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REVIEW 5 major objections 3 minor 60 references

Two-Dimensional Materials-Based Josephson Junctions

T0 review · 5 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper proposes a gate-tunable two-state switch built from a monolayer MoS2 Josephson junction, with a sinusoidal supercurrent in one state and zero supercurrent in the other.

desk verdict A TB-NEGF exercise that recycles known MoS2 topological and Andreev results into a two-state switch, but the central numerics are not there: the 'sinusoidal' current is flat to 1e-7 and the 'closed state' is inferred from a phase-independent DOS rather than computed from a current-phase relation. read the letter →

arxiv 2506.23737 v1 pith:MZVS3IZS submitted 2025-06-30 cond-mat.supr-con

Hamidreza Simchi This is my paper · ORCID
classification cond-mat.supr-con PACS 74.45.+c05.60.Gg74.50.+r74.47.Tf74.20.Rp
keywords JosephsonjunctionMoS2monolayertopologicalsuperconductorMajoranazeromodesAndreevboundstatesnon-equilibriumGreenfunctionChernnumbertwo-stateswitch
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

This paper argues that a monolayer MoS2 Josephson junction can serve as a two-state switch whose state is controlled by the chemical potential and by whether the superconducting leads are ordinary or topological. With ordinary leads and $\mu \ge 0.8$ eV, the model produces a sinusoidal Josephson current carried by Andreev bound states. With topological leads and $|\mu|$ much smaller than the pairing potential, no Andreev bound states form, the total current is zero, and Majorana zero modes with Chern number two appear in the leads. The paper takes this as evidence that a two-dimensional-material Josephson device could be a useful building block for topological quantum computers.

What carries the argument

The load-bearing machinery is a tight-binding Bogoliubov-de Gennes Hamiltonian on the Mo sublattice of monolayer MoS2, solved with non-equilibrium Green function self-energies for semi-infinite leads. The Josephson current is the energy integral of the trace of the current operator with $\tau_z$, and Andreev bound states are identified as real singularities of the total density of states $\mathrm{DOS}(E) = \frac{1}{2\pi}\mathrm{tr}\, i(G^r - G^a)$. Two reductions carry the argument: the lead-to-flake hopping enters through $\beta$ matrices multiplied by $10^{-3}$, and for topological leads the wave vector is fixed to $k = 0$ ($\mu = 0$) or $k = 0.025$ ($\mu = 0.015$ eV), the gap-closing points of the isolated lead; a phase-independent DOS in the window $-\Delta_0 \times 10^{-3} \le E \le \Delta_0 \times 10^{-3}$ is then read as the absence of Andreev levels and hence zero supercurrent.

What would settle it

Compute the full two-dimensional NEGF Josephson current for topological leads without fixing $k$ to $0$ or $0.025$ and without the $10^{-3}$ barrier factor: a non-zero or phase-dependent supercurrent, or phase-dependent DOS peaks, would falsify the zero-current claim. An experiment measuring a supercurrent at $\mu$ below $0.8$ eV in a MoS2 junction with topological leads would likewise contradict the closed-state prediction.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes a single model that produces both branches of a two-state switch. With ordinary s-wave superconducting leads and $\mu \ge 0.8$ eV, Andreev bound states form and the total Josephson current follows $I_0 \sin(\Delta \varphi)$, the standard sinusoidal current-phase relation in the anti-crossing regime. With topological superconducting leads and small or zero chemical potential, the Andreev bound states do not form, the total Josephson current is zero, and the leads instead host Majorana zero modes described by Chern number two. The conclusion is that an MoS2-based Josephson junction can switch between a conducting open state and a non-conducting closed state by adjusting the chemical potential, and that trivial Andreev states cannot mimic the Majorana zero-bias signature in this setup.

Load-bearing premise

The central assumption is that a one-dimensional effective chain, with the lead wave vector frozen at its gap-closing value and the lead-flake coupling weakened by an ad hoc factor of $10^{-3}$, represents the full two-dimensional junction well enough to conclude that a phase-independent density of states means zero Josephson current.

Editorial extensions

If this is right

  • Below the switching threshold, the junction current vanishes in the topological-lead configuration, so the same device can be open or closed by adjusting the chemical potential.
  • With ordinary leads and $\mu \ge 0.8$ eV, the supercurrent is sinusoidal in the phase difference, a direct signature of Andreev bound states.
  • The topological leads support Majorana zero modes with Chern number two when the chemical potential is near zero, giving a concrete platform for studying non-Abelian physics.
  • Because Andreev bound states are absent in the topological-lead branch, a zero-bias conductance peak in this system would not be a trivial Andreev mimic.
  • The proposed switch suggests that two-dimensional-material Josephson junctions could be placed on a research roadmap for topological quantum computing hardware.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The authors do not address whether a full two-dimensional transverse-mode sum would keep the zero-current result; if the frozen-$k$ reduction is responsible for the flat DOS, the closed state may be weaker in wider or multi-mode junctions.
  • The $0.8$ eV threshold is a MoS2-specific number tied to its band gap and spin-orbit parameters; in other two-dimensional semiconductors the switching threshold would shift, so the switch concept rather than the specific voltage is the transferable claim.
  • Because the same $10^{-3}$ barrier attenuation is used for both lead types, part of the zero-current result could reflect numerical suppression rather than topology alone; varying the barrier factor would separate the two effects.
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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

5 major / 3 minor

Summary. The manuscript presents a tight-binding non-equilibrium Green function (TB-NEGF) study of a monolayer MoS2-based Josephson junction with semi-infinite ordinary and topological superconducting leads. It claims that with ordinary leads and chemical potential above 0.8 eV, Andreev bound states produce a sinusoidal Josephson current and a Gaussian density of states, while with topological leads and |µ| much smaller than the pairing potential no Andreev bound states form and the Josephson current vanishes, so the junction can serve as a two-state switch. The paper further claims that the topological leads host Majorana zero modes with Chern number two.

Significance. If established, a material-specific, gate-tunable Josephson switch would be valuable for proposed topological quantum computing architectures. The paper makes a useful attempt to connect the known topological superconducting phase of MoS2 (Ref. [34]) to a concrete device model, and it provides explicit tight-binding Hamiltonians and NEGF formulas. However, the numerical evidence does not support the central claims: the purported sinusoidal current and Gaussian DOS are flat to numerical precision, and the zero-current state for topological leads is inferred from a phase-flat total DOS rather than computed from a current-phase relation. The significance of the proposed switch is therefore not established by the present manuscript.

major comments (5)
  1. [Sec. VI.D.A, Fig. 7] Fig. 7(a) does not show a sinusoidal Josephson current: the plotted total current varies only between about -0.51335934 and -0.51335925 (a relative variation of roughly 10^-7) around a constant offset, which is numerically indistinguishable from a flat line. Likewise, Fig. 7(b) shows a DOS constant to about 10^-12 around 7191.7618, with no Gaussian peak structure. These figures therefore do not demonstrate the formation of Andreev bound states or an I0 sin(Δφ) current, so the open-state branch of the proposed switch is not supported by the data shown.
  2. [Sec. VI.D.B and Eq. (33)] The conclusion that I_t = 0 for topological leads is inferred solely from the phase independence of the total DOS in Fig. 8 together with Eq. (33). This inference is invalid: the Josephson current is not a direct function of the total DOS; it is the phase derivative of the free energy (see Eq. (27) and Appendix A), and continuum states as well as occupied quasiparticle and Andreev levels can contribute even when the integrated DOS is phase-flat. Moreover, the topological-lead calculation fixes k = 0 or 0.025 and multiplies the lead-to-flake self-energy by the ad hoc 10^-3 factor in Eqs. (29)-(32), reducing the two-dimensional junction to a single-momentum, effectively one-dimensional model that cannot capture transverse edge modes and cannot address the expected 4π-periodic topological supercurrent.
  3. [Appendix A and Sec. VI.D.B] The absence of Andreev bound states for the topological leads is guaranteed by the parameter choice rather than by the physics of topological pairing. Appendix A states that ABS are observed only under t ≫ µ ≫ Δ0, while Sec. VI.D.B chooses µ = 0 or 0.015 eV with Δ0 = 0.01 eV, i.e., |µ| ≪ Δ0, which is the same regime used by Ref. [34] to define the topological phase. The reported absence of ABS is therefore a consequence of the adopted parameter regime, not a computed property of the topological junction, and the conclusion that the junction is closed is circular with respect to the ABS observation condition.
  4. [Sec. V and Abstract] The 0.8 eV switching threshold is not derived from the junction calculation. It is imported from the Andreev-conductance result of Ref. [44] (for µS = -1.5 eV and |µN| < 0.8 eV) through the statement in Sec. V that a zero Andreev conductance is 'expected' to imply zero Josephson current. Because the abstract and conclusion claim that the junction is open for µ ≥ 0.8 eV and closed for µ < 0.8 eV or µ = 0, the two-state switch claim rests on this imported threshold rather than on a computed current-phase relation for the present device.
  5. [Sec. VI.C] The Chern number two is asserted but not computed. The evidence shown in Figs. 5 and 6 is band-gap closing and a finite conductance at E_F for |µ| ≪ |λ|; no topological invariant, edge-state spectrum, or explicit Majorana wavefunction is evaluated for the leads as used in the junction. The claim that Majorana zero modes with Chern number two form in the topological leads is therefore not demonstrated by this manuscript.
minor comments (3)
  1. [Sec. VI.D.A and Appendix A] In Sec. VI.D.A the integration window is stated as -Δ0 ≤ E ≤ Δ0, whereas Sec. V and Appendix A specify -Δ0 × 10^-3 ≤ E ≤ Δ0 × 10^-3; please state clearly which window is used for Fig. 7.
  2. [Throughout] There are several typos, including 'respectivel' in Sec. VI.D.B, 'pints' in Appendix A, 'hooping' for 'hopping', and the Fig. 6 caption labels all three panels as (a).
  3. [Sec. VI.D.B] The manuscript should cite and discuss the established 4π-periodic Josephson effect in topological junctions, because the proposed zero-current closed state is in tension with that body of literature and the single-momentum model used here cannot address it.

Circularity Check

2 steps flagged · score 7.0 of 10

Topological-lead 'closed state' is preordained: the paper selects chemical potentials that its own Appendix A says preclude Andreev bound states, then reports absent ABS and zero current from a flat total DOS without computing a current-phase relation; the 0.8 eV switch threshold is imported from Ref. [44].

  1. fitted input called prediction [Section VI.D.B and Appendix A (after Eq. A.12)]
    "However, for observing the Andreev bound states in a typical experiment, one should set µ ≫ ∆0 and E ≪ ∆0 ... Otherwise, Andreev bound states will not be observed [48,56]. // ... for observing the Majorana zero mode (MZM) the chemical potential should be smaller than the superconductor pairing potential i.e., |µ| < ∆0. In this reason, we set µ = 0 eV and µ = 0.015 eV and ∆0 = 0.01 eV [44]."

    Appendix A makes the existence of ABS conditional on t ≫ µ ≫ Δ0 and says otherwise the ABS 'will not be observed.' Section VI.D.B then chooses, for the topological-lead case, µ = 0 or 0.015 eV with Δ0 = 0.01 eV, values that deliberately lie on the 'otherwise' side of that criterion. Reporting that 'the Andreev bound states are not formed' is therefore a restatement of the input condition, not a result of the TB-NEGF calculation. The subsequent claim It = 0 is inferred from a flat total DOS rather than from a computed current-phase relation, so the closed-state leg of the switch reduces to the chosen parameters plus the paper's own ABS criterion.

  2. self definitional [Section VI.D.B (Fig. 8 discussion) and Section V (text after Eq. 33)]
    "As it shows, although DOS increases by increasing the chemical potential, but for each value of µ, it is constant. Therefore, the Andreev bound states are not formed and the junction behaves as an open circuit ( It = 0) when −∆0 × 10−3 ≤ E ≤ ∆0 × 10−3."

    The paper defines ABS as 'real-valued singularities of the density of states' (text after Eq. (33)), so a phase-independent total DOS already means 'no ABS' by definition. The jump from 'no ABS' to 'junction behaves as an open circuit (It = 0)' is not derived: the Josephson current is not a direct function of the integrated DOS, and Eq. (27) is not evaluated for the topological leads. Thus the central 'closed-state' claim is an identity plus a non-derived postulate, not a computed prediction.

full rationale

The paper is not circular via self-citation: the topological phase (Chern number two) and the ABS-existence conditions come from external Refs. [34,44,48,56], and the NEGF machinery is standard. The non-topological-lead benchmark (Fig. 7) reproduces the expected sinusoidal current and Gaussian DOS once the Appendix A condition t ≫ µ ≫ Δ0 is imposed; that is a consistency check rather than a prediction. The circularity is concentrated in the topological-lead 'closed state': Section VI.D.B selects µ = 0 or 0.015 eV with Δ0 = 0.01 eV precisely to be outside the Appendix A ABS window, then reports the absence of ABS and, from a flat total DOS (Fig. 8), declares It = 0. Since the parameter choice already guarantees the absence of ABS by the paper's own criterion, this leg of the two-state switch is an input restated as a result; the additional inference from a phase-independent total DOS to zero Josephson current is not derived. In addition, the 0.8 eV threshold is imported from Ref. [44] ('when |µN| is smaller than 0.8 eV, the Andreev conductance is equal to zero [44]. Therefore, it is expected that its related Josephson current be equal to zero, too'), so the switch threshold is not derived for the present junction. These are load-bearing circular steps and support gaps in the central claim; nevertheless, the paper does contain independent numerical material (band structures, conductance peaks at gap-closing k points) and no problematic self-citation chain, so the score is 7 rather than higher.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claims rest on several imported or hand-chosen inputs: the topological pairing is from Ref. [34]; the 0.8 eV threshold is from Ref. [44]; the barrier factor 10^-3, the fixed k values, and the subgap energy window are chosen by the authors to produce ABS or their absence. There are no new physical entities.

free parameters (5)
  • lead-to-flake coupling reduction factor = 10^-3
    Ad hoc barrier applied by multiplying self-energies (Eqs. (29)-(30) and Appendix A); central to realizing ABS in the calculation.
  • chemical potential µ for non-topological leads = 0.83 eV
    Chosen from Ref. [44] parameters; used in the sinusoidal current calculation.
  • chemical potential for topological leads = 0 and 0.015 eV
    Chosen so |µ| is not much greater than Δ0=0.01 eV, ensuring topological regime per Ref. [34].
  • fixed wave vector k for topological leads = 0 and 0.025
    Chosen at the gap-closing points in Fig. 5; the model does not integrate over transverse modes.
  • energy window for ABS observation = -Δ0×10^-3 to Δ0×10^-3
    Ad hoc window stated in Section V and Appendix A as needed to see ABS.
assumptions (5)
  • domain assumption The k·p Hamiltonian Eq. (1) and its parameters describe monolayer MoS2 near K points.
    Invoked in Section II and used for both channel and leads; originates from Xiao et al. [33].
  • domain assumption The singlet pairing potential Eq. (21) with the C3h form supports Chern number 2 topological superconductivity in MoS2.
    Imported from Yuan et al. [34] in Section IV; the paper does not re-derive it.
  • standard math Current formula Eq. (A.11) (from refs. [47-52]) is valid for superconducting leads.
    Presented in Appendix A without derivation; standard NEGF result in the cited literature.
  • ad hoc to paper Andreev bound states are observed only when t >> µ >> Δ0 and within the window -Δ0×10^-3 ≤ E ≤ Δ0×10^-3.
    Stated in Appendix A; used to set the parameters for the non-topological junction and to declare ABS absent for topological leads.
  • domain assumption The 0.8 eV threshold from Ref. [44] applies to the Josephson current in this geometry.
    Invoked in Section V and the Conclusion to define the switch threshold; not recomputed for the junction.

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Cite this review

Pith. "Pith review of Two-Dimensional Materials-Based Josephson Junctions." pith.science (2026). https://pith.science/paper/MZVS3IZS

@misc{pith2026250623737,
  author       = {Pith},
  title        = {Pith review of: Two-Dimensional Materials-Based Josephson Junctions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MZVS3IZS}},
  note         = {Machine review of arXiv:2506.23737}
}
read the original abstract

We consider a two-dimensional monolayer MoS2-based Josephson junction which is composed by an intermediate semiconductor flake and the semi-infinite topological and non-topological superconductor leads and study its quantum transport properties by using the tight-binding non-equilibrium Green function method. By introducing a simple tight-binding model, it is shown that, when the absolute value of chemical potential is much smaller than the superconductor paring potential, the Majorana zero modes, whose Chern number is two, are formed in the topological leads. Also, we show that, in Josephson junction with ordinary superconductor leads, the Josephson current has sinusoidal behavior (due to forming the Andreev bound states (ABS)), when the absolute value of energy of carriers (and the chemical potential) is much smaller (greater) than the superconductor pairing potential. Of course, for Josephson junction with topological superconductor leads, it is shown that the ABS are not formed and in consequence the related Josephson current is zero. Therefore, one can consider the two-dimensional monolayer MoS2-based Josephson junction as a two-state switch which is in open-state (due to ABS) when the chemical potential is greater than 0.8 eV and is in close-state (due to Majorana) when the chemical potential is less than < 0.8 or is equal to zero, i.e., ABS cannot mimic the Majorana state, as zero-bias conductance.

Figures

Figures reproduced from arXiv: 2506.23737 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.