arxiv: 2604.26862 · v1 · submitted 2026-04-29 · ❄️ cond-mat.supr-con · quant-ph

Recognition: unknown

Non-local Tunneling Spectroscopy of Inelastic Quasiparticle Relaxation in Superconducting 1-D Wires

Detlef Beckmann, Kevin M. Ryan, Venkat Chandrasekhar

Pith reviewed 2026-05-07 11:58 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con quant-ph

keywords non-local tunnelingquasiparticle relaxationinelastic scatteringsuperconducting wiresNIS tunnel junctionspair-breakingenergy imbalance

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The pith

Non-local tunneling in superconducting wires shows anti-symmetric conductance features from inelastic quasiparticle relaxation at energies near 3Δ.

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

This paper develops a dual-bias tunneling method to probe how quasiparticles lose energy in one-dimensional superconductors. By measuring non-local conductance between three terminals in copper-aluminum devices, the authors separate the effects of energy imbalance from other processes using symmetry. They find distinct conductance signals that turn on sharply when tunneling starts at about three times the superconducting gap energy. Comparing the data to simulations that include inelastic scattering gives estimates for how quickly quasiparticles relax at different energies. This approach works at millikelvin temperatures and directly accesses both charge and energy imbalance over coherence-length scales.

Core claim

In mesoscopic three-terminal Cu and Al NIS devices, a dual-bias scheme extracts the effect of quasiparticle energy imbalance on the self-consistent pair potential via symmetry considerations. Non-local conductance features due to pair-breaking are observed that are anti-symmetric with respect to voltage bias polarity, showing a sharp onset during single-electron tunneling at energies around 3Δ. These findings are compared with quasiclassical simulations including inelastic effects to estimate the energy-dependent inelastic scattering time. Kinetic effects from applied supercurrent are also captured and decomposed with respect to particle-hole symmetry and supercurrent direction.

What carries the argument

Dual-bias non-local tunneling spectroscopy, which uses detector biases above and below the gap to isolate quasiparticle energy imbalance effects on the pair potential through anti-symmetric conductance signatures.

If this is right

The method yields estimates of the energy-dependent inelastic scattering time in superconducting wires.
Supercurrent-induced kinetic effects can be isolated and decomposed according to particle-hole symmetry and current direction.
Non-local measurements provide spectroscopic access to quasiparticle transport and relaxation at millikelvin temperatures over coherence-length distances.
The dual-bias symmetry approach can be extended to study further inelastic and nonequilibrium processes in similar devices.

Where Pith is reading between the lines

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

This non-local method could quantify quasiparticle relaxation rates relevant to poisoning in superconducting qubits or detectors.
Applying the technique across different wire lengths or materials might map how geometry and disorder influence inelastic processes.
Combining the approach with supercurrent control could separate relaxation channels that are otherwise mixed in local measurements.

Load-bearing premise

The anti-symmetric non-local conductance features are caused only by the quasiparticle energy imbalance changing the pair potential, without meaningful interference from local heating, multiple scattering, or other effects.

What would settle it

If quasiclassical simulations without an inelastic scattering term still reproduce the observed anti-symmetric non-local conductance features with a sharp onset at 3Δ.

Figures

Figures reproduced from arXiv: 2604.26862 by Detlef Beckmann, Kevin M. Ryan, Venkat Chandrasekhar.

**Figure 1.** Figure 1: FIG. 1. False Color SEM Micrograph of one device. The view at source ↗

**Figure 2.** Figure 2: FIG. 2. Normalized local conductance of the three junctions view at source ↗

**Figure 3.** Figure 3: FIG. 3. Normalized non-local conductance due to charge view at source ↗

**Figure 4.** Figure 4: FIG. 4. a.)+b.) Normalized non-local conductance between the view at source ↗

**Figure 5.** Figure 5: FIG. 5. a.) Heatmap plot of the local conductance of the view at source ↗

**Figure 7.** Figure 7: FIG. 7. a.) Heatmap of the local conductance of the injector view at source ↗

**Figure 10.** Figure 10: FIG. 10. a.) Symmetric part view at source ↗

**Figure 11.** Figure 11: b shows this via the distribution function view at source ↗

**Figure 11.** Figure 11: FIG. 11. a.) Normalized self-consistent pair potential ∆ as view at source ↗

**Figure 13.** Figure 13: FIG. 13. Asymmetric part view at source ↗

**Figure 15.** Figure 15: FIG. 15. Sub-gap region of the non-local conductance data view at source ↗

read the original abstract

Non-local conductance experiments using tunnel junctions can provide valuable spectroscopic information on both the transport and relaxation of quasiparticles in superconductors, as these techniques directly probe the quasiparticle charge and energy imbalance even at mK temperatures. In this work, we employ mesoscopic three terminal Cu and Al NIS devices to study non-local quasiparticle transport over length-scales on the order of the superconducting coherence length in this regime. Via a dual-bias scheme, which utilizes detector biases both above and below the superconducting gap, we are able to extract the effect of quasiparticle energy imbalance via its impact on the self consistent pair potential by symmetry considerations. We observe non-local conductance features due to pair-breaking which are anti-symmetric with respect to the polarity of the voltage bias, with a sharp onset during single electron tunneling at energies around $3\Delta$. We compare these findings with quasiclassical simulations including inelastic effects to obtain estimates of the energy dependent inelastic scattering time. In addition, we demonstrate kinetic effects due to a large applied supercurrent which can also be captured in this formalism and decomposed with respect to the particle-hole symmetry and supercurrent direction, and discuss further opportunities for the advancement of this method.

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

Dual-bias non-local tunneling isolates an anti-symmetric signal at 3Δ that they fit to inelastic relaxation, but the exclusion of heating and other odd-parity backgrounds is not yet tight.

read the letter

The main takeaway here is that this work introduces a dual-bias non-local tunneling method to isolate quasiparticle energy imbalance effects in superconducting wires, leading to estimates of energy-dependent inelastic scattering times from features at around 3Δ. What stands out is the use of symmetry in the dual-bias scheme to separate the anti-symmetric signal due to pair-breaking from symmetric contributions. They observe this in Cu/Al NIS devices over coherence length scales at millikelvin temperatures, and match it to quasiclassical simulations that include inelastic processes. Extending it to supercurrent effects shows they can decompose those too. This seems like a practical advance for probing relaxation in mesoscopic superconductors. On the soft side, the quantitative inelastic times come from fitting the data to the simulations, so they depend on the chosen model parameters for inelastic scattering. The stress-test note raises a fair point: it's not obvious from the description how they bound contributions from local heating or multiple Andreev reflections that might also produce odd signals under bias. Without seeing the full data, error analysis, or explicit checks where inelastic channels are suppressed, it's hard to be fully confident the signal is purely from the intended mechanism. This paper is aimed at people working on superconducting quantum devices and quasiparticle dynamics in 1D systems. A reader interested in new spectroscopic tools for relaxation times would get something out of it. I think it should go to peer review. The observations look real and the method has potential, even if the interpretation needs tighter controls in revision.

Referee Report

2 major / 2 minor

Summary. The paper reports non-local conductance measurements in three-terminal mesoscopic Cu/Al NIS devices using a dual-bias scheme to isolate anti-symmetric features in the detector signal. These features, with a sharp onset at energies around 3Δ during single-electron tunneling, are attributed to pair-breaking induced by quasiparticle energy imbalance that modifies the self-consistent superconducting gap. The observations are compared to quasiclassical simulations that incorporate inelastic scattering to extract an energy-dependent inelastic scattering time; the work also examines kinetic effects from an applied supercurrent that can be decomposed by particle-hole symmetry and supercurrent direction.

Significance. If the attribution to inelastic quasiparticle relaxation holds after background controls, the dual-bias symmetry method offers a spectroscopic probe of energy-dependent inelastic times at millikelvin temperatures, which is relevant for quasiparticle dynamics in superconducting circuits and detectors. The approach builds on existing non-local tunneling techniques by leveraging symmetry to separate energy-imbalance effects from charge imbalance.

major comments (2)

[Abstract / dual-bias method description] Abstract and the description of the dual-bias scheme: the central claim that the observed anti-symmetric non-local conductance features arise exclusively from quasiparticle energy imbalance acting on the self-consistent pair potential requires quantitative bounds on possible contributions from local heating, multiple Andreev reflections, or charge-imbalance relaxation. The manuscript provides no explicit simulations or experimental checks demonstrating that these polarity-odd backgrounds are negligible after dual-bias subtraction or that the feature vanishes when inelastic channels are suppressed.
[Simulation comparison section] Comparison with quasiclassical simulations: the energy-dependent inelastic scattering time is obtained by fitting experimental curves to the model; however, the manuscript does not report the fitting procedure, parameter uncertainties, goodness-of-fit metrics, or sensitivity analysis to the choice of inelastic-process parameters. This makes it difficult to assess whether the extracted times are robust or model-dependent.

minor comments (2)

[Abstract] Notation for the superconducting gap and coherence length should be defined consistently at first use; the abstract uses Δ without prior definition.
[Figure captions] Figure captions for the non-local conductance plots should explicitly state the bias configuration (which junction is biased, which is the detector) and the subtraction procedure used to obtain the anti-symmetric component.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify the presentation of our results. We address each major comment below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract / dual-bias method description] Abstract and the description of the dual-bias scheme: the central claim that the observed anti-symmetric non-local conductance features arise exclusively from quasiparticle energy imbalance acting on the self-consistent pair potential requires quantitative bounds on possible contributions from local heating, multiple Andreev reflections, or charge-imbalance relaxation. The manuscript provides no explicit simulations or experimental checks demonstrating that these polarity-odd backgrounds are negligible after dual-bias subtraction or that the feature vanishes when inelastic channels are suppressed.

Authors: We agree that quantitative bounds on residual backgrounds would strengthen the central claim. The dual-bias scheme isolates the anti-symmetric (odd) component of the non-local conductance, which by particle-hole symmetry arguments eliminates even-in-bias contributions such as local heating and charge-imbalance relaxation. Multiple Andreev reflections are suppressed by the tunnel-junction transparency and bias range used. Nevertheless, the manuscript does not contain explicit simulations bounding any residual odd-parity backgrounds or a demonstration that the feature disappears when inelastic scattering is suppressed. In the revised version we will add an appendix with (i) estimates of the magnitude of possible MAR and heating contributions under our experimental conditions and (ii) a theoretical discussion, supported by additional quasiclassical simulations, showing that the anti-symmetric pair-breaking feature vanishes in the absence of inelastic quasiparticle relaxation (e.g., when the inelastic scattering time is taken to infinity). revision: yes
Referee: [Simulation comparison section] Comparison with quasiclassical simulations: the energy-dependent inelastic scattering time is obtained by fitting experimental curves to the model; however, the manuscript does not report the fitting procedure, parameter uncertainties, goodness-of-fit metrics, or sensitivity analysis to the choice of inelastic-process parameters. This makes it difficult to assess whether the extracted times are robust or model-dependent.

Authors: We acknowledge that the fitting details were not reported with sufficient rigor. The energy-dependent inelastic scattering time τ(ε) was obtained by minimizing the squared deviation between the measured anti-symmetric conductance and the quasiclassical solution for a range of bias voltages. In the revised manuscript we will (i) describe the fitting algorithm and the functional form assumed for τ(ε), (ii) report the reduced χ² values and the covariance matrix for the fitted parameters, (iii) provide one-standard-deviation uncertainties on the extracted τ(ε), and (iv) include a sensitivity analysis in which the inelastic scattering kernel (electron-phonon versus other processes) and the gap-suppression model are varied. These additions will allow readers to judge the robustness of the reported energy dependence. revision: yes

Circularity Check

0 steps flagged

No significant circularity: direct observation plus standard model fitting for inelastic time

full rationale

The paper reports an experimental observation of anti-symmetric non-local conductance features with onset at ~3Δ, extracted via dual-bias symmetry in a three-terminal NIS setup. It then compares these data to quasiclassical simulations that incorporate inelastic scattering to extract an energy-dependent scattering time. This comparison is ordinary parameter fitting to match observed curves; the fitted value is not presented as an independent first-principles prediction, nor does any equation reduce to its own input by construction. No self-definitional loops, load-bearing self-citations, or renamed known results appear in the provided abstract or description. The central experimental claim stands on its own data and symmetry argument without requiring the fit for validity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of quasiclassical theory to the mesoscopic devices and the validity of symmetry arguments for isolating energy imbalance; the inelastic scattering time is estimated rather than independently measured.

free parameters (1)

energy-dependent inelastic scattering time
Obtained by matching measured non-local conductance to quasiclassical simulations that include inelastic effects.

axioms (2)

domain assumption Quasiclassical Usadel or Eilenberger equations adequately describe quasiparticle transport and relaxation in the 1D wires at the studied length scales.
Invoked when comparing data to simulations that include inelastic scattering.
domain assumption Symmetry considerations cleanly separate the energy-imbalance contribution from other effects in the dual-bias configuration.
Stated as the basis for extracting the pair-potential impact.

pith-pipeline@v0.9.0 · 5525 in / 1518 out tokens · 70283 ms · 2026-05-07T11:58:33.775576+00:00 · methodology

discussion (0)

Reference graph

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