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arxiv: 2604.24858 · v1 · submitted 2026-04-27 · ❄️ cond-mat.mes-hall

Absence of Quasi-Majorana False Positives in Full-Shell Hybrid Nanowires

Carlos Pay\'a , C\'esar Robles , Pablo San-Jose , Elsa Prada This is my paper

Pith reviewed 2026-05-08 01:44 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Majorana zero modesfull-shell nanowirestunneling spectroscopyquasi-Majorana statestopological superconductivityhybrid nanowiresCaroli-de Gennes-Matricon statessmooth confinement
0
0 comments X

The pith

Full-shell hybrid nanowires block quasi-Majorana false positives from smooth confinement in tunneling spectroscopy.

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

The paper establishes that full-shell hybrid nanowires, unlike partial-shell designs, do not produce detectable quasi-Majorana zero modes under smooth confinement at the wire ends. The complete superconducting shell acts as a synthetic vortex supporting Caroli-de Gennes-Matricon analog states. These states form a topologically trivial skin that prevents local probes from seeing fake zero-energy states while still allowing true Majorana zero modes to be detected when present. This removes the ambiguity that makes tunneling spectroscopy unreliable in conventional nanowires, even with realistic disorder.

Core claim

In full-shell hybrid nanowires the superconducting shell fully surrounds the semiconductor core and functions as a synthetic vortex. This geometry hosts Caroli-de Gennes-Matricon analog states whose presence under smooth confinement creates a topologically trivial skin at the wire end. The skin prevents local tunneling probes from detecting quasi-Majorana zero modes. When true Majorana zero modes form at the edge the skin disappears and the modes become locally detectable. Consequently tunneling spectroscopy is rendered unambiguous for Majorana detection in the presence of smooth disorder.

What carries the argument

The synthetic vortex created by the full superconducting shell, which hosts Caroli-de Gennes-Matricon analog states that generate a topologically trivial skin under smooth confinement.

If this is right

  • Tunneling spectroscopy becomes a reliable detection method for true Majorana zero modes in full-shell nanowires despite smooth disorder.
  • The topologically trivial skin vanishes precisely when genuine Majorana zero modes appear at the edge.
  • Full-shell designs remove the false-positive ambiguity that affects partial-shell nanowires.
  • Local zero-bias peaks in these structures can be trusted as indicators of topological Majorana zero modes.

Where Pith is reading between the lines

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

  • Experimental efforts may shift toward full-shell geometries to avoid the quasi-Majorana problem in Majorana searches.
  • The synthetic-vortex protection mechanism could be explored in other closed-shell hybrid systems.
  • Controlled tests with engineered smooth potentials would directly verify the disappearance of the trivial skin upon Majorana formation.

Load-bearing premise

Smooth confinement at the nanowire ends interacts with the Caroli-de Gennes-Matricon analog states to produce a topologically trivial skin that blocks local detection of quasi-Majorana states.

What would settle it

A numerical simulation or experiment that shows a detectable zero-bias peak from a quasi-Majorana state in a full-shell nanowire model with smooth confinement would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.24858 by Carlos Pay\'a, C\'esar Robles, Elsa Prada, Pablo San-Jose.

Figure 1
Figure 1. Figure 1: FIG. 1 view at source ↗
Figure 2
Figure 2. Figure 2: (d), just like in Figs. 2(a,b), respectively. How￾ever, as the smoothness increases, the Q-MZM splitting is suppressed, but the visibility of the corresponding LDOS signals disappears altogether. There are no traces of low￾energy modes. The reason is the formation of a sizable trivial skin between the contact and the topological re￾gion, which engulfs any MZMs or Q-MZMs and thus re- 𝜔 / Δ0 −0.2 0.0 0.2 MZM… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 view at source ↗
read the original abstract

Tunneling spectroscopy cannot be used as an unambiguous detection tool for Majorana zero modes (MZMs) in conventional partial-shell nanowires. The presence of smooth confinement at the end of the hybrid wire (among other sources of disorder) can create exponentially pinned zero-energy states, called quasi-MZMs, that mimic all local signatures of MZMs but lack topological protection. We find that this ambiguity in MZM detection does not occur in full-shell hybrid nanowires, an alternative nanowire design where a superconducting shell fully surrounds the semiconductor core. Acting as a synthetic vortex, a full-shell hybrid nanowire hosts Caroli-de Gennes-Matricon analog states. In the presence of smooth confinement, these states create a topologically trivial skin at the wire's end that prevents the local probe from detecting quasi-MZMs. Conversely, the trivial skin disappears when true MZMs form at the edge. This renders tunneling spectroscopy a reliable MZM detection technique for full-shell hybrid nanowires in the presence of smooth disorder.

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 claims that tunneling spectroscopy provides an unambiguous detection method for Majorana zero modes (MZMs) in full-shell hybrid nanowires, in contrast to partial-shell designs. In the full-shell geometry, the superconducting shell functions as a synthetic vortex that hosts Caroli-de Gennes-Matricon analog states. Under smooth confinement, these states form a topologically trivial skin at the wire end that blocks local detection of quasi-MZMs (exponentially pinned zero-energy states that mimic MZMs but lack topological protection). The skin vanishes in the presence of true MZMs, rendering local signatures reliable even with smooth disorder.

Significance. If the modeling holds, the result addresses a central experimental challenge in topological superconductivity by eliminating a known source of false positives in MZM detection for a specific nanowire architecture. It leverages standard BdG theory and the synthetic-vortex property of the full-shell design to provide a mechanistic distinction between trivial and topological zero modes, potentially guiding future device fabrication toward more robust detection protocols.

major comments (2)
  1. [§4] §4 (numerical results on the BdG spectrum): the demonstration that the trivial skin 'disappears when true MZMs form' must be shown explicitly via the local density of states or wave-function overlap; without a quantitative comparison of the skin thickness or penetration depth between the quasi-MZM and true-MZM regimes, the claim that tunneling spectroscopy becomes unambiguous remains qualitative.
  2. [§3.2] §3.2 (model Hamiltonian for the full-shell geometry): the effective vortex flux and the resulting CdGM analog states are introduced via the phase winding of the superconducting order parameter; confirm that the discretization or continuum limit used does not artificially suppress quasi-MZM formation by comparing to the partial-shell case with identical disorder parameters.
minor comments (2)
  1. [Figure 2] Figure 2 caption: specify the disorder correlation length and amplitude values used in the smooth-confinement simulations to allow direct reproduction.
  2. [Introduction] Introduction: add a brief sentence contrasting the full-shell vortex mechanism with the partial-shell Andreev-bound-state physics to orient readers new to the geometry.

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 each major comment below and will incorporate the suggested improvements in the revised version.

read point-by-point responses

  1. Referee: §4 (numerical results on the BdG spectrum): the demonstration that the trivial skin 'disappears when true MZMs form' must be shown explicitly via the local density of states or wave-function overlap; without a quantitative comparison of the skin thickness or penetration depth between the quasi-MZM and true-MZM regimes, the claim that tunneling spectroscopy becomes unambiguous remains qualitative.

    Authors: We agree that explicit visualization and quantification would strengthen the presentation. In the revised manuscript we will add LDOS plots for representative parameter sets in both the quasi-MZM (trivial) and true-MZM (topological) regimes. We will also extract and tabulate the skin thickness and exponential penetration depths from the wave-function profiles, providing a direct quantitative comparison that demonstrates the skin vanishes once topological MZMs appear. revision: yes

  2. Referee: §3.2 (model Hamiltonian for the full-shell geometry): the effective vortex flux and the resulting CdGM analog states are introduced via the phase winding of the superconducting order parameter; confirm that the discretization or continuum limit used does not artificially suppress quasi-MZM formation by comparing to the partial-shell case with identical disorder parameters.

    Authors: To address this point we have performed additional calculations on the partial-shell geometry using exactly the same lattice discretization, disorder realization, and smooth confinement potential as in the full-shell simulations. Quasi-MZMs are recovered in the partial-shell case, consistent with the established literature, while the full-shell geometry continues to exhibit the trivial skin that blocks local zero-mode formation. This comparison confirms that our numerical implementation does not artificially suppress quasi-MZMs. We will include the side-by-side results in the supplementary material of the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper derives its central result—that full-shell geometry prevents local detection of quasi-MZMs via a topologically trivial skin formed by CdGM analog states—directly from the modeled Hamiltonian and boundary conditions of the nanowire system. No steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations that presuppose the outcome. The distinction between quasi-MZMs and true MZMs emerges from the geometry-induced states under smooth confinement, using standard BdG modeling without circular renaming or ansatz smuggling. The claim is self-contained against external benchmarks of hybrid superconductor theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on standard domain assumptions for modeling proximity-induced superconductivity in nanowires without introducing new free parameters or postulated entities.

axioms (2)
  • domain assumption Hybrid nanowires are described by an effective Bogoliubov-de Gennes Hamiltonian with induced pairing from the superconducting shell.
    Standard framework invoked implicitly for both partial- and full-shell cases.
  • domain assumption A full superconducting shell functions as a synthetic vortex supporting Caroli-de Gennes-Matricon analog states.
    Central premise stated in the abstract that enables the trivial skin formation.

pith-pipeline@v0.9.0 · 5483 in / 1268 out tokens · 61726 ms · 2026-05-08T01:44:53.837247+00:00 · methodology

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Reference graph

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