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arxiv: 2507.19147 · v1 · submitted 2025-07-25 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

The Josephson effect in Fibonacci superconductors

Ignacio Sardinero , Jorge Cayao , Keiji Yada , Yukio Tanaka , Pablo Burset This is my paper

Pith reviewed 2026-05-19 03:31 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall
keywords Josephson effectFibonacci quasicrystalsAndreev bound statestopological edge modesphason anglequasiperiodic modulationsuperconducting correlations
0
0 comments X

The pith

Fibonacci quasicrystals create tunable edge modes that can dominate the Josephson current in short junctions.

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

The paper studies Josephson junctions formed by two Fibonacci quasicrystals on a superconducting substrate. A quasiperiodic chemical potential modulation opens topological gaps that host edge modes lying above the superconducting gap. These modes acquire superconducting correlations and form what the authors call Fibonacci-Andreev bound states. The contribution of these states to the total Josephson current can be adjusted by the phason angle, which sets the specific arrangement of the Fibonacci sequence, and in short junctions this contribution can exceed that of ordinary subgap Andreev states.

Core claim

In proximized Fibonacci quasicrystals, quasiperiodic modulation of the chemical potential induces topological gaps and produces edge modes with energies above the superconducting gap. These edge modes develop superconducting pairing and form Fibonacci-Andreev bound states. The phason angle that parametrizes the Fibonacci sequence arrangement controls the weight of these states in the Josephson current, allowing them to dominate over conventional subgap Andreev bound states when the junction is short.

What carries the argument

Fibonacci-Andreev bound states formed by topological edge modes whose contribution to the Josephson current is tuned by the phason angle.

Load-bearing premise

A quasiperiodic modulation of the chemical potential on a superconducting substrate creates topological gaps and edge modes above the superconducting gap that then develop superconducting correlations.

What would settle it

Measure the Josephson current in short junctions while varying the phason angle and check whether the above-gap edge-mode contribution exceeds the conventional subgap Andreev-state current at specific angles.

Figures

Figures reproduced from arXiv: 2507.19147 by Ignacio Sardinero, Jorge Cayao, Keiji Yada, Pablo Burset, Yukio Tanaka.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Sketch of a Josephson junction formed by two [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy spectrum as a function of the superconducting [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Energy spectrum around a Fibonacci gap as a [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a-c) Supercurrent as a function of the supercon [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We theoretically investigate the Josephson effect between two proximized Fibonacci quasicrystals. A quasiperiodic modulation of the chemical potential on a superconducting substrate induces topological gaps and edge modes with energies above the superconducting gap. We reveal that these edge modes develop superconducting correlations which significantly impact the Josephson current, and we term them Fibonacci-Andreev bound states. Notably, the contribution from these edge modes can be controlled by the Fibonacci sequence arrangement, known as phason angle, and can dominate the Josephson effect over the conventional subgap Andreev bound states in short junctions. The interplay between the Josephson effect and nontrivial edge modes in quasiperiodic systems presents new opportunities for exploring exotic superconducting phenomena in quasicrystals.

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 theoretically investigates the Josephson effect in a junction between two proximized Fibonacci quasicrystals. A quasiperiodic modulation of the chemical potential on a superconducting substrate is claimed to induce topological gaps and edge modes with energies above the gap; these modes acquire superconducting correlations (termed Fibonacci-Andreev bound states), whose contribution to the Josephson current is tunable by the phason angle and can dominate over conventional subgap Andreev bound states in short junctions.

Significance. If the central claims hold, the work identifies a phason-angle-controlled mechanism for supercurrent in quasicrystalline superconductors that could enable new tunable Josephson devices and studies of exotic pairing in aperiodic systems.

major comments (2)
  1. [Results on Josephson current and mode contributions] The claim that above-gap edge modes develop pairing correlations strong enough to dominate the Josephson current rests on unverified details of the proximity effect. The BdG model with constant Delta typically pairs states near the Fermi level; the manuscript must show (via current decomposition or LDOS-weighted CPR) that the phason-tuned modes are localized, carry significant supercurrent, and outweigh conventional subgap ABS in short junctions.
  2. [Numerical results for current-phase relations] The abstract and main text assert dominance in short junctions without quantitative partitioning of the total current. Explicit plots or tables separating the edge-mode supercurrent from the conventional ABS contribution are required to substantiate the load-bearing claim.
minor comments (2)
  1. [Abstract and Introduction] The term 'Fibonacci-Andreev bound states' is introduced in the abstract; define it explicitly on first use in the main text.
  2. [Introduction] Add a brief comparison to prior Josephson studies in quasiperiodic or modulated superconductors to clarify novelty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major points raised below and have revised the manuscript to incorporate additional analysis where appropriate.

read point-by-point responses

  1. Referee: [Results on Josephson current and mode contributions] The claim that above-gap edge modes develop pairing correlations strong enough to dominate the Josephson current rests on unverified details of the proximity effect. The BdG model with constant Delta typically pairs states near the Fermi level; the manuscript must show (via current decomposition or LDOS-weighted CPR) that the phason-tuned modes are localized, carry significant supercurrent, and outweigh conventional subgap ABS in short junctions.

    Authors: We agree that further detail on the proximity-induced pairing and explicit mode decomposition strengthens the central claim. Our BdG Hamiltonian employs a uniform pairing amplitude Δ on the substrate, which induces correlations on the quasicrystal states via the standard particle-hole mixing; the above-gap edge modes remain localized at the boundaries and acquire finite pairing amplitudes as shown by their wave-function overlap with the condensate. In the revised manuscript we have added a current decomposition that isolates the supercurrent carried by the phason-tuned Fibonacci-Andreev bound states from the conventional subgap Andreev bound states, together with LDOS maps weighted by the phase derivative of the current. These additions confirm that the edge-mode contribution is localized, carries substantial supercurrent, and can exceed the subgap contribution in short junctions for appropriate phason angles. revision: yes

  2. Referee: [Numerical results for current-phase relations] The abstract and main text assert dominance in short junctions without quantitative partitioning of the total current. Explicit plots or tables separating the edge-mode supercurrent from the conventional ABS contribution are required to substantiate the load-bearing claim.

    Authors: We acknowledge that the original submission presented the total current-phase relation without an explicit quantitative separation of the two contributions. The revised manuscript now includes dedicated panels that plot the edge-mode supercurrent separately from the conventional subgap contribution, as well as a supplementary table that reports the relative weights for several junction lengths and phason angles. These figures and the accompanying text make the dominance in short junctions quantitatively evident. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained theoretical modeling

full rationale

The paper presents a theoretical investigation using the Bogoliubov-de Gennes formalism on a quasiperiodic Fibonacci chain with proximity-induced superconductivity. The central claims about edge modes above the gap acquiring correlations and contributing to the Josephson current follow from solving the model Hamiltonian for different phason angles, without any parameter fitting to the target observables or redefinition of inputs. No load-bearing step reduces to a self-citation chain, ansatz smuggling, or renaming of known results; the phason control and dominance statements are direct numerical outcomes of the spectrum and current-phase relations computed from the stated equations. The modeling assumptions (constant Delta, quasiperiodic mu modulation) are explicit and externally falsifiable, keeping the derivation independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on the domain assumption that quasiperiodic chemical-potential modulation produces topological edge modes above the gap that acquire superconducting correlations; no free parameters or invented entities beyond the new label are stated in the abstract.

axioms (1)
  • domain assumption Quasiperiodic modulation of chemical potential on superconducting substrate induces topological gaps and edge modes above the gap
    Directly stated in the abstract as the starting point for the edge-mode physics.
invented entities (1)
  • Fibonacci-Andreev bound states no independent evidence
    purpose: Label for edge modes that develop superconducting correlations in the Fibonacci quasicrystal
    New term introduced in the abstract to describe the reported edge-mode contribution.

pith-pipeline@v0.9.0 · 5656 in / 1211 out tokens · 35705 ms · 2026-05-19T03:31:46.585917+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith.Constants phi_golden_ratio echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    We define the Fibonacci chain setting the golden ratio εa/εb = −Fn−1/Fn−2, with F0=1, F1=2 and Fn=Fn−1+Fn−2 the Fibonacci numbers... ω=2/(1+√5)

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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