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arxiv: 2511.00837 · v2 · submitted 2025-11-02 · ❄️ cond-mat.supr-con

Instability toward Superconducting Stripe Phase in Altermagnets with Strong Rashba Spin-Orbit Coupling

Kohei Mukasa , Yusuke Masaki This is my paper

Pith reviewed 2026-05-18 01:44 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords altermagnetsRashba spin-orbit couplingstripe superconductivityfinite-momentum pairingnoncentrosymmetric materialsFermi surface deformationd-wave spin splittinglinearized gap equation
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The pith

Noncentrosymmetric altermagnets with strong Rashba coupling develop an instability to a superconducting stripe phase with multiple pair momenta.

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

The paper examines how superconductivity with finite center-of-mass momentum behaves in noncentrosymmetric altermagnets that have d-wave spin splitting and intense Rashba spin-orbit coupling. Numerical calculations produce phase diagrams that distinguish a stripe phase featuring multiple pair momenta from a simpler helical phase with a single momentum. The stripe phase appears preferentially at low temperatures and reenters as the altermagnetic splitting is varied. The underlying reason is traced to the anisotropic warping of the Fermi surfaces by the altermagnetic order, which creates a distinctive pairing channel when solved in the linearized gap equation.

Core claim

In noncentrosymmetric metallic altermagnets with d-wave spin-splitting and strong Rashba-type spin-orbit coupling, numerical investigation reveals that a superconducting stripe phase, in which Cooper pairs acquire multiple center-of-mass momenta, emerges at low temperatures and exhibits reentrant behavior as a function of the altermagnetic splitting strength. Analysis within the linearized gap equation uncovers that the pairing formation mechanism unique to this stripe phase originates from the anisotropic deformation of the Fermi surfaces induced by the altermagnetic splitting.

What carries the argument

Anisotropic deformation of the Fermi surfaces induced by the d-wave altermagnetic splitting, which drives the unique pairing instability in the stripe phase as captured by the linearized gap equation.

If this is right

  • Phase diagrams reveal boundaries separating the stripe phase from the helical phase.
  • The stripe phase emerges at low temperatures and exhibits reentrant behavior as a function of altermagnetic splitting strength.
  • The pairing mechanism is unique to the stripe phase and originates from anisotropic Fermi surface deformation.
  • The results highlight the interplay between spin-orbit coupling and altermagnetic splitting in determining the superconducting order.

Where Pith is reading between the lines

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

  • Tuning Rashba coupling or altermagnetic order parameter could experimentally control transitions between helical and stripe phases.
  • Similar instabilities may occur in other systems with competing spin orders and strong spin-orbit coupling, broadening searches for finite-momentum superconductivity.
  • Momentum-resolved spectroscopy or transport measurements could detect signatures of multiple pair momenta in the low-temperature phase.

Load-bearing premise

The numerical model assumes a metallic altermagnet with d-wave spin-splitting and strong Rashba-type spin-orbit coupling in a noncentrosymmetric setting, together with the validity of the linearized gap equation for capturing the stripe-phase instability.

What would settle it

A calculation or measurement showing the stripe-phase instability and reentrant behavior vanish when the altermagnetic splitting is made isotropic or when the Rashba coupling strength is set to zero.

read the original abstract

We numerically investigate finite-momentum superconductivity in noncentrosymmetric metallic altermagnets with $d$-wave spin-splitting and strong Rashba-type spin-orbit coupling. Focusing on a stripe phase in which Cooper pairs acquire multiple center-of-mass momenta, we construct phase diagrams that reveal phase boundaries between the stripe phase and a helical phase characterized by a single center-of-mass momentum. Our results show that the stripe phase emerges at low temperatures and exhibits a reentrant behavior as a function of the strength of the altermagnetic splitting. We further analyze the stripe phase within a linearized gap equation, and uncover the mechanism of the pairing formation unique to the stripe phase. This mechanism originates from the anisotropic deformation of the Fermi surfaces induced by the altermagnetic splitting, highlighting the intriguing interplay between the spin-orbit coupling and the altermagnets.

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 / 2 minor

Summary. The manuscript numerically investigates finite-momentum superconductivity in noncentrosymmetric metallic altermagnets with d-wave spin-splitting and strong Rashba-type spin-orbit coupling. It constructs phase diagrams revealing boundaries between a stripe phase (multiple center-of-mass momenta for Cooper pairs) and a helical phase (single center-of-mass momentum). The stripe phase is reported to emerge at low temperatures and to exhibit reentrant behavior as a function of altermagnetic splitting strength. The pairing mechanism unique to the stripe phase is analyzed via the linearized gap equation and traced to anisotropic deformation of the Fermi surfaces induced by the altermagnetic splitting.

Significance. If the numerical results and mechanism hold, the work identifies a distinctive finite-momentum pairing instability arising from the interplay of altermagnetic order and Rashba spin-orbit coupling. This adds a concrete example of stripe superconductivity in a noncentrosymmetric setting and supplies a Fermi-surface-based explanation that could guide searches for similar phases in candidate materials. The reentrant behavior versus splitting strength constitutes a falsifiable prediction.

major comments (1)
  1. [Numerical results section (phase diagrams)] Numerical results section (phase diagrams): The reported phase boundaries and reentrant behavior are presented without error bars, explicit convergence tests with respect to momentum-space discretization or system size, or details on how the critical temperatures and momenta were extracted from the gap equation solutions. These omissions make it difficult to judge the robustness of the central claim that the stripe phase is stable over a finite range of parameters.
minor comments (2)
  1. [Abstract and setup] The abstract and main text refer to 'multiple center-of-mass momenta' for the stripe phase; a brief clarification of how these momenta are selected or discretized in the numerical implementation would improve reproducibility.
  2. [Linearized gap equation analysis] The linearized gap equation analysis would benefit from an explicit statement of the cutoff or regularization scheme employed when solving for the instability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation of our work and for the constructive comment on the numerical results. We address the concern point by point below and will revise the manuscript to improve clarity and robustness.

read point-by-point responses

  1. Referee: Numerical results section (phase diagrams): The reported phase boundaries and reentrant behavior are presented without error bars, explicit convergence tests with respect to momentum-space discretization or system size, or details on how the critical temperatures and momenta were extracted from the gap equation solutions. These omissions make it difficult to judge the robustness of the central claim that the stripe phase is stable over a finite range of parameters.

    Authors: We agree that the current presentation would benefit from additional numerical details to allow readers to assess robustness. In the revised manuscript we will expand the Numerical results section (and add a dedicated methods subsection) to include: (i) error bars on the reported phase boundaries, obtained from the numerical tolerance of the gap-equation solver and from repeated solutions with small random perturbations; (ii) explicit convergence tests with respect to momentum-space discretization (e.g., grids of 64×64, 128×128 and 256×256 points) and effective system size, shown both in the main text and supplementary material; and (iii) a clear description of the extraction procedure, namely that Tc is identified as the temperature at which the largest eigenvalue of the linearized gap-equation matrix crosses unity and that the center-of-mass momenta are determined by maximizing the pairing susceptibility over a dense sampling of the Brillouin zone. These additions will not alter the reported phase boundaries or the reentrant behavior but will make the supporting evidence fully transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper reports a numerical study of finite-momentum pairing instabilities in a model Hamiltonian that includes explicit d-wave altermagnetic splitting plus Rashba SOC on a noncentrosymmetric lattice. Phase boundaries, reentrant behavior, and the pairing mechanism are obtained by solving the linearized gap equation on the resulting anisotropic Fermi surfaces; these outputs are direct consequences of the stated microscopic model rather than redefinitions or self-consistent fits of the target quantities. No load-bearing self-citations, ansatz smuggling, or uniqueness theorems imported from prior author work are invoked to force the central results. The approach follows standard mean-field practice for incommensurate superconductivity and remains externally falsifiable against the model assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger records the modeling assumptions stated there; no free parameters, invented entities, or additional axioms can be extracted beyond the domain assumptions of the altermagnet-plus-Rashba setup.

axioms (1)
  • domain assumption The system is a noncentrosymmetric metallic altermagnet possessing d-wave spin-splitting together with strong Rashba-type spin-orbit coupling.
    This is the explicit physical setting used for the numerical investigation and phase-diagram construction.

pith-pipeline@v0.9.0 · 5678 in / 1415 out tokens · 31073 ms · 2026-05-18T01:44:23.916097+00:00 · methodology

discussion (0)

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Reference graph

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