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Andreev exceptional points in Josephson junctions formed by minimal Kitaev chains

T0 review · 1 major / 2 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read Josephson junctions of minimal Kitaev chains host second-order Andreev exceptional points controlled by the superconducting phase difference.

desk verdict Reservoir coupling adds phase-tunable Andreev exceptional points to minimal Kitaev Josephson junctions. read the letter →

arxiv 2606.23956 v1 pith:JOOWZCVJ submitted 2026-06-22 cond-mat.mes-hall cond-mat.supr-con

Jorge Cayao , Masatoshi Sato This is my paper
classification cond-mat.mes-hallcond-mat.supr-con
keywords AndreevexceptionalpointsJosephsonjunctionsminimalKitaevchainsnon-Hermitiantopologysuperconductingphasedifferencetopologicalstatesconductancesignaturesopenquantumsystems
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

The paper studies Josephson junctions built from two minimal Kitaev chains that are coupled to normal reservoirs, turning the system into an open non-Hermitian setup with a complex Andreev spectrum. It finds that this spectrum contains second-order exceptional points where eigenvalues and eigenvectors coalesce, and these points are tuned entirely by the superconducting phase difference. The location of the points at zero or finite energy depends on how the non-Hermiticity is distributed spatially across the junction. When parameters such as onsite energies or cotunneling are varied, the points extend into lines that enclose protected two-dimensional regions of zero real energy. The work also outlines conductance measurements as a route to detect these features.

What carries the argument

The complex Andreev spectrum of the phase-biased non-Hermitian Josephson junction, in which second-order exceptional points arise from the interplay of non-Hermiticity and the superconducting phase difference.

What would settle it

Observation of conductance features showing eigenvalue coalescence at phase-difference values predicted by the model, with the coalescence points shifting between zero and finite energy when the spatial distribution of reservoir coupling is changed.

Watch

Extended reading notes

Core claim

In Josephson junctions formed by minimal Kitaev chains, coupling to normal reservoirs generates a non-Hermitian open system whose complex Andreev spectrum hosts second-order exceptional points that are fully controlled by the superconducting phase difference. Depending on the spatial distribution of non-Hermiticity, the points appear at zero or finite energies and, upon tuning of onsite energies, non-Hermiticity strength, or electron cotunneling, develop into Andreev exceptional lines that enclose protected two-dimensional areas of zero real energy. These features enable stable topological states absent from the corresponding Hermitian problem.

Load-bearing premise

Coupling the minimal Kitaev chains to normal reservoirs produces a non-Hermitian open system whose complex spectrum faithfully captures stable topological states absent from the corresponding Hermitian problem.

Editorial extensions

If this is right

  • Exceptional points move between zero and finite energy when the spatial distribution of non-Hermiticity is altered.
  • Tuning onsite energies, non-Hermiticity strength, or cotunneling converts the points into lines that enclose protected zero-real-energy regions.
  • Local and nonlocal conductance signatures can reveal the exceptional points and the enclosed protected areas.
  • The non-Hermitian setup produces topological states that have no counterpart in the Hermitian Josephson junction.

Reading between the lines

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

  • The phase-difference control of exceptional points could be used to switch between different non-Hermitian topological regimes without changing microscopic parameters.
  • The protected zero-energy areas may appear as robust features in transport or noise measurements beyond the conductance signatures discussed.
  • Similar non-Hermiticity engineering might be applied to longer Kitaev chains or other topological Josephson platforms to generate higher-order exceptional structures.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 2 minor

Summary. The paper studies Josephson junctions formed by two minimal Kitaev chains coupled to normal reservoirs, rendering the system non-Hermitian with a complex Andreev spectrum. It claims that this spectrum hosts second-order exceptional points fully controlled by the superconducting phase difference; depending on the spatial distribution of non-Hermiticity, these points appear at zero or finite energies and can form Andreev exceptional lines that enclose protected two-dimensional regions of zero real energy. The work also discusses conductance-based detection schemes and positions non-Hermiticity from reservoirs as a resource for engineering non-Hermitian topological phases absent in the Hermitian limit.

Significance. If the central claims hold, the results would demonstrate a concrete, experimentally accessible route to phase-tunable exceptional points and non-Hermitian protected zero-energy areas in minimal Kitaev-chain Josephson junctions, extending the platform beyond Hermitian topological superconductivity. The discussion of local and nonlocal conductance signatures provides a direct link to measurable quantities.

major comments (1)
  1. [Abstract / non-Hermiticity modeling section] Abstract and modeling of non-Hermiticity (paragraph on coupling to normal reservoirs): the central claim that the reported exceptional points and enclosed zero-real-energy regions constitute stable topological features absent from the Hermitian problem requires an explicit comparison showing that these structures disappear or lose their protection when all imaginary parts of the self-energies are removed. Without such a comparison to the Hermitian limit or to the full Liouvillian spectrum, it remains possible that the exceptional lines are truncation artifacts of the effective non-Hermitian model rather than robust non-Hermitian topology.
minor comments (2)
  1. [Abstract] The abstract states that exceptional points are 'fully controlled by the superconducting phase difference' but does not specify whether this control is parameter-free or requires additional tuning of onsite energies or cotunneling amplitudes; a clarifying sentence would help.
  2. [Results section on spatial distribution] Notation for the spatial distribution of non-Hermiticity (unequal vs. symmetric) should be defined explicitly when first introduced, as it determines whether exceptional points sit at zero or finite energy.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below and will incorporate the requested comparison in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract / non-Hermiticity modeling section] Abstract and modeling of non-Hermiticity (paragraph on coupling to normal reservoirs): the central claim that the reported exceptional points and enclosed zero-real-energy regions constitute stable topological features absent from the Hermitian problem requires an explicit comparison showing that these structures disappear or lose their protection when all imaginary parts of the self-energies are removed. Without such a comparison to the Hermitian limit or to the full Liouvillian spectrum, it remains possible that the exceptional lines are truncation artifacts of the effective non-Hermitian model rather than robust non-Hermitian topology.

    Authors: We agree that an explicit comparison to the Hermitian limit is required to substantiate the claim that the exceptional points, lines, and protected zero-real-energy regions are absent in the Hermitian case. In the revised manuscript we will add a dedicated comparison (new figure and accompanying text) in which the imaginary parts of all self-energies are set to zero while keeping all other parameters fixed; this will show that the exceptional structures disappear and that the spectrum reverts to the conventional Hermitian Andreev spectrum without protected zero-real-energy areas. We will also add a short discussion clarifying the regime of validity of the effective non-Hermitian model relative to the full Liouvillian spectrum for weak reservoir coupling. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: claims presented as model-derived results without reduction to inputs

full rationale

The abstract and provided text describe the emergence of phase-controlled second-order exceptional points and protected zero-real-energy regions in the complex Andreev spectrum of an open non-Hermitian model as direct findings from the Josephson junction setup. No equations, fitted parameters, or self-citations are exhibited that would make any reported feature equivalent to its own definition or a renamed input. The non-Hermiticity assumption is stated explicitly as an external modeling choice rather than derived internally, leaving the derivation chain self-contained against the given content.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

Abstract-only; the central claim rests on standard non-Hermitian eigenvalue theory and the assumption that the open-system model of Kitaev chains plus reservoirs is adequate. No free parameters, invented entities, or ad-hoc axioms are visible.

assumptions (2)
  • standard math Non-Hermitian eigenvalue problem for open quantum systems yields complex spectra whose exceptional points are physically meaningful
    Invoked implicitly when the abstract states that the complex Andreev spectrum hosts exceptional points.
  • domain assumption Coupling to normal reservoirs renders the Josephson junction non-Hermitian while preserving the topological character of the minimal Kitaev chains
    Central modeling step stated in the abstract paragraph on non-Hermiticity from normal reservoirs.

how reviews work

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Cite this review

Pith. "Pith review of Andreev exceptional points in Josephson junctions formed by minimal Kitaev chains." pith.science (2026). https://pith.science/paper/JOOWZCVJ

@misc{pith2026260623956,
  author       = {Pith},
  title        = {Pith review of: Andreev exceptional points in Josephson junctions formed by minimal Kitaev chains},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JOOWZCVJ}},
  note         = {Machine review of arXiv:2606.23956}
}
read the original abstract

We consider Josephson junctions formed by two minimal Kitaev chains and investigate how the interplay between non-Hermiticity and superconducting phase difference enables the realization of stable topological states that do not exist in the Hermitian realm. In particular, we focus on non-Hermiticity produced by coupling the minimal Kitaev chain Josephson junction to normal reservoirs, which renders the system open and characterized by a complex Andreev spectrum. Interestingly, we find that this complex spectrum hosts second order exceptional points, where a pair of eigenvalues and their respective eigenvectors coalesce, and are fully controlled by the superconducting phase difference. Depending on the spatial unequal distribution of non-Hermiticity, these Andreev exceptional points can appear at zero or finite energies connecting stable energy lines protected by non-Hermitian topology. Moreover, tuning the system parameters, such as onsite energies, non-Hermiticity, or electron cotunneling, the Andreev exceptional points give rise to Andreev exceptional lines enclosing protected two-dimensional zero real energy areas. We also discuss potential detection schemes of Andreev exceptional points by using local and nonlocal conductance signatures. Our results demonstrate the utility of non-Hermiticity from normal reservoirs as a useful resource for engineering non-Hermitian topological phases in minimal Kitaev chain Josephson junctions.

Figures

Figures reproduced from arXiv: 2606.23956 by the authors.

Figure 1
Figure 1. FIG. 1. A phase-biased Josephson junction formed by two [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 1
Figure 1. The spectral low-energy properties of this non [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Energy spectrum as a function of the superconducting [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: (a). We verified that the ends of the zero Re energy line correspond to the formation of exceptional points (EPs), where the eigenvalues and also the corresponding eigenfunctions coalesce. Unlike Hermitian degeneracies, the energy behavior around such EPs is not linear…
Figure 4
Figure 4. Figure 4: FIG. 4. (a,b) Real (blue) and imaginary (red) parts of the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: as functions of ω and ϕ; note that this sweet spot regime corresponds to the reported in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: (b). In contrast to the signals at the leftmost QD, accessing the spectral function in the second QD of the left chain offers a clearer way to identify ABSs and, inter￾estingly, also reveal the emergence of the zero Re energy line connecting EPs, see cyan arrow in [PI…

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Cited by 1 Pith paper

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Pith tools

Reviewed June 26, 2026 · model on record in the stance chip above.