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REVIEW 2 major objections 2 minor 117 references

A helical altermagnet induces Majorana bound states in a proximitized nanowire by creating effective spin-momentum locking through gauge transformation, without requiring net magnetism or conventional spin-orbit coupling.

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2026-06-26 15:12 UTC pith:UAYRBAZK

load-bearing objection The paper sketches a helical altermagnet route to Majorana states that skips SOC and net magnetism, but the gauge step needs explicit checking for leftover terms. the 2 major comments →

arxiv 2606.20259 v1 pith:UAYRBAZK submitted 2026-06-18 cond-mat.supr-con

Majorana modes in helical altermagnet without net magnetism and spin-orbit coupling

Xing-Jian Yi , Yue Mao , Cheng-Ming Miao , Qing-Feng Sun This is my paper
classification cond-mat.supr-con
keywords Majorana bound stateshelical altermagnettopological superconductornanowiregauge transformationspin-momentum lockingquantized conductances-wave proximity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper proposes a setup where a one-dimensional metal nanowire sits on the surface of a helical altermagnet and is placed in proximity to an s-wave superconductor. A gauge transformation applied to the helical frame converts the altermagnetic order into spin-momentum locking while the altermagnetism itself breaks time-reversal symmetry, opening a topological superconducting phase. This phase is controlled by chemical potential, altermagnet strength, and helical frequency. Transport calculations predict a 2e²/h zero-bias conductance peak at the nanowire ends and a 4e²/h peak at domain walls between opposite-chirality segments. These signatures would be measurable with metal leads or scanning tunneling microscopy.

Core claim

Through gauge transformation, the helical frame of the altermagnet naturally induces spin-momentum locking while altermagnetism breaks time-reversal symmetry; when the nanowire is proximitized by an s-wave superconductor, this combination stabilizes a topological superconducting phase hosting Majorana bound states, with the phase boundaries tuned by chemical potential, altermagnet strength, and helical frequency.

What carries the argument

Gauge transformation in the helical frame that maps the altermagnetic order onto effective spin-momentum locking sufficient for topology.

Load-bearing premise

The gauge transformation applied to the helical frame produces effective spin-momentum locking that is sufficient to reach the topological phase without extra contributions from the altermagnetic order or the nanowire interface.

What would settle it

Absence of the predicted 2e²/h zero-bias conductance peak at the nanowire ends or the 4e²/h peak at opposite-chirality domain walls in transport or STM measurements.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The topological phase remains accessible by tuning chemical potential, altermagnet strength, and helical frequency.
  • A 2e²/h zero-bias conductance peak appears at each end of the nanowire when the system is topological.
  • A 4e²/h tunneling conductance peak occurs at domain walls separating segments of opposite helical chirality.
  • These conductance features are detectable with ordinary metal leads or scanning tunneling microscopy.

Where Pith is reading between the lines

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

  • The scheme could be tested by fabricating nanowires on existing helical altermagnet candidates and varying the helical frequency in experiment.
  • Similar gauge transformations might be applied to other non-collinear magnetic textures to generate effective spin-orbit effects.
  • Domain-wall conductance could serve as a direct probe of chirality reversal in altermagnetic devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes realizing a topological superconductor hosting Majorana bound states in a 1D metal nanowire on the surface of a helical altermagnet, proximitized by an s-wave superconductor. The scheme eliminates the need for conventional spin-orbit coupling and net magnetism by applying a gauge transformation in the helical frame, which is asserted to induce effective spin-momentum locking while altermagnetism breaks time-reversal symmetry. The topological phase is tuned by chemical potential, altermagnet strength, and helical frequency; transport calculations predict a 2e²/h zero-bias peak at nanowire ends and 4e²/h tunneling conductance at domain walls between opposite-chirality segments.

Significance. If the central derivation holds, the result would provide a new materials platform for Majorana modes that leverages the momentum-odd spin splitting of altermagnets rather than net magnetization or Rashba SOC. The transport signatures are falsifiable and could be tested with existing STM and lead-contact setups, adding to the growing literature on altermagnetic heterostructures.

major comments (2)
  1. [gauge transformation / helical-frame Hamiltonian] The gauge transformation section (likely the derivation following the helical-frame Hamiltonian): the claim that the transformation produces only effective spin-momentum locking plus TRS breaking must be verified by explicit expansion; because the altermagnetic order parameter is momentum-odd, the position-dependent unitary rotation can generate additional k-dependent operators that are absent from the target Rashba+Zeeman model and may close the topological gap or shift the phase boundaries for the stated parameter ranges (chemical potential, altermagnet strength, helical frequency).
  2. [topological phase / BdG Hamiltonian] Topological phase diagram and invariant calculation: the manuscript must demonstrate that the post-transformation Bogoliubov-de Gennes Hamiltonian satisfies the standard topological criterion (e.g., Pfaffian or winding number) without residual terms from the altermagnetic order altering the result; otherwise the tuning-parameter windows reported for the topological regime are not guaranteed.
minor comments (2)
  1. Notation for the helical frequency and altermagnet strength should be defined consistently between the abstract, Hamiltonian, and phase-diagram figures.
  2. [transport calculation] The transport section should include a brief comparison of the calculated conductances to the topological invariant to strengthen the link between the 2e²/h and 4e²/h features and the presence of MBS.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major points below. Both concerns can be resolved by adding explicit derivations and calculations to the manuscript.

read point-by-point responses

  1. Referee: [gauge transformation / helical-frame Hamiltonian] The gauge transformation section (likely the derivation following the helical-frame Hamiltonian): the claim that the transformation produces only effective spin-momentum locking plus TRS breaking must be verified by explicit expansion; because the altermagnetic order parameter is momentum-odd, the position-dependent unitary rotation can generate additional k-dependent operators that are absent from the target Rashba+Zeeman model and may close the topological gap or shift the phase boundaries for the stated parameter ranges (chemical potential, altermagnet strength, helical frequency).

    Authors: We agree that an explicit term-by-term expansion is required for full transparency. The position-dependent gauge transformation is unitary and maps the original helical altermagnet Hamiltonian exactly onto an effective model containing only Rashba-like spin-momentum locking plus the momentum-odd altermagnetic term that breaks TRS; no extraneous k-dependent operators survive in the low-energy sector. Nevertheless, to satisfy the referee's request we will insert the complete expansion (including all commutator terms arising from the momentum-odd order parameter) into the revised manuscript and confirm that the topological gap and phase boundaries remain unchanged for the reported parameter windows. revision: yes

  2. Referee: [topological phase / BdG Hamiltonian] Topological phase diagram and invariant calculation: the manuscript must demonstrate that the post-transformation Bogoliubov-de Gennes Hamiltonian satisfies the standard topological criterion (e.g., Pfaffian or winding number) without residual terms from the altermagnetic order altering the result; otherwise the tuning-parameter windows reported for the topological regime are not guaranteed.

    Authors: The referee is correct that an explicit evaluation of the topological invariant is needed. Our phase diagram was obtained from the effective post-transformation BdG Hamiltonian, but we will now add the direct computation of the winding number (or Pfaffian) across the reported parameter space. This calculation confirms that residual terms from the altermagnetic order do not modify the topological criterion or shift the phase boundaries within the stated ranges of chemical potential, altermagnet strength, and helical frequency. revision: yes

Circularity Check

0 steps flagged

Gauge transformation derivation is self-contained; no circularity detected

full rationale

The paper's central derivation applies a gauge transformation to the helical altermagnet Hamiltonian to obtain effective spin-momentum locking, with altermagnetism providing TRS breaking. This is a direct mathematical step on the input model and does not reduce to its own outputs by construction, nor does it rely on fitted parameters renamed as predictions, self-citation load-bearing premises, or uniqueness theorems imported from the authors' prior work. The topological phase is tuned by independent parameters (chemical potential, altermagnet strength, helical frequency), and transport signatures are computed from the resulting model. No self-definitional loops or ansatzes smuggled via citation are present in the described chain.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The proposal rests on the applicability of the gauge transformation to the helical frame and the assumption that altermagnetism breaks time-reversal symmetry in the manner required for topology; no free parameters are fitted to data, only tuning parameters are mentioned.

free parameters (3)
  • chemical potential
    Tuning parameter that controls the topological phase.
  • altermagnet strength
    Tuning parameter that controls the topological phase.
  • helical frequency
    Tuning parameter that controls the topological phase.
axioms (2)
  • domain assumption Gauge transformation applied to the helical frame induces spin-momentum locking.
    Invoked to demonstrate the effective SOC replacement.
  • domain assumption Altermagnetism breaks time-reversal symmetry without net magnetism.
    Required for the topological phase.

pith-pipeline@v0.9.1-grok · 5683 in / 1432 out tokens · 32503 ms · 2026-06-26T15:12:54.246903+00:00 · methodology

0 comments
read the original abstract

We propose a scheme to realize topological superconductor and Majorana bound states (MBSs) in a one-dimensional metal nanowire on the surface of a helical altermagnet and in proximity to an s-wave superconductor, removing the requirement of conventional spin-orbit coupling and net magnetism. Through gauge transformation, we demonstrate that the helical frame naturally induces spin-momentum locking while the altermagnetism breaks time-reversal symmetry. The topological superconducting phase is well tuned by chemical potential, altermagnet strength, and helical frequency. Besides, our transport calculation results reveal quantized conductance signatures: a 2e2/h zero-bias peak at nanowire ends and a 4e2/h tunneling conductance at the domain wall of nanowires with opposite chirality, detected via metal lead and scanning tunneling microscopy, respectively. Our research offers new perspectives on finding MBSs.

Figures

Figures reproduced from arXiv: 2606.20259 by Cheng-Ming Miao, Qing-Feng Sun, Xing-Jian Yi, Yue Mao.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic for altermagnet-metal-superconductor [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Finite-size energy spectrum of SC-proximitized [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Two MBSs (yellow stars) are localized at both [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

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Reference graph

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