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REVIEW 3 major objections 4 minor 43 references

Theory of reentrant superconductivity in Corbino Josephson junctions

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Reentrant superconductivity in non-circular Corbino Josephson junctions has a period set by the number of corners, and this period is halved on topological insulator surfaces.

desk verdict A clean analytic selection rule for conventional Corbino junctions, plus a topological period-halving prediction that is promising but numerically under-supported. read the letter →

arxiv 2601.14364 v1 pith:HGR7TZL7 submitted 2026-01-20 cond-mat.mes-hall cond-mat.supr-con

Omri Lesser , Joon Young Park , Yuval Ronen , Thomas Werkmeister , Philip Kim , Yuval Oreg This is my paper
classification cond-mat.mes-hallcond-mat.supr-con
keywords junctionstopologicaljosephsonperiodsuperconductivitycorbinocriticalcurrent
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

A Josephson junction is two superconductors separated by a thin normal region; current flows through it without resistance up to a maximum 'critical' current. If you bend such a junction into a closed ring, the magnetic field threading the ring can only take discrete values. In a circular ring, any nonzero flux kills superconductivity, because the current contributions from different angles cancel. This paper shows that if the ring is not circular—for instance, a square—superconductivity comes back at special flux values. The number of flux quanta needed is a multiple of the number of corners: four for a square, six for a hexagon. The reason is that the corners break the symmetry that caused the cancellation. The authors then consider the same ring built on the surface of a three-dimensional topological insulator, a material whose surface conducts electrons in a special way described by Majorana-like modes. Using a numerical model of those modes, they find that the special flux values are halved: a square ring now shows reentrant superconductivity for every even number of flux quanta, not just multiples of four. The effect requires an even number of corners, so triangles show no difference. This halving is a qualitative change, and the authors propose it as an experimental fingerprint of topological superconductivity. However, they note that other mechanisms could in principle produce the same halving, so the signature needs to be studied carefully together with a planned experiment.
Extended reading notes

Core claim

In non-circular Corbino Josephson junctions on a 3D topological insulator surface, the reentrant critical current has a period half that of conventional junctions when the number of corners is even. For a square (nc=4), the critical current is nonzero for all even nv rather than multiples of 4: 'the topological junction shows Ic ≠ 0 for all even nv where the non-topological junction only does so for multiples of four.' In general, 'in the topological case the condition is nv = (m/2) nc, i.e., the reentrance period is halved.'

Load-bearing premise

The result depends on the low-energy description of the 3DTI surface junction as two counter-propagating Majorana modes with coupling Δ cos(ϕ/2), Eq. (6), following Potter-Fu. This description is valid only in the narrow-junction limit 'where the width of the normal region W is shorter than the coherence length ξ' (after Eq. 6), and assumes the bulk gap is much larger than the pair potential so that bulk states do not mix in. If the junction is not narrow, or disorder/bulk states mix into the surface modes, the period halving could be washed out or altered. This is a structural assumption distinct from the central numerical claim.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies Corbino (annular) Josephson junctions formed by two superconductors separated by a normal region on the surface of a three-dimensional topological insulator (3DTI) or on a conventional metal. The authors first show analytically, using a single-harmonic phase model, that for a conventional non-circular junction reentrant superconductivity occurs only when the number of threaded flux quanta n_v is an integer multiple of the number of corners n_c [Eqs. (4)-(5)]. They then generalize to the topological case by modeling the 3DTI surface as two counter-propagating Majorana modes coupled by a phase-dependent term [Eq. (6)], regularized by a two-leg Majorana ladder [Eqs. (7)-(8)]. Using numerical diagonalization for a square geometry, they find that the topological junction has nonzero I_c for all even n_v, in contrast to the conventional case where only multiples of four contribute; this is described as a halving of the reentrance period. The Supplemental Material shows that such a period halving is consistent with a sin(2φ) contribution to the current-phase relation. The paper also mentions a Josephson diode effect when inversion symmetry is broken and discusses experimental implications.

Significance. If the period-halving prediction is correct, it would provide an experimentally accessible and geometry-specific signature of the helical Majorana surface modes in 3DTI-superconductor hybrid junctions. The conventional part of the paper is clean: the Fourier selection rule leading to n_v = m n_c is elegant and matches the exact-phase numerics. The paper is also honest in listing limitations. However, the central topological claim is currently supported by a single numerical realization without convergence tests or an independent analytic derivation; the SI consistency check does not prove that the sin(2φ) component exists. The significance is therefore conditional: the idea is attractive, but the evidence as presented is not yet at the level of a demonstrated 'theory'.

major comments (3)
  1. [Topological Corbino junctions] The central prediction of period halving rests on a single tight-binding realization with N=400 and the fixed parameters t0=1, t1=0.6, t2=0.3, Δ=0.2. No convergence in N, no sweep of Δ or t1−2t2, and no check of the cutoff dependence are provided. In the log-scale figures the half-order peaks (e.g., n_v=2 for n_c=4) appear at the 10^-3 (main text) or 5×10^-3 (SI) floor, so it is unclear whether the plotted values are resolved currents or clamped artifacts. Since the claim "the topological junction shows I_c ≠ 0 for all even n_v" is precisely the existence of these weak peaks, this numerical evidence is load-bearing. Please provide tabulated I_c values before the cutoff, N-convergence data (e.g., N=200, 400, 800, 1600), and parameter sweeps around the gapless point.
  2. [SI Sec. I] The period-halving explanation assumes a nonzero I_0^{(2)} in the current-phase relation and shows that a sin(2φ) term yields the observed selection rule. However, the paper does not derive from Hamiltonian (6) why a sin(2φ) component should be present; the only evidence for it is the same numerical diagonalization. This is a consistency check, not an independent derivation. Given the title and abstract promise a theory, the mechanism for half-periodicity remains unexplained. An analytic estimate or a perturbative argument showing that the Majorana coupling generates I_0^{(2)} would substantially strengthen the claim.
  3. [After Eq. (6), Outlook] The low-energy Hamiltonian (6) is stated to be valid in the narrow-junction limit W < ξ, but no estimate of W/ξ for the simulated geometry is given, and the ladder parameters are not mapped to continuum quantities. The redundant Majorana modes and the mixed periodic/anti-periodic boundary conditions are a specific regularization choice; the circular topological result (zero I_c for all n_v > 0) is a nontrivial consequence of this model and is not checked against a continuum solution. These omissions do not disprove the claim, but they increase the risk that the small half-order signals are lattice or boundary artifacts rather than a robust topological effect.
minor comments (4)
  1. [SI Fig. S1] The caption lists n = 1, 2, 5, 20, but the panels are labeled n = 1, 2, 10, 40. Please correct the mismatch.
  2. [After Eq. (5)] The sentence contains a typo: "where and J_m is the mth Bessel function" should read "where J_m is the mth Bessel function."
  3. [Fig. 2, SI Fig. S3] The main text states a 10^-3 cutoff while the SI uses 5×10^-3. Clarify whether the plotted points at the floor are actual data or clamped; if clamped, state so explicitly and give the unresolved values in a table.
  4. [Topological Corbino junctions] The Josephson diode effect is asserted without any numerical or analytical demonstration. If this result is part of the paper's claims, please include at least one illustrative calculation or figure; otherwise, move it to the outlook discussion.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; central results are forward simulations from explicit models, with only minor non-load-bearing self-citations.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The conventional reentrance condition nv = m nc follows from evaluating the explicit integral in Eq. (5) for the single-harmony phase model Eq. (4); the constant a is a perturbation amplitude, not a fitted parameter, and the exact numerical evaluation of Eq. (3) with Eq. (2) independently confirms the same condition. The topological period halving is obtained by numerically diagonalizing the explicitly written tight-binding Hamiltonian in Eqs. (7)-(8), with fixed parameters (N=400, t0=1, t1=0.6, t2=0.3, Δ=0.2); no parameter is adjusted to reproduce the halved period. The Supplemental Material's demonstration that a sin(2ϕ) current-phase-relation term would produce period halving is an ex post consistency check, not an input to the simulation; the paper states it 'suggest[s]' such a term, rather than using it to derive the numerical result. The ladder model is attributed to Grover–Sheng–Vishwanath [33] and to Li–Ebisu–Sahoo–Oreg–Franz [34], the latter co-authored by one of the present authors, and Ref. [37] is a self-authored upcoming experiment invoked as 'consistent.' Neither self-citation is load-bearing: the ladder Hamiltonian is fully reproduced in Eq. (7), and the experimental citation is not used to justify the theoretical claim. The acknowledged limitations (narrow-junction validity, bulk-gap hierarchy, alternative mechanisms for period halving) are correctness and assumption risks, not circularity. We therefore find no step in which a prediction is equivalent by construction to its input.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

The central claims rest on standard Fourier analysis and on domain assumptions about Corbino JJs (fluxoid quantization, sinusoidal current-phase relation) and about 3DTI surface junctions (1D Majorana description, narrow-junction limit, decoupled bulk). No new entities are introduced. The free parameters are model knobs (lattice sizes, hoppings, pair potential, corner sharpness) that are not fitted to data; their values are chosen to realize the desired gapless point and are not swept to demonstrate robustness.

free parameters (7)
  • a = not specified (|a| < nv/nc)
    Amplitude of corner perturbation in single-harmony model Eq (4). The selection rule nv = m nc is independent of the value of a, so this is a model knob, not fitted to data.
  • n (corner sharpness) = 10
    Polar shape parameter in Eq (2); used to model square in numerics. Larger n is more square; result depends only on nc=4, not n.
  • N (sites per chain) = 400
    Lattice size for tight-binding diagonalization; no convergence study provided, so quantitative results may depend on N.
  • t0 = 1
    Intra-chain hopping in ladder model; energy scale, arbitrary.
  • t1 = 0.6
    Inter-chain hopping chosen such that t1 = 2 t2 = 0.6, placing the ladder at the gapless point with two chiral Majorana modes.
  • t2 = 0.3
    Inter-chain hopping; with t1=2t2 gives the gapless GSV point.
  • Delta = 0.2
    SC pair potential in the ladder model; chosen in units of t0; no experimental mapping given.
assumptions (8)
  • standard math Jacobi-Anger expansion and Fourier orthogonality
    Used in Eq (5) to derive the selection rule for the critical current.
  • domain assumption Conventional current-phase relation I ∝ sin(ϕ) for metallic junctions
    Used in Eq (3) to compute critical current in the conventional case.
  • domain assumption Fluxoid quantization restricts Φ/Φ0 to integers
    Main text after Eq (1); fundamental for the Corbino geometry.
  • domain assumption Magnetic field only penetrates the normal region; phase of inner SC constant
    Before Eq (2); needed for the phase-gradient formula.
  • domain assumption 3DTI surface junction described by two counter-propagating Majorana modes with coupling Δ cos(ϕ/2)
    Eq (6), following Potter-Fu (Ref [10]); central to the topological model.
  • domain assumption Narrow junction limit W < ξ
    After Eq (6); needed for the 1D description along θ.
  • domain assumption Bulk gap much larger than Δ, surface states decoupled from bulk
    Outlook; stated limitation of the model.
  • domain assumption GSV ladder faithfully represents the continuum Majorana model; spurious modes removed by |E|<5Δ cutoff
    Main text after Eq (8); the cutoff procedure is an ad hoc step in the numerics.

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Pith. "Pith review of Theory of reentrant superconductivity in Corbino Josephson junctions." pith.science (2026). https://pith.science/paper/HGR7TZL7

@misc{pith2026260114364,
  author       = {Pith},
  title        = {Pith review of: Theory of reentrant superconductivity in Corbino Josephson junctions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HGR7TZL7}},
  note         = {Machine review of arXiv:2601.14364}
}
read the original abstract

Josephson junctions made of conventional superconductors display Fraunhofer-like oscillations of the critical current as a function of the threaded magnetic flux. When the superconductors are deposited on the surface of a three-dimensional topological insulator, this pattern is slightly modified due to the presence of chiral Majorana modes. Here we calculate the critical current of a Corbino Josephson junction, where the fluxoid becomes quantized and the superconducting phase has an integer winding. We discover that circular junctions exhibit similar behavior in both topologically trivial and non-trivial scenarios, while non-circular junctions demonstrate a remarkable distinction. Using a simple analytical model, we show that these non-circular junctions exhibit reentrant superconductivity with a period related to their number of corners, and numerically we find that this period is halved in the topological case. The period halving may help establish the existence of topological superconductivity in hybrid topological insulator-superconductor junctions.

Figures

Figures reproduced from arXiv: 2601.14364 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Illustration of a Corbino Josephson junction. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Critical current as a function of the number of vortices [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Majorana ladder corresponding to the variant [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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