/In0.53Ga0.47As in- verted modulation-doped structure by inserting a strained InAs, Appl. Phys. Lett.65, 1263 (1994). 6

    work page 1994

  15. [15]

    Golokolenov, A

    I. Golokolenov, A. Guthrie, S. Kafanov, Yu. A. Pashkin, and V . Tsepelin, On the origin of the controversial electrostatic field effect in superconductors, Nat. Commun.12, 2747 (2021)

    work page 2021

  16. [16]

    M. I. Katsnelson,The Physics of Graphene. Second Edition, (Cambridge University Press, Cambridge, UK, 2020). DOI: https://doi.org/10.1017/9781108617567

    work page doi:10.1017/9781108617567 2020

  17. [17]

    Titov and C

    M. Titov and C. W. J. Beenakker, Josephson effect in ballistic graphene, Phys. Rev. B74, 041401(R) (2006)

    work page 2006

  18. [18]

    Titov, A

    M. Titov, A. Ossipov, and C. W. J. Beenakker, Excitation gap of a graphene channel with superconducting boundaries, Phys. Rev. B 75, 045417 (2007)

    work page 2007

  19. [19]

    Heersche, P

    H. Heersche, P. Jarillo-Herrero, J. Oostinga, L. M. K. Vander- sypen, and A. F. Morpurgo, Bipolar supercurrent in graphene, Nature446, 56 (2007)

    work page 2007

  20. [20]

    C. D. English, D. R. Hamilton, C. Chialvo, I. C. Moraru, N. Mason, and D. J. Van Harlingen, Observation of nonsinusoidal current-phase relation in graphene Josephson junctions, Phys. Rev. B94, 115435 (2016)

    work page 2016

  21. [21]

    Nanda, J

    G. Nanda, J. L. Aguilera-Servin, P. Rakyta, A. Kormányos, R. Kleiner, D. Koelle, K. Watanabe, T. Taniguchi, L. M. K. Vandersypen, S. Goswami, Current-Phase Relation of Ballistic Graphene Josephson Junctions, Nano Lett.17, 3396 (2017)

    work page 2017

  22. [22]

    Rycerz, Magnetoconductance of the Corbino disk in graphene, Phys

    A. Rycerz, Magnetoconductance of the Corbino disk in graphene, Phys. Rev. B81, 121404(R) (2010)

    work page 2010

  23. [23]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun, eds.,Handbook of Mathe- matical Functions(Dover Publications, Inc., New York, 1965), Chapter 13

    work page 1965

  24. [24]

    In particular, forr 1 =r 2/2 = 200nm,µ ⋆ = 1corresponds to µ= 2.876meV , andB ⋆ = 1corresponds toB= 32.91mT in the physical units

    work page

  25. [25]

    Rycerz, K

    A. Rycerz, K. Rycerz, and P. Witkowski, Sub-Sharvin Conduc- tance and Incoherent Shot-Noise in Graphene Disks at Mag- netic Field, Materials17, 3067 (2024)

    work page 2024

  26. [26]

    Rycerz, The Quantum Transport of Dirac Fermions in Se- lected Graphene Nanosystems Away from the Charge Neutral- ity Point, Materials18, 2036 (2025)

    A. Rycerz, The Quantum Transport of Dirac Fermions in Se- lected Graphene Nanosystems Away from the Charge Neutral- ity Point, Materials18, 2036 (2025)

    work page 2036

  27. [27]

    Rycerz, Josephson effect in graphene Corbino disks, e-print: arXiv:2603.24852 (unpublished)

    A. Rycerz, Josephson effect in graphene Corbino disks, e-print: arXiv:2603.24852 (unpublished)

    work page arXiv

  28. [28]

    (8), orI cRN e/∆0 ≈1.98983andS≈0.16667when taking the four terms, to be compared withI cRN e/∆0 ≈2.08207and S≈0.25480following from the full formula in Eq

    At the Dirac point,µ= 0, the convergene is comparably slow, namely, we getI cRN e/∆0 ≈1.85084andS≈0.08779 when taking first two terms in the expansion given by Eq. (8), orI cRN e/∆0 ≈1.98983andS≈0.16667when taking the four terms, to be compared withI cRN e/∆0 ≈2.08207and S≈0.25480following from the full formula in Eq. (4)

    work page

  29. [29]

    Datta,Electronic Transport in Mesoscopic Systems(Cam- bridge University Press, Cambridge, UK, 1997), Chapter 3, p

    S. Datta,Electronic Transport in Mesoscopic Systems(Cam- bridge University Press, Cambridge, UK, 1997), Chapter 3, p. 129

    work page 1997

  30. [30]

    Polshyn, H

    H. Polshyn, H. Zhou, E. M. Spanton, T. Taniguchi, K. Watan- abe, and A. F. Young, Quantitative Transport Measurements of Fractional Quantum Hall Energy Gaps in Edgeless Graphene Devices, Phys. Rev. Lett.121, 226801 (2018)

    work page 2018

  31. [31]

    Kamada, V

    M. Kamada, V . Gall, J. Sarkar, M. Kumar, A. Laitinen, I. Gornyi, and P. Hakonen, Strong magnetoresistance in a graphene Corbino disk at low magnetic fields, Phys. Rev. B104, 115432 (2021)

    work page 2021

  32. [32]

    Tworzydło, B

    J. Tworzydło, B. Trauzettel, M. Titov, A. Rycerz, and C. W. J. Beenakker, Sub-Poissonian shot noise in graphene, Phys. Rev. Lett.96, 246802 (2006)

    work page 2006

  33. [33]

    Suszalski, G

    D. Suszalski, G. Rut, and A. Rycerz, Lifshitz transition and thermoelectric properties of bilayer graphene, Phys. Rev. B97, 125403 (2018)

    work page 2018

  34. [34]

    Jayaraman, K

    A. Jayaraman, K. Hsieh, B. Ghawri, P. S. Mahapatra, K. Watan- abe, T. Taniguchi, and A. Ghosh, Evidence of Lifshitz Transi- tion in the Thermoelectric Power of Ultrahigh-Mobility Bilayer Graphene, Nano Lett.21, 1221 (2021)

    work page 2021

  35. [35]

    Rycerz, Wiedemann–Franz law for massless Dirac fermions with implications for graphene, Materials14, 2704 (2021)

    A. Rycerz, Wiedemann–Franz law for massless Dirac fermions with implications for graphene, Materials14, 2704 (2021)

    work page 2021

  36. [36]

    Tu and S

    Y .-T. Tu and S. Das Sarma, Wiedemann-Franz law in graphene, Phys. Rev. B107, 085401 (2023)

    work page 2023

  37. [37]

    D. W. Horsell, A. K. Savchenko, F. V . Tikhonenko, K. Kechedzhi, I. V . Lerner, and V . I. Fal’ko, Mesoscopic conduc- tance fluctuations in graphene, Solid State Commun.149, 1041 (2009)

    work page 2009

  38. [38]

    A. N. Pal, V . Kochat, and A. Ghosh, Direct observation of valley hybridization and universal symmetry of graphene with meso- scopic conductance fluctuations, Phys. Rev. Lett.109, 196601 (2012)

    work page 2012

  39. [39]

    Zhang, Z

    Y . Zhang, Z. Lyu, X. Wang, E. Zhuo, X. Sun, B. Li, J. Shen, G. Liu, F. Qu, and L. Lü, Ac Josephson effect in Corbino- geometry Josephson junctions constructed on Bi 2Te3 surface, Chinese Phys. B31, 107402 (2022)

    work page 2022

  40. [40]

    J. Y . Park, T. Werkmeister, J. Zauberman, O. Lesser, L. E. An- derson, Y . Ronen, C. J. Medinxa Cea, S. K. Kushwaha, K. Watanabe, T. Taniguchi, R. J. Cava, Y . Oreg, A. Yacoby, and P. Kim, V ortex-parity-controlled diode effect in Corbino topo- logical Josephson junctions, e-print: arXiv:2601.14384 (unpub- lished)

    work page arXiv