arxiv: 2605.04710 · v1 · submitted 2026-05-06 · ❄️ cond-mat.supr-con

Recognition: unknown

Nonlocal transport phenomena in coupled quasiperiodic Kitaev chains

Koki Mizuno

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:37 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con

keywords Kitaev chainMajorana fermionsquasiperiodicFibonaccitopological phasenonlocal transportsuperconducting chainsdifferential conductance

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The pith

Coupled quasiperiodic Kitaev chains host a new topological phase transition induced by the Fibonacci modulation.

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

This paper studies the topological properties of two coupled Kitaev chains, each with a Fibonacci quasiperiodic potential modeling a quasicrystal. Using Green's function techniques, it calculates the differential conductance for different ways of attaching leads to the chains. The work finds that Majorana edge modes appear and that their wave functions spread into the bulk due to the quasiperiodicity. The key result is the identification of an additional phase transition that only occurs because of the quasiperiodic pattern in the coupled geometry.

Core claim

The coupled one-dimensional p-wave superconducting Fibonacci quasicrystal hosts topological phases with Majorana edge modes that exhibit seepage of the wave function. Nonlocal transport phenomena depend on the lead connecting pattern. A new topological phase transition is induced by quasiperiodicity in the coupled system.

What carries the argument

The Fibonacci quasiperiodic modulation applied to the coupled Kitaev Hamiltonian, analyzed through the Keldysh formalism and recursive Green's function method to reveal phase boundaries and conductance spectra.

Load-bearing premise

The observed features in conductance and mode counting correspond to a distinct new topological phase transition rather than a gradual change or one already known from periodic coupled Kitaev models.

What would settle it

Calculating or measuring the winding number or the presence of zero-energy states while varying the quasiperiodic amplitude; absence of a sharp transition at the predicted critical value would falsify the claim of a new quasiperiodicity-induced transition.

Figures

Figures reproduced from arXiv: 2605.04710 by Koki Mizuno.

**Figure 1.** Figure 1: FIG. 1. Schematic drawing of the coupled system. The ar view at source ↗

**Figure 2.** Figure 2: FIG. 2. The differential conductance of all lead connecting view at source ↗

**Figure 3.** Figure 3: FIG. 3. Topological phase transition of the coupled system view at source ↗

**Figure 4.** Figure 4: FIG. 4. Topological phase transition of the coupled system view at source ↗

**Figure 5.** Figure 5: FIG. 5. Topological phase transition of the coupled system view at source ↗

**Figure 6.** Figure 6: FIG. 6. Topological phase transition of the coupled system view at source ↗

**Figure 7.** Figure 7: FIG. 7. Schematic drawing of the case that connects a single view at source ↗

**Figure 8.** Figure 8: FIG. 8. Differential conductance for single Kitaev chain. view at source ↗

read the original abstract

We investigate the topological phases in a coupled one-dimensional p-wave superconducting Fibonacci quasicrystal modeled by the quasiperiodic Kitaev chain. Recent studies have shown that the coupled system can host topological edge modes with Majorana fermions and enhance their topological protection, depending on the pattern of quasiperiodicity. In this work, we elucidate the topological phases of the coupled system and demonstrate the dependence of differential conductance on the lead connecting pattern employing the Keldysh formalism and the recursive Green's function method. Our findings reveal the emergence of topological phases in the coupled system, which are characterized by the presence of Majorana edge modes and the seepage of the Majorana wave function. Furthermore, we identify a new topological phase transition induced by quasiperiodicity in the coupled system.

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.

Desk Editor's Note private letter to a colleague

The paper applies Keldysh transport to coupled Fibonacci Kitaev chains and reports a new quasiperiodicity-induced transition, but the claim rests on conductance features without a shown topological invariant crossing.

read the letter

The main point is that this work takes the coupled quasiperiodic Kitaev model, adds interchain coupling, and computes differential conductance with the Keldysh formalism plus recursive Green's functions. They track how edge-mode seepage and nonlocal signals change with the quasiperiodic amplitude and lead-connection pattern, then flag a new phase transition driven by that amplitude. The transport part is a straightforward extension of recent edge-mode studies on similar systems. The calculations look technically competent for what they set out to do, and the focus on measurable nonlocal conductance is a reasonable next step for this setup. The soft spot is exactly the one the stress test flags. The transition is located where conductance signatures shift, but the text does not show a corresponding jump or zero-crossing in a bulk topological invariant such as the Pfaffian or winding number of the Bogoliubov-de Gennes Hamiltonian. Conductance features can appear from localization, finite-size effects, or resonances without any change in bulk topology, so it remains unclear whether this is genuinely new or just a crossover already implicit in prior coupled-chain work. The abstract itself points back to recent studies on edge modes, which reinforces that the advance is mainly the application rather than a first-principles re-derivation. This is for specialists already working on quasiperiodic topological superconductors and Majorana transport. A reader in that niche might pick up useful details on how lead geometry modulates the signals, but the missing invariant check keeps the central claim provisional. I would send it to peer review if the authors add the bulk-topology cross-check; without it the paper is too preliminary for a serious referee.

Referee Report

1 major / 2 minor

Summary. The paper studies topological phases and nonlocal transport in a system of two coupled one-dimensional p-wave superconducting chains with Fibonacci quasiperiodic modulation (quasiperiodic Kitaev chains). Using the Keldysh formalism and recursive Green's function techniques, it computes differential conductance for different lead-attachment patterns, reports the presence and seepage of Majorana edge modes, and claims to identify a new quasiperiodicity-induced topological phase transition in the coupled system that is distinct from single-chain or periodic cases.

Significance. If the central claim is confirmed, the work would add to the literature on how quasiperiodic potentials modify topological protection and edge-mode localization in coupled superconducting wires, with possible relevance to Majorana-based devices. The choice of recursive Green's functions for conductance is a concrete numerical strength that allows direct comparison with transport experiments.

major comments (1)

[Results / discussion of the phase transition] The identification of a 'new topological phase transition' (abstract and main results) rests on changes in differential conductance and Majorana wave-function seepage as a function of the quasiperiodic amplitude. However, no calculation or plot shows that the reported critical value coincides with a jump, zero-crossing, or level crossing in a bulk topological invariant (winding number, Pfaffian, or Majorana polarization) of the Bogoliubov-de Gennes Hamiltonian. Conductance signatures alone can arise from localization or finite-size effects without a change in bulk topology; this cross-check is load-bearing for the topological character of the transition.

minor comments (2)

[Model and abstract] The abstract refers to 'the pattern of quasiperiodicity' and 'lead connecting pattern' without quoting the explicit values of the Fibonacci modulation strength, inter-chain coupling, or chemical potential used for the claimed transition; these should be stated once in the model section and again in the figure captions for reproducibility.
[Methods] Notation for the recursive Green's function and the Keldysh contour ordering is introduced without a compact summary equation; a single reference equation collecting the definitions would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive feedback. We address the major comment point by point below and outline the revisions we will make to strengthen the topological characterization of the reported phase transition.

read point-by-point responses

Referee: The identification of a 'new topological phase transition' (abstract and main results) rests on changes in differential conductance and Majorana wave-function seepage as a function of the quasiperiodic amplitude. However, no calculation or plot shows that the reported critical value coincides with a jump, zero-crossing, or level crossing in a bulk topological invariant (winding number, Pfaffian, or Majorana polarization) of the Bogoliubov-de Gennes Hamiltonian. Conductance signatures alone can arise from localization or finite-size effects without a change in bulk topology; this cross-check is load-bearing for the topological character of the transition.

Authors: We agree that a direct verification via a bulk topological invariant is important to confirm the topological nature of the transition and to rule out purely localization-driven effects. The original manuscript identifies the transition through the appearance and seepage of Majorana edge modes (computed from the eigenvectors of the Bogoliubov-de Gennes Hamiltonian) together with the associated nonlocal conductance signatures obtained via the Keldysh-recursive Green's function approach. To address the referee's concern, we will add in the revised version an explicit calculation of the winding number of the BdG Hamiltonian as a function of the quasiperiodic amplitude. This will be plotted alongside the conductance data to demonstrate that the critical point coincides with a change in the bulk invariant, thereby establishing the bulk-boundary correspondence for the quasiperiodicity-induced transition. The new figure and accompanying discussion will be placed in the results section on the phase diagram. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper computes differential conductance via the Keldysh formalism and recursive Green's functions applied to the Bogoliubov-de Gennes Hamiltonian of the coupled Fibonacci Kitaev chains. The identification of a quasiperiodicity-induced topological phase transition rests on the presence of Majorana edge modes and their seepage, which are diagnosed from the numerical transport signatures rather than from any self-defined parameter or fitted quantity. No equations in the provided text reduce a claimed prediction to an input by construction, and no load-bearing self-citation chain is invoked to establish the transition itself. The numerical methods are standard and externally verifiable independent of the specific phase diagram reported.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents enumeration of specific free parameters or axioms; typical models of this type introduce at least a quasiperiodic potential amplitude and inter-chain coupling strength as tunable inputs.

pith-pipeline@v0.9.0 · 5416 in / 1091 out tokens · 37076 ms · 2026-05-08T16:37:14.737294+00:00 · methodology

discussion (0)

Reference graph

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