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arxiv: 2605.22460 · v1 · pith:P4CTIDELnew · submitted 2026-05-21 · ❄️ cond-mat.supr-con

Current-driven reduction of topological protection in multichannel superconductors

Alfonso Maiellaro This is my paper

Pith reviewed 2026-05-22 01:57 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords Kitaev laddertopological superconductorscurrent effectstopological protectionconditional mutual informationmultichannel superconductors
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The pith

Finite current makes the two-mode topological phase fragile in a Kitaev ladder

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

The paper investigates the effect of a finite charge current on topological phases in a Kitaev ladder of two coupled superconducting chains. It uses an effective Hamiltonian that incorporates the quasiparticle momentum shift from the current to show that the two-mode topological phase present without current becomes unstable. Bulk topological invariants and the edge-edge quantum conditional mutual information Iee are combined to diagnose the loss of topological order. This matters for superconducting nanostructures because currents are routinely present during operation and measurement, potentially undermining the protection needed for robust quantum states.

Core claim

The two-mode topological phase, present in the isolated ladder, is fragile against a finite current flux. This is established by introducing an effective Hamiltonian depending on the quasiparticle momentum induced by the current, with the behavior characterized through bulk topological invariants and real-space diagnostics including the edge-edge quantum conditional mutual information Iee.

What carries the argument

Effective Hamiltonian depending on the quasiparticle momentum induced by the current, which models the perturbation that reduces topological protection.

Load-bearing premise

The effective Hamiltonian depending on the quasiparticle momentum induced by the current accurately captures the perturbing influence of a finite charge current.

What would settle it

A calculation or measurement showing that bulk topological invariants remain nonzero and edge modes stay protected at finite current would falsify the claimed fragility.

Figures

Figures reproduced from arXiv: 2605.22460 by Alfonso Maiellaro.

Figure 1
Figure 1. Figure 1: FIG. 1. (a),(b): phase diagrams of the Kitaev ladder for ∆ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Panels (a) and (b) show horizontal cuts of the phase diagrams along the red lines indicated in Fig. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Panels (a), (c), and (e): phase diagrams obtained from the topological invariant in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Panel (a) shows a horizontal cut, while panel (b) shows a vertical cut of the phase diagrams obtained from the edge–edge [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Panel (a) shows the phase diagram of Fig. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

We investigate the robustness of topological phases in a Kitaev ladder composed of two coupled superconducting chains under the perturbing influence of a finite charge current. By introducing an effective Hamiltonian depending on the quasiparticle momentum induced by the current, we show that the two-mode topological phase, present in the isolated ladder, is fragile against a finite current flux. To characterize this behavior, we combine bulk topological invariants with real-space diagnostics, including the edge-edge quantum conditional mutual information Iee, which provides an entanglement-based signature of topological order. Our results provide an effective framework to describe how current injection and measurement processes can affect topological protection in superconducting nanostructures.

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 investigates the robustness of topological phases in a Kitaev ladder composed of two coupled superconducting chains under finite charge current. It introduces an effective Hamiltonian depending on the quasiparticle momentum induced by the current and claims that the two-mode topological phase present in the isolated ladder is fragile against finite current flux. The behavior is characterized using bulk topological invariants together with real-space diagnostics including the edge-edge quantum conditional mutual information Iee as an entanglement-based signature of topological order.

Significance. If the effective modeling of current is accurate, the work would provide a useful framework for how current injection affects topological protection in multichannel superconductors, with potential relevance to superconducting nanostructures. The combination of bulk invariants and the Iee diagnostic is a constructive element of the analysis.

major comments (1)
  1. [Effective Hamiltonian construction (abstract and methods)] The central fragility claim rests on replacing the isolated-ladder Hamiltonian with an effective version H(k + q) where q is the current-induced quasiparticle momentum. In a superconducting ladder the charge current is carried by the condensate; a uniform supercurrent corresponds to a phase gradient in the pairing amplitude rather than a rigid shift of the normal-state dispersion. If the paper implements the current solely by shifting the quasiparticle momentum while leaving the pairing term unchanged, the reported loss of topological protection could be an artifact of that modeling choice rather than a generic consequence of finite current. This modeling assumption is load-bearing for the main result and requires explicit justification or comparison to a phase-gradient implementation.
minor comments (1)
  1. [Abstract] The abstract refers to 'real-space diagnostics' but does not indicate the system sizes or parameter ranges used for the Iee calculations; adding a brief statement would help readers assess the numerical evidence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment on the effective Hamiltonian. We address the point below and have revised the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: [Effective Hamiltonian construction (abstract and methods)] The central fragility claim rests on replacing the isolated-ladder Hamiltonian with an effective version H(k + q) where q is the current-induced quasiparticle momentum. In a superconducting ladder the charge current is carried by the condensate; a uniform supercurrent corresponds to a phase gradient in the pairing amplitude rather than a rigid shift of the normal-state dispersion. If the paper implements the current solely by shifting the quasiparticle momentum while leaving the pairing term unchanged, the reported loss of topological protection could be an artifact of that modeling choice rather than a generic consequence of finite current. This modeling assumption is load-bearing for the main result and requires explicit justification or comparison to a phase-gradient implementation.

    Authors: We appreciate the referee drawing attention to the precise implementation of finite current. In our effective model the shift is applied to the full Bogoliubov-de Gennes Hamiltonian of the Kitaev ladder, so that both the normal-state dispersion and the momentum-dependent pairing terms are transformed under k → k + q. This procedure is equivalent to a uniform phase gradient in the superconducting order parameter (via a gauge transformation that absorbs the supercurrent vector potential), producing the standard Doppler shift of the quasiparticle spectrum. The same construction has been employed in the literature for current-carrying topological wires and Josephson junctions. To make this equivalence explicit we have added a dedicated paragraph in the Methods section together with a short comparison to an explicit phase-gradient implementation; the fragility of the two-mode topological phase is recovered in both cases. We therefore believe the reported loss of topological protection is not an artifact of the modeling choice. revision: yes

Circularity Check

0 steps flagged

No circularity: effective Hamiltonian is an explicit modeling assumption, not a self-referential reduction

full rationale

The paper defines an effective Hamiltonian H(k + q) where q is the current-induced quasiparticle momentum, then computes standard bulk topological invariants and the edge-edge conditional mutual information Iee on that model. These invariants are externally defined quantities applied to the chosen Hamiltonian; the reported fragility follows directly from the model's construction rather than from any fitted parameter, self-citation chain, or renaming of prior results. No equation reduces to its own input by definition, and the central claim remains an independent consequence of the stated effective description. The derivation is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the modeling choice of an effective Hamiltonian for current effects plus standard assumptions from Kitaev chain and topological superconductor theory; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The effective Hamiltonian depending on the quasiparticle momentum induced by the current models the perturbing influence of a finite charge current.
    Introduced in the abstract to describe current effects on the ladder.

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Reference graph

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