Finite-momentum superconducting states due to odd-frequency Cooper pairing correlations

Satoru Hayami; Shingo Kobayashi; Takumi Sato; Yasuhiro Asano

arxiv: 2503.01673 · v2 · pith:K2CCIXWQnew · submitted 2025-03-03 · ❄️ cond-mat.supr-con

Finite-momentum superconducting states due to odd-frequency Cooper pairing correlations

Takumi Sato , Satoru Hayami , Shingo Kobayashi , Yasuhiro Asano This is my paper

Pith reviewed 2026-05-25 08:50 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con

keywords finite-momentum superconductivityodd-frequency pairingCooper pairing correlationspair fluctuation propagatorinhomogeneous superconductivityweak-coupling superconductors

0 comments

The pith

Finite-momentum superconducting states form when odd-frequency pairing correlations reach large amplitudes in uniform superconductors.

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

This paper examines how Cooper pairs with finite center-of-mass momentum can form in superconductors. It uses the pair fluctuation propagator to identify instabilities in the normal state. The key finding is that sufficiently strong odd-frequency pairing correlations in an otherwise uniform superconducting state trigger these finite-momentum states. This approach offers a way to understand inhomogeneous superconductivity through weak-coupling analysis.

Core claim

The finite-momentum superconducting state is realized when the odd-frequency pairing correlations in the uniform superconducting state are expected to have sufficiently large amplitudes. The analysis relies on locating the pole of the pair fluctuation propagator in weak-coupling superconductors.

What carries the argument

The pole of the pair fluctuation propagator, which signals the instability of the normal state to finite-momentum pairing when odd-frequency correlations have large amplitudes.

If this is right

Finite-momentum states can appear in weak-coupling superconductors when odd-frequency amplitudes are large.
Uniform states with prominent odd-frequency correlations become unstable to nonuniform pairing.
This supplies a perspective for understanding inhomogeneous superconductivity and related phenomena.

Where Pith is reading between the lines

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

Similar pole conditions could be examined in systems with other pairing symmetries that support odd-frequency components.
Measurements that quantify odd-frequency correlation strength might be used to predict the threshold for finite-momentum instability.
The weak-coupling assumption could be tested by adding retardation or strong-coupling corrections to the propagator equation.

Load-bearing premise

The pole of the pair fluctuation propagator in the weak-coupling regime directly signals the instability toward finite-momentum states without additional strong-coupling or retardation effects altering the conclusion.

What would settle it

A calculation showing the absence of a pole indicating finite-momentum instability even when odd-frequency pairing amplitudes are large in a uniform state would falsify the central claim.

Figures

Figures reproduced from arXiv: 2503.01673 by Satoru Hayami, Shingo Kobayashi, Takumi Sato, Yasuhiro Asano.

read the original abstract

This paper discusses the origin of a nonuniform superconducting state in which Cooper pairs have a small but finite center-of-mass momentum. We analyze the instability of the normal state to such finite-momentum states using the pole of the pair fluctuation propagator in weak-coupling superconductors. The finite-momentum superconducting state is realized when the odd-frequency pairing correlations in the uniform superconducting state are expected to have sufficiently large amplitudes. We provide a perspective for a comprehensive understanding of inhomogeneous superconductivity and related phenomena.

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 frames odd-frequency correlations as the driver for finite-momentum states via a pole in the pair fluctuation propagator, but offers only a perspective without new derivations or checks.

read the letter

The core claim is that large odd-frequency pairing amplitudes in a uniform superconductor produce a pole in the fluctuation propagator at finite momentum, signaling instability to nonuniform states. This is presented as a unifying perspective for inhomogeneous superconductivity in weak-coupling systems. The authors position the result as a way to connect several phenomena under one mechanism. What stands out is the explicit tie between odd-frequency correlations and the propagator pole; prior work on odd-frequency pairing exists, but this specific route through the instability analysis is the angle they highlight. The paper does a reasonable job of stating the logic in plain terms and keeping the scope narrow to weak coupling. No new data or machine-checked results appear, and the argument stays conceptual. The main limitation is that the central step assumes the propagator pole maps directly to the finite-momentum instability. Retardation effects or frequency dependence in the interaction could shift or remove that pole once odd-frequency amplitudes grow, yet nothing in the description shows those corrections were examined or shown to be small. The analysis is also limited to the normal-state instability rather than the actual paired state. This is the sort of short perspective that can spark discussion in the unconventional superconductivity community, especially among people already working on odd-frequency or inhomogeneous pairing. It is not a finished calculation, so it would need expansion before publication, but the framing is coherent enough on its own terms to merit referee input rather than an immediate desk reject.

Referee Report

1 major / 1 minor

Summary. The manuscript analyzes the instability of the normal state toward finite-momentum superconducting states (small but finite Cooper-pair center-of-mass momentum) via the pole of the pair fluctuation propagator in weak-coupling superconductors. It concludes that such states are realized precisely when odd-frequency pairing correlations within the uniform superconducting state attain sufficiently large amplitudes, and frames this as a perspective on inhomogeneous superconductivity.

Significance. If the mapping from odd-frequency amplitude to propagator pole holds, the work supplies a concrete link between two previously separate lines of inquiry in superconductivity. The approach employs a standard weak-coupling diagnostic (propagator pole), which is reproducible in principle, but the result's utility rests on whether the weak-coupling limit remains representative once odd-frequency components dominate.

major comments (1)

[Analysis of pair fluctuation propagator (weak-coupling regime)] The central claim equates a pole in the pair-fluctuation propagator (weak-coupling regime) with an instability to finite-momentum order. The manuscript does not examine whether frequency-dependent (retarded) interactions, which are known to shift or suppress poles at finite center-of-mass momentum, remain negligible when odd-frequency amplitudes become large; this assumption is load-bearing for the stated conclusion.

minor comments (1)

[Abstract and introduction] The abstract and introduction would benefit from an explicit statement of the microscopic Hamiltonian or interaction kernel employed in the propagator calculation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the single major comment below and indicate the revisions we will make to clarify the scope of the weak-coupling analysis.

read point-by-point responses

Referee: [Analysis of pair fluctuation propagator (weak-coupling regime)] The central claim equates a pole in the pair-fluctuation propagator (weak-coupling regime) with an instability to finite-momentum order. The manuscript does not examine whether frequency-dependent (retarded) interactions, which are known to shift or suppress poles at finite center-of-mass momentum, remain negligible when odd-frequency amplitudes become large; this assumption is load-bearing for the stated conclusion.

Authors: We agree that the analysis is performed strictly within the weak-coupling limit using the standard (instantaneous-interaction) pair-fluctuation propagator. The central result—that sufficiently large odd-frequency amplitudes in the uniform state produce a pole at finite center-of-mass momentum—is derived and valid inside this controlled approximation. We do not claim that the same mapping necessarily survives once strong retardation is introduced. To address the referee’s concern we will add an explicit paragraph in the discussion section stating the assumptions on the interaction, noting that frequency-dependent effects lie outside the present scope, and indicating that extensions to retarded interactions remain an open question for future work. revision: partial

Circularity Check

0 steps flagged

No circularity; derivation uses standard weak-coupling analysis without self-referential reductions

full rationale

The abstract and provided text present the central claim as arising from analysis of the pair fluctuation propagator pole in the weak-coupling regime, conditioned on large odd-frequency amplitudes in the uniform state. No equations, fitted parameters, or self-citations are exhibited that would make any prediction equivalent to its inputs by construction. The derivation chain is self-contained against external benchmarks such as standard BCS or fluctuation theory, with the reader's score of 2.0 reflecting absence of detectable circular steps rather than any load-bearing self-reference.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The abstract invokes weak-coupling superconductivity and the pair fluctuation propagator without listing explicit free parameters or new entities; the central claim rests on the standard assumption that the propagator pole indicates instability.

axioms (1)

domain assumption Weak-coupling approximation is valid for the superconductors under consideration
The analysis is performed 'in weak-coupling superconductors' as stated in the abstract.

pith-pipeline@v0.9.0 · 5606 in / 1118 out tokens · 31071 ms · 2026-05-25T08:50:34.440906+00:00 · methodology

discussion (0)

Reference graph

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