Supercurrent-induced phonon angular momentum

Takehito Yokoyama

arxiv: 2604.12701 · v1 · submitted 2026-04-14 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Supercurrent-induced phonon angular momentum

Takehito Yokoyama This is my paper

Pith reviewed 2026-05-10 14:37 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con

keywords supercurrent-induced phonon angular momentummixed parity superconductorss-wave superconductorsspin-orbit couplingperturbative calculationelectron-phonon interactionangular momentum transfer

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The pith

Supercurrents induce angular momentum in phonons in mixed-parity and spin-orbit-coupled superconductors.

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

The paper proposes that a supercurrent flowing through certain superconductors can induce angular momentum in the phonons, which are the quanta of lattice vibrations. This is shown for mixed parity superconductors and for conventional s-wave superconductors that include spin-orbit coupling. Analytical expressions for this induced angular momentum are derived using perturbative methods. If this holds, it reveals a direct coupling between the superconducting current and the mechanical degrees of freedom of the crystal lattice, potentially allowing control of phonon properties through electrical means.

Core claim

We propose a mechanism of supercurrent-induced phonon angular momentum in mixed parity superconductors and s-wave superconductors with spin orbit coupling. We derive analytical expressions of phonon angular momentum induced by the supercurrent by perturbative calculation. The physical interpretation of this effect is also discussed.

What carries the argument

Perturbative calculation of supercurrent-induced phonon angular momentum via electron-phonon coupling in the presence of mixed-parity pairing or spin-orbit coupling.

Load-bearing premise

The perturbative calculation remains valid for the supercurrent-induced phonon angular momentum and the chosen models for mixed-parity pairing and spin-orbit coupling accurately capture the relevant physics.

What would settle it

An experimental observation of zero phonon angular momentum in a supercurrent-carrying mixed-parity superconductor would falsify the proposed mechanism.

Figures

Figures reproduced from arXiv: 2604.12701 by Takehito Yokoyama.

**Figure 2.** Figure 2: FIG. 2: The diagrammatic representations of the phonon [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: The diagrammatic representations of the phonon [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: The diagrammatic representations of the phonon [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

read the original abstract

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

Yokoyama derives perturbative expressions for supercurrent-induced phonon angular momentum in mixed-parity and SOC s-wave superconductors, but the validity range for finite currents stays unclear.

read the letter

The core of this paper is a set of analytical expressions for phonon angular momentum generated by supercurrent in mixed-parity superconductors and in s-wave ones that include spin-orbit coupling. Yokoyama starts from standard Bogoliubov-de Gennes models, applies perturbation theory in the supercurrent, and extracts the induced angular momentum along with a physical picture of the coupling. That is the new piece: a concrete mechanism linking supercurrent to phonon angular momentum that had not been written down in this form before. The closed-form results make the dependence on pairing parameters and SOC strength easy to read off, which is useful for anyone thinking about angular-momentum transfer in hybrid devices. The derivation itself appears internally consistent with the models chosen, and the discussion of interpretation is straightforward. The main limitation is that the perturbative expansion is not bounded. There is no explicit condition given on how small the supercurrent velocity or pair momentum must be relative to the gap or critical current, nor any estimate of the size of second-order corrections for realistic parameter values. Without that, it is hard to know whether the expressions apply to measurable currents or only to an infinitesimal regime. The paper stays within its specialized subfield and does not claim broad technological impact, which keeps the claims proportionate. This is the kind of work that belongs in a mesoscopic superconductivity or phonon-dynamics reading group. A reader already familiar with mixed-parity pairing and SOC effects will get the most out of it and can judge whether the expressions are worth testing numerically or experimentally. It is worth sending to peer review so that the derivation can be checked in detail and the range of validity clarified; the central idea is new enough and the approach standard enough that referees can evaluate it on its own terms.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a mechanism for supercurrent-induced phonon angular momentum in mixed-parity superconductors and in s-wave superconductors with spin-orbit coupling. It derives analytical expressions for the induced phonon angular momentum via perturbative calculations starting from standard superconducting models and discusses the physical interpretation of the effect.

Significance. If the perturbative expressions are valid and reduce correctly to known limits, the result would identify a previously unexplored channel for angular-momentum transfer between supercurrent and lattice degrees of freedom. The analytical character of the derivation is a potential strength, but the absence of explicit validity bounds or consistency checks limits immediate impact on the field.

major comments (2)

[Abstract / derivation] Abstract and derivation section: the perturbative expressions for phonon angular momentum are presented without an explicit bound on the expansion parameter (supercurrent velocity or pair momentum q) relative to the gap Δ or critical current. This is load-bearing for the central claim, as higher-order corrections could dominate for any realistic finite supercurrent (see skeptic note on perturbative validity).
[Results / discussion] No reduction to known limits is shown (e.g., vanishing SOC strength, pure s-wave without parity mixing, or q→0). Without these checks the expressions cannot be validated against established results for phonon or quasiparticle angular momentum.

minor comments (2)

[Abstract] The abstract states that analytical expressions were derived but does not display the leading-order formula or the key assumptions (pairing symmetry, SOC term, phonon mode). Adding the explicit first-order result would improve clarity.
[Throughout] Notation for phonon angular momentum (e.g., L_ph) and the supercurrent-induced correction should be defined once at first use and used consistently.

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 the major points below and will revise the manuscript to strengthen the presentation of the perturbative regime and consistency checks.

read point-by-point responses

Referee: [Abstract / derivation] Abstract and derivation section: the perturbative expressions for phonon angular momentum are presented without an explicit bound on the expansion parameter (supercurrent velocity or pair momentum q) relative to the gap Δ or critical current. This is load-bearing for the central claim, as higher-order corrections could dominate for any realistic finite supercurrent (see skeptic note on perturbative validity).

Authors: We agree that an explicit statement of the validity range is important for the central claim. In the revised manuscript we will add a dedicated paragraph in the derivation section specifying the perturbative condition q v_F ≪ Δ (with v_F the Fermi velocity) under which the leading-order expressions are controlled, together with a brief estimate of how this compares to the critical current in representative materials. revision: yes
Referee: [Results / discussion] No reduction to known limits is shown (e.g., vanishing SOC strength, pure s-wave without parity mixing, or q→0). Without these checks the expressions cannot be validated against established results for phonon or quasiparticle angular momentum.

Authors: We acknowledge that explicit reductions to known limits would strengthen the validation of the analytic expressions. In the revised version we will include calculations demonstrating that the phonon angular momentum vanishes when the spin-orbit coupling is set to zero, in the pure s-wave case without parity mixing, and in the q → 0 limit; these checks will be placed in the results section. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation starts from standard models via perturbation

full rationale

The paper proposes a mechanism and derives analytical expressions for supercurrent-induced phonon angular momentum using perturbative calculations on mixed-parity superconductors and s-wave superconductors with spin-orbit coupling. No steps reduce by construction to fitted inputs, self-definitions, or self-citation chains; the expressions are obtained from standard BCS-like Hamiltonians and perturbative expansions without renaming known results or smuggling ansatze via prior self-citations. The approach is self-contained against external benchmarks of superconducting theory.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are stated. The work relies on standard perturbative methods and existing superconductivity models.

pith-pipeline@v0.9.0 · 5316 in / 1030 out tokens · 22427 ms · 2026-05-10T14:37:57.727356+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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