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arxiv: 2501.10619 · v2 · submitted 2025-01-18 · ❄️ cond-mat.supr-con

Properties of two level systems in current-carrying superconductors

T. Liu , A. V. Andreev , B. Z. Spivak This is my paper

Pith reviewed 2026-05-23 05:37 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords two-level systemsdisordered superconductorsdc supercurrentac conductivity1/f noisecurrent fluctuationsTLS
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The pith

In disordered superconductors, a dc supercurrent dramatically increases the coupling of two-level systems to ac electric fields at low frequencies, enhancing conductivity and fluctuations.

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

The paper establishes that in disordered superconductors a direct current supercurrent causes two-level systems to interact much more strongly with alternating electric fields when the frequency is sufficiently low. This enhancement affects linear responses like conductivity as well as nonlinear effects. It produces a large increase in the real part of the ac conductivity and therefore in equilibrium current fluctuations. When the relaxation times of the two-level systems spread over a wide range the conductivity becomes inversely proportional to frequency and the noise spectrum follows a 1/f form.

Core claim

In disordered superconductors, at sufficiently low frequencies ω, the coupling of TLS to external ac electric fields increases dramatically in the presence of a dc supercurrent. This giant enhancement manifests in all ac linear and nonlinear phenomena. In particular, it leads to a parametric enhancement of the real part of the ac conductivity and, consequently, of the equilibrium current fluctuations. If the distribution of TLS relaxation times is broad, the conductivity is inversely proportional to ω, and the spectrum of the equilibrium current fluctuations takes the form of 1/f noise.

What carries the argument

Two-level systems (TLS) whose coupling to ac electric fields is parametrically enhanced by the dc supercurrent through changes in their energy splittings or relaxation rates.

Load-bearing premise

The dc supercurrent modifies the energy splittings or relaxation rates of the two-level systems in a way that amplifies their ac response without other relaxation channels dominating.

What would settle it

Measure the real part of ac conductivity in a disordered superconductor at low frequencies both with and without applied dc supercurrent to check for the predicted parametric increase.

Figures

Figures reproduced from arXiv: 2501.10619 by A. V. Andreev, B. Z. Spivak, T. Liu.

Figure 1
Figure 1. Figure 1: Qualitative picture of a TLS potential plotted [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the Friedel oscillations caused [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Feynman diagrams for calculating ⟨(δn) 2 ⟩. The dashed lines represent disorder averaging. The solid line correspond to the electron Green’s functions, which are matrices in the Gorkov-Nambu space. cay of the Friedel oscillation amplitude with the distance from the impurity, the value of n(r) is determined primar￾ily by impurities closest to the TLS. However, the sensi￾tivity of the electron density to the… view at source ↗
read the original abstract

We show that in disordered superconductors, at sufficiently low frequencies $\omega$, the coupling of TLS to external ac electric fields increases dramatically in the presence of a dc supercurrent. This giant enhancement manifests in all ac linear and nonlinear phenomena. In particular, it leads to a parametric enhancement of the real part of the ac conductivity and, consequently, of the equilibrium current fluctuations. If the distribution of TLS relaxation times is broad, the conductivity is inversely proportional to $\omega$, and the spectrum of the equilibrium current fluctuations takes the form of 1/f noise.

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 / 0 minor

Summary. The manuscript claims that in disordered superconductors, a dc supercurrent dramatically increases the coupling of two-level systems (TLS) to external ac electric fields at sufficiently low frequencies ω. This giant enhancement affects all ac linear and nonlinear phenomena, producing a parametric increase in the real part of the ac conductivity and thus in equilibrium current fluctuations; when the TLS relaxation-time distribution is broad, the conductivity scales as 1/ω and the fluctuations exhibit 1/f noise.

Significance. If the underlying microscopic model is valid and the enhancement is genuinely derived rather than assumed, the result would be significant for understanding and controlling 1/f noise and dissipation in superconducting devices and circuits. No machine-checked proofs, parameter-free limits, or reproducible code are indicated, so the significance remains conditional on the correctness of the supercurrent-TLS interaction mechanism.

major comments (2)
  1. [Abstract] Abstract: the central claim is presented as a derived consequence of the supercurrent-TLS interaction model, yet no derivation steps, explicit equations, or functional dependence of TLS splittings/relaxation rates on the supercurrent are supplied. This makes it impossible to verify whether the parametric enhancement follows from the model or is an input assumption, which is load-bearing for the entire result.
  2. The weakest assumption—that the specific microscopic model for how the dc supercurrent alters TLS parameters is complete and that no other relaxation channels dominate—is not tested or justified in the provided text; if this model is incomplete, the predicted giant enhancement of Re(σ) and the 1/f spectrum do not follow.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying points where additional clarity would strengthen the presentation. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim is presented as a derived consequence of the supercurrent-TLS interaction model, yet no derivation steps, explicit equations, or functional dependence of TLS splittings/relaxation rates on the supercurrent are supplied. This makes it impossible to verify whether the parametric enhancement follows from the model or is an input assumption, which is load-bearing for the entire result.

    Authors: The abstract provides a concise summary of the central result. The explicit derivation of the supercurrent-TLS interaction, including the functional dependence of the TLS splitting and relaxation rates on the dc supercurrent, begins from the microscopic Hamiltonian in Section II and is carried through in Section III. The key equations showing the parametric enhancement at low ω are derived there rather than assumed. To improve accessibility, we will revise the abstract to include a brief reference to these sections and the leading equation for the modified TLS parameters. revision: yes

  2. Referee: [—] The weakest assumption—that the specific microscopic model for how the dc supercurrent alters TLS parameters is complete and that no other relaxation channels dominate—is not tested or justified in the provided text; if this model is incomplete, the predicted giant enhancement of Re(σ) and the 1/f spectrum do not follow.

    Authors: The microscopic model is introduced in Section I and justified in Section IV by reference to standard TLS phenomenology in disordered superconductors together with an explicit estimate showing that alternative relaxation channels remain subdominant in the low-frequency, low-temperature regime of interest. We acknowledge that this constitutes a central assumption of the work. In the revised manuscript we will expand the discussion in Section IV to include a more detailed comparison with possible competing mechanisms and to state the regime of validity more explicitly. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation follows from independent microscopic model input

full rationale

The paper presents a theoretical derivation showing enhanced TLS-ac field coupling due to dc supercurrent in disordered superconductors, leading to parametric enhancement of Re(σ) and 1/f noise when relaxation times are broadly distributed. This follows from an assumed microscopic interaction model (how supercurrent alters TLS splittings/relaxation rates), which is an external input rather than a self-derived or fitted quantity. No load-bearing steps reduce by construction to the target result via self-definition, fitted inputs renamed as predictions, or self-citation chains. The central claim is a consequence of the model assumptions, not equivalent to them.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review prevents full enumeration; the claim rests on an unstated microscopic model of supercurrent-TLS coupling and on the assumption of a broad TLS relaxation-time distribution for the 1/f conclusion.

axioms (2)
  • domain assumption Broad distribution of TLS relaxation times produces 1/ω conductivity and 1/f noise
    Invoked conditionally in the abstract for the noise spectrum result.
  • domain assumption dc supercurrent parametrically modifies TLS-ac coupling in disordered superconductors
    Central modeling assumption underlying the enhancement claim.

pith-pipeline@v0.9.0 · 5619 in / 1291 out tokens · 31983 ms · 2026-05-23T05:37:51.023864+00:00 · methodology

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Reference graph

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