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arxiv: 2504.00524 · v3 · pith:RKOBROQJnew · submitted 2025-04-01 · ❄️ cond-mat.mes-hall

Signatures of exceptional points in multiterminal superconductor-normal metal junctions

Oliver Solow , Karsten Flensberg This is my paper

Pith reviewed 2026-05-22 22:12 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords exceptional pointsAndreev statesJosephson currentnon-Hermitian systemsmultiterminal junctionssuperconductor-normal metalspectroscopy
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The pith

Exceptional points in multiterminal SN junctions appear in Andreev state spectroscopy but leave the Josephson current largely unaffected.

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

The paper examines a non-Hermitian multiterminal superconductor-normal system built from a single spinful level, spin-dependent normal leads, and a noncollinear magnetic field. This minimal setup supports both topologically protected and symmetry-protected exceptional points. An exact transport formalism is used to show that the points produce clear features in the spectrum of Andreev states. The same points cause only small modifications to the Josephson current. The authors argue that the same pattern holds when interactions are added.

Core claim

In the minimal non-Hermitian SN junction, exceptional points leave visible signatures in Andreev-state spectroscopy while producing only minor changes to the Josephson current; the signatures persist with interactions.

What carries the argument

Exact transport formalism applied to the non-Hermitian effective Hamiltonian of the single-level SN junction, which maps exceptional-point locations onto observable Andreev-state features.

If this is right

  • Andreev-state spectroscopy provides a practical route to detect both topological and symmetry-protected exceptional points.
  • Josephson-current measurements are insensitive to the exceptional points in this class of devices.
  • The minor effect on current and the spectroscopic visibility both survive the inclusion of interactions.
  • The same transport approach can be applied to other non-Hermitian SN geometries.

Where Pith is reading between the lines

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

  • Spectroscopy may be a more reliable experimental probe than current for non-Hermitian features in hybrid superconducting systems.
  • Similar Andreev signatures could be sought in larger multiterminal devices or different lead configurations.
  • The separation between spectral visibility and current insensitivity might guide design of sensors that exploit exceptional points without disrupting supercurrent.

Load-bearing premise

The chosen minimal model with one spinful level and noncollinear field is representative of generic experimental signatures of exceptional points in multiterminal SN systems.

What would settle it

If spectroscopy of the Andreev states in a fabricated junction shows no distinct features at the parameter values where the formalism predicts exceptional points, the claimed visibility of those signatures would be falsified.

Figures

Figures reproduced from arXiv: 2504.00524 by Karsten Flensberg, Oliver Solow.

Figure 1
Figure 1. Figure 1: (a) Schematic of the multi-terminal SNS setup. The gray leads are superconductors, the FM lead is ferromagnetic, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Spectral function computations for single-level system. The red lines marks the real part of the poles of the spectral [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Josephson current for a multiterminal junction [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Spectral function of the junction with finite ∆. Subfigures (a), (b) and (c) correspond to ∆ [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Spectral function for junction with finite [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

We study a non-Hermitian, multiterminal superconducting-normal system in order to identify experimental signatures of exceptional points. We focus on a minimal setting with a single spinful level, spin-dependent normal leads, and a noncollinear magnetic field. This system hosts both topologically-protected, as well as symmetry-protected exceptional points. Using an exact transport formalism, we show that the exceptional points leave signatures visible through spectroscopy of the Andreev states, but that they have a minor effect on the Josephson current. We also argue that these findings hold with interactions.

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

1 major / 1 minor

Summary. The manuscript studies a minimal non-Hermitian multiterminal SN junction consisting of a single spinful level coupled to spin-dependent normal leads under a noncollinear magnetic field. This setup hosts both topologically protected and symmetry-protected exceptional points. Using an exact transport formalism, the authors show that these EPs produce visible signatures in Andreev-state spectroscopy while exerting only a minor influence on the Josephson current; they further argue that the conclusions remain valid in the presence of interactions.

Significance. If the minimal-model results prove representative, the work would supply a concrete, experimentally accessible route to detect exceptional points via Andreev spectroscopy in superconducting hybrids, while clarifying that the same points leave the supercurrent largely unaffected. The use of an exact transport method and the explicit check with interactions are positive features.

major comments (1)
  1. [Setup and Discussion sections (minimal-model justification)] The central claim that the reported separation between spectroscopic visibility and Josephson-current insensitivity constitutes generic experimental signatures of EPs in multiterminal SN systems rests on a single minimal Hamiltonian (single spinful level + spin-dependent leads + noncollinear B). No explicit test is provided showing that the same separation survives the addition of extra levels, altered junction geometry, or a different number of terminals. This assumption is load-bearing for the title and abstract statements about multiterminal SN junctions in general.
minor comments (1)
  1. [Methods/Transport formalism] The abstract states that an 'exact transport formalism' is employed but supplies no equations or parameter values; the main text should include the explicit scattering-matrix or Green's-function expressions used to compute the Andreev spectrum and current.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The primary concern is the extent to which our conclusions about spectroscopic visibility versus Josephson-current insensitivity can be viewed as generic for multiterminal SN junctions. We address this point directly below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Setup and Discussion sections (minimal-model justification)] The central claim that the reported separation between spectroscopic visibility and Josephson-current insensitivity constitutes generic experimental signatures of EPs in multiterminal SN systems rests on a single minimal Hamiltonian (single spinful level + spin-dependent leads + noncollinear B). No explicit test is provided showing that the same separation survives the addition of extra levels, altered junction geometry, or a different number of terminals. This assumption is load-bearing for the title and abstract statements about multiterminal SN junctions in general.

    Authors: We agree that the manuscript presents results for a single minimal Hamiltonian and does not contain explicit calculations for multi-level systems, different geometries, or varying terminal numbers. The choice of the minimal model was deliberate: it isolates the non-Hermitian physics responsible for both topologically and symmetry-protected exceptional points while remaining exactly solvable via the transport formalism. The observed separation—clear Andreev-state signatures accompanied by only weak effects on the supercurrent—originates from the structure of the non-Hermitian eigenvalue problem and the way the leads couple to the Andreev bound states, features we expect to be robust. Nevertheless, we acknowledge that this expectation is not numerically verified beyond the minimal case. We will therefore (i) revise the abstract and title to refer explicitly to signatures in a minimal multiterminal SN junction, (ii) add a paragraph in the Discussion section that qualifies the generality claim and outlines why the underlying mechanism should persist, and (iii) note the absence of additional numerical tests as a limitation. These changes will be made in the revised manuscript. revision: partial

Circularity Check

0 steps flagged

No circularity: standard transport formalism applied to explicit minimal model

full rationale

The derivation applies an established exact transport formalism to an explicitly defined minimal Hamiltonian (single spinful level with spin-dependent leads and noncollinear field). No step reduces a claimed prediction to a fitted parameter by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames an input as an output. The spectroscopic signatures and minor Josephson-current effect are direct outputs of the formalism on the stated model; the interaction argument is presented as an extension rather than a definitional closure. The setup is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the minimal model itself is treated as given.

pith-pipeline@v0.9.0 · 5616 in / 1113 out tokens · 33656 ms · 2026-05-22T22:12:58.555147+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Non-Hermitian skin effect and electronic nonlocal transport

    cond-mat.mes-hall 2025-10 unverdicted novelty 6.0

    Non-Hermitian skin effect in Rashba nanowire with ferromagnetic lead produces nonreciprocal nonlocal conductance detectable by transport spectroscopy, with exceptional points shifting under open boundary conditions.

Reference graph

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