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arxiv: 2602.06781 · v2 · pith:7TQ4WQ4Unew · submitted 2026-02-06 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Current precision in interacting hybrid Normal-Superconducting systems

Nahual Sobrino , Fabio Taddei , Rosario Fazio , Michele Governale This is my paper

Pith reviewed 2026-05-16 06:22 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords Andreev transportCoulomb interactionsquantum dotscurrent fluctuationsthermodynamic uncertainty relationshybrid systemsmaster equationfull counting statistics
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0 comments X

The pith

Coulomb interactions reduce the precision of Andreev-mediated currents in normal-superconducting quantum dots by renormalizing resonances and suppressing coherence.

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

The paper studies Andreev transport and fluctuations in interacting normal-superconducting quantum-dot systems using a real-time diagrammatic master equation and full counting statistics in the large superconducting-gap limit. It shows that Coulomb interactions shift resonant conditions and weaken superconducting coherence, which sharply lowers current precision even in regimes where the average current changes only weakly. These effects become especially visible at high temperatures, where thermal smearing erases standard Coulomb-blockade signatures in the mean current yet leaves noise and entropy production highly responsive. The analysis of thermodynamic uncertainty relations further indicates that interactions suppress violations of the quantum bound observed without interactions while the hybrid bound continues to hold.

Core claim

In normal-superconducting quantum-dot systems, Coulomb interactions modify Andreev-mediated transport by renormalizing resonant conditions and suppressing superconducting coherence. This produces a pronounced reduction in current precision, even when the average current is only weakly affected. The reduction appears clearly at high temperatures where conventional Coulomb-blockade features are thermally smeared, yet fluctuation properties remain sensitive. Thermodynamic uncertainty relations show that interactions progressively reduce violations of the quantum bound present in the noninteracting case, while the hybrid bound remains satisfied.

What carries the argument

Real-time diagrammatic master equation with full counting statistics applied in the large superconducting-gap limit to obtain steady-state current, zero-frequency noise, and entropy production.

Load-bearing premise

The calculation assumes the large superconducting-gap limit and that the real-time diagrammatic master equation remains valid when Coulomb interactions are included.

What would settle it

Measure the ratio of zero-frequency noise to the square of the average current (Fano factor) while tuning Coulomb interaction strength in a quantum dot coupled to normal and superconducting leads; the claim would be falsified if precision fails to drop with increasing interaction while the mean current stays nearly constant.

Figures

Figures reproduced from arXiv: 2602.06781 by Fabio Taddei, Michele Governale, Nahual Sobrino, Rosario Fazio.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic setup representation of the two interacting [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Superconducting current, (b) Noise, and (c) Rate of entropy production in the single dot setup as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Violation of the quantum TUR in the single dot as [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (Up) Superconducting current, (Center) Noise, and [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Violation of the quantum TUR in the single dot as [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Superconducting current, and (b) noise as a func [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Superconducting current, and (b) noise as a func [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Superconducting current [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Superconducting current, zero-frequency noise, and classical and quantumTURs of a single quantum dot, shown as [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Superconducting current, zero-frequency noise, and classical and quantum TURs of a Cooper-pair splitter, shown as [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
read the original abstract

We study Andreev-mediated transport and current fluctuations in interacting normal-superconducting quantum-dot systems. Using a generalized master equation based on real-time diagrammatics and full counting statistics, we compute the steady-state current, zero-frequency noise, and rate of entropy production in the large superconducting-gap limit. We show how Coulomb interactions modify Andreev-mediated transport by renormalizing resonant conditions and suppressing superconducting coherence, leading to a pronounced reduction of current precision even when average currents are only weakly affected. These effects are particularly evident at high temperatures, where conventional Coulomb-blockade features are thermally smeared while fluctuation properties remain highly sensitive. By analyzing thermodynamic uncertainty relations, we demonstrate that violations of the quantum bound present in the noninteracting regime are progressively reduced and eventually suppressed as interactions increase, whereas the recently proposed hybrid bound remains satisfied. Our results clarify how Coulomb interactions, and nonequilibrium fluctuations jointly determine transport properties in hybrid superconducting devices, and establish current precision as a robust benchmark for interacting Andreev transport beyond the noninteracting limit.

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

3 major / 2 minor

Summary. The paper studies Andreev-mediated transport and current fluctuations in interacting normal-superconducting quantum-dot systems. Using a generalized master equation based on real-time diagrammatics and full counting statistics, it computes the steady-state current, zero-frequency noise, and entropy production rate in the large superconducting-gap limit. The central result is that Coulomb interactions renormalize resonant conditions, suppress superconducting coherence, and produce a pronounced reduction in current precision even when average currents remain only weakly affected; these effects persist at high temperatures where Coulomb-blockade features are thermally smeared. The work further shows that violations of the quantum thermodynamic uncertainty relation present in the noninteracting case are progressively suppressed with increasing interaction strength, while a recently proposed hybrid bound remains satisfied.

Significance. If the master-equation framework is validated, the results would be significant for hybrid superconducting devices: they establish current precision (noise-to-current ratio) as a sensitive diagnostic of interaction effects that survives thermal smearing and provide concrete evidence that interactions can eliminate quantum-bound violations while preserving a hybrid bound. The combination of full-counting statistics with diagrammatic resummation for finite U offers a practical route to fluctuation properties beyond the noninteracting limit.

major comments (3)
  1. [§2] §2 (model and master equation): The derivation of the generalized real-time diagrammatic master equation for finite U in the Δ→∞ limit is presented without explicit benchmarks against exact methods (e.g., numerical renormalization group or exact diagonalization for small dot levels). Because the central claims on resonance renormalization and coherence suppression rest on this equation, the absence of such checks leaves open whether interaction-induced shifts in Andreev bound-state energies or coherence factors are correctly captured.
  2. [§4.2] §4.2 (thermodynamic uncertainty relations): The reported suppression of quantum-bound violations with increasing U is shown only for the steady-state current and noise; it is unclear whether the same trend holds for the entropy-production rate when the large-gap projection is relaxed or when higher-order tunneling processes are retained.
  3. [§3.1] §3.1 (high-temperature regime): The statement that fluctuation properties remain highly sensitive while average currents are weakly affected is illustrated for specific parameter sets; a systematic scan of the noise-to-current ratio versus U and temperature, including the noninteracting reference curve, is needed to quantify the claimed “pronounced reduction.”
minor comments (2)
  1. Notation for the counting field and the cumulant-generating function should be unified between the main text and the supplementary material to avoid confusion when comparing current and noise expressions.
  2. Figure captions for the precision plots should explicitly state the value of the superconducting gap (taken to infinity) and the tunnel-coupling asymmetry used in each panel.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the careful reading, positive assessment of significance, and constructive suggestions. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [§2] §2 (model and master equation): The derivation of the generalized real-time diagrammatic master equation for finite U in the Δ→∞ limit is presented without explicit benchmarks against exact methods (e.g., numerical renormalization group or exact diagonalization for small dot levels). Because the central claims on resonance renormalization and coherence suppression rest on this equation, the absence of such checks leaves open whether interaction-induced shifts in Andreev bound-state energies or coherence factors are correctly captured.

    Authors: We agree that explicit benchmarks would strengthen the validation of the master equation. In the Δ→∞ limit the diagrammatic resummation reproduces the exact non-interacting (U=0) results by construction, and we have cross-checked limiting cases against known perturbative expansions. To address the concern directly we will add an appendix that compares the interacting results for a minimal two-level dot to exact diagonalization of the corresponding rate matrix, confirming that the resonance shifts and coherence suppression are captured correctly within the large-gap projection. revision: yes

  2. Referee: [§4.2] §4.2 (thermodynamic uncertainty relations): The reported suppression of quantum-bound violations with increasing U is shown only for the steady-state current and noise; it is unclear whether the same trend holds for the entropy-production rate when the large-gap projection is relaxed or when higher-order tunneling processes are retained.

    Authors: The suppression of quantum TUR violations is demonstrated consistently within the large-gap master equation used throughout the work; the entropy-production rate is obtained from the same steady-state probabilities and transition rates, so the trend is internally consistent. Relaxing the large-gap projection or retaining higher-order processes would require an entirely different methodological framework (e.g., full Keldysh diagrammatics without the Δ→∞ projection) that lies outside the scope of the present study. We will add a clarifying paragraph in §4.2 stating the approximation limits and noting that the hybrid bound remains satisfied under the same controlled conditions. revision: partial

  3. Referee: [§3.1] §3.1 (high-temperature regime): The statement that fluctuation properties remain highly sensitive while average currents are weakly affected is illustrated for specific parameter sets; a systematic scan of the noise-to-current ratio versus U and temperature, including the noninteracting reference curve, is needed to quantify the claimed “pronounced reduction.”

    Authors: We thank the referee for this suggestion. We will add a new figure in §3.1 that systematically plots the zero-frequency noise-to-current ratio as a function of interaction strength U and temperature T, with the corresponding non-interacting (U=0) reference curve shown for direct comparison. This will quantify the pronounced reduction across the relevant parameter space and make the high-temperature sensitivity explicit. revision: yes

standing simulated objections not resolved
  • Demonstrating the TUR trend for the entropy-production rate after relaxing the large-gap projection, as this requires a different computational approach beyond the present framework.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper derives current, noise, and entropy production from a generalized real-time diagrammatic master equation in the large-gap limit, with inputs consisting of standard parameters (tunneling amplitudes, Coulomb interaction U, temperature, bias). The central results on interaction-induced renormalization of Andreev resonances and suppression of current precision follow from solving this master equation and applying full counting statistics; they are not equivalent to the inputs by construction. No self-citations are invoked as load-bearing uniqueness theorems or ansatze. Thermodynamic uncertainty relations are evaluated on the computed quantities rather than presupposed. The approach is externally benchmarkable against known noninteracting limits and standard diagrammatic techniques.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the large-gap approximation and the diagrammatic master-equation framework; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Large superconducting-gap limit
    Invoked to simplify the model to Andreev processes only.

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