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Subgap Linear Thermoelectricity in Superconducting Quantum Hall Systems

T0 review · 2 major / 2 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read An integer quantum Hall setup proximized by superconductors exhibits subgap linear thermoelectric effects when triplet correlations are present.

desk verdict The paper derives an analytical subgap linear Seebeck coefficient of order k_B/e from Andreev processes in a proximized QH edge, but only when triplet correlations dominate. read the letter →

arxiv 2606.21599 v1 pith:JR2O6IUD submitted 2026-06-19 cond-mat.mes-hall

Leonardo Pierattelli , Fabio Taddei , Alessandro Romito , Alessandro Braggio This is my paper · ORCID
classification cond-mat.mes-hall
keywords quantumHallsuperconductivitythermoelectricitySeebeckeffectAndreevreflectiontripletpairingproximity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper shows that proximitizing integer quantum Hall edge states with superconductors can generate a thermoelectric response inside the superconducting gap in the linear regime, but only if triplet pairing correlations are induced. A minimal device setup is constructed that produces a nonzero Seebeck coefficient through Andreev processes. This coefficient is predicted to reach magnitudes on the order of k_B/e near the center of the quantum Hall plateau. Both the presence of triplet correlations and spin polarization of the edges turn out to be required, even with the linear dispersion of the states. The dependence on system parameters and temperature is derived analytically.

What carries the argument

Andreev-mediated Seebeck effect induced by triplet superconducting correlations in spin-polarized quantum Hall edge states.

What would settle it

Measuring a zero Seebeck coefficient in an otherwise identical setup where either spin polarization or triplet pairing is suppressed.

Watch

Extended reading notes

Core claim

In superconducting quantum Hall systems, triplet superconducting correlations enable a subgap Seebeck effect mediated by Andreev processes in the linear-response regime, with the coefficient reaching order k_B/e in the plateau center, provided spin polarization is present.

Load-bearing premise

Triplet superconducting correlations can be induced in the quantum Hall edge states such that they dominate over other pairing channels.

Editorial extensions

If this is right

  • The Seebeck coefficient reaches values on the order of k_B/e in the middle of the quantum Hall plateau.
  • Both triplet correlations and spin polarization are essential for the thermoelectric effect.
  • The effect persists despite the linear band dispersion of the edge states.
  • The response can be characterized as a function of Hamiltonian parameters and temperature regime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • This mechanism could allow thermoelectric generation at temperatures well below the superconducting gap without exciting quasiparticles.
  • Similar subgap thermoelectric responses might be engineered in other hybrid topological-superconducting systems.
  • Device applications would require precise control over the induced pairing symmetry to favor the triplet channel.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper claims that an integer quantum Hall edge proximitized by a superconductor can exhibit a nonzero linear-response Seebeck coefficient of order k_B/e inside the plateau when triplet superconducting correlations are present. It devises a minimal setup, analytically demonstrates that both triplet correlations and spin polarization are required for an Andreev-mediated thermoelectric effect despite linear edge dispersion, and characterizes the dependence on Hamiltonian parameters and temperature.

Significance. If the analytical derivation is sound and the minimal setup permits triplet dominance, the result would be significant for mesoscopic superconductivity: it identifies a concrete mechanism for subgap linear thermoelectricity in chiral hybrid systems that relies on unconventional pairing. The analytical (parameter-free in the stated sense) demonstration and the explicit necessity of triplet plus spin polarization are strengths that could guide experiments.

major comments (2)
  1. [§2] §2 (minimal setup and Hamiltonian): the proximity-induced pairing term must be written explicitly (including the relative amplitudes of triplet vs. singlet channels and any spin-polarization or Zeeman factors) so that the claim of triplet dominance can be verified; without this, it is impossible to confirm that competing channels remain subdominant and that the finite Andreev Seebeck coefficient survives.
  2. [Analytical derivation] Analytical derivation of the Seebeck coefficient (main text, around the linear-response formulas): the calculation should explicitly track how the linear dispersion is overcome by the triplet Andreev processes and confirm that the result is not an artifact of any auxiliary fitting parameter or self-consistent assumption; any suppression mechanism for singlet components must be shown to be robust.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the temperature regime and the value of the spin-polarization parameter used.
  2. [Results section] A short table summarizing the dependence of the Seebeck coefficient on the key Hamiltonian parameters (pairing amplitudes, Zeeman field) would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below and will revise the manuscript accordingly to improve clarity and completeness.

read point-by-point responses

  1. Referee: [§2] §2 (minimal setup and Hamiltonian): the proximity-induced pairing term must be written explicitly (including the relative amplitudes of triplet vs. singlet channels and any spin-polarization or Zeeman factors) so that the claim of triplet dominance can be verified; without this, it is impossible to confirm that competing channels remain subdominant and that the finite Andreev Seebeck coefficient survives.

    Authors: We agree that the explicit form of the proximity-induced pairing term is needed for verification. In the revised manuscript we will write the full pairing Hamiltonian in §2, specifying the relative amplitudes of the triplet and singlet channels together with the spin-polarization (Zeeman) factors. We will also add a short discussion of parameter regimes in which triplet components dominate, confirming that the finite Andreev Seebeck coefficient remains robust. revision: yes

  2. Referee: [Analytical derivation] Analytical derivation of the Seebeck coefficient (main text, around the linear-response formulas): the calculation should explicitly track how the linear dispersion is overcome by the triplet Andreev processes and confirm that the result is not an artifact of any auxiliary fitting parameter or self-consistent assumption; any suppression mechanism for singlet components must be shown to be robust.

    Authors: We will expand the analytical derivation in the main text to show each step of the linear-response calculation, explicitly demonstrating how the triplet Andreev scattering overcomes the linear dispersion without introducing auxiliary fitting parameters. The derivation will be presented in a fully analytic, parameter-free manner within the stated approximations. We will also include an explicit argument for the robustness of singlet suppression under the triplet-dominant conditions already identified in the model. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: analytical derivation from triplet correlations in minimal setup

full rationale

The paper's central result is an analytical demonstration that triplet superconducting correlations plus spin polarization produce a nonzero Andreev-mediated Seebeck coefficient inside the QH plateau, despite linear edge dispersion. The abstract frames this as a direct consequence of the devised minimal Hamiltonian rather than a fit, renaming, or reduction to prior self-citation. No quoted equations or steps reduce the predicted thermoelectric response to a parameter fitted from the same data or to an unverified self-citation chain. The derivation is therefore self-contained against the stated Hamiltonian assumptions.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities can be extracted from the provided text.

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Cite this review

Pith. "Pith review of Subgap Linear Thermoelectricity in Superconducting Quantum Hall Systems." pith.science (2026). https://pith.science/paper/JR2O6IUD

@misc{pith2026260621599,
  author       = {Pith},
  title        = {Pith review of: Subgap Linear Thermoelectricity in Superconducting Quantum Hall Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JR2O6IUD}},
  note         = {Machine review of arXiv:2606.21599}
}
abstract

We show that an integer quantum Hall setup proximized by superconductors can exhibit subgap thermoelectric effects in the linear-response regime when triplet superconducting correlations are present. We devise a minimal setup that enables a nonzero Seebeck effect mediated by Andreev processes and predict that the corresponding Seebeck coefficient can reach values on the order of $k_B/e$ in the middle of the quantum Hall plateau. We analytically show that both triplet correlations and spin polarization are essential for the emergence of the thermoelectric effect, which arises despite the linear band dispersion of the edge states. We characterize the dependence of the thermoelectric response on the Hamiltonian parameters and the system's temperature regime.

Figures

Figures reproduced from arXiv: 2606.21599 by the authors.

Figure 1
Figure 1. FIG. 1. Sketch of the QH bar (yellow) at [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Transport coefficients as functions of length [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. (b) shows the oscillatory dependence of the Seebeck coefficient on the triplet coupling strength v˜∆, evaluated at fixed L˜ and ψ = 0, for three representa￾tive values of θ. This behavior can be attributed to the fact that varying v˜∆ produces a shift in the position of the Seebeck resonance, analogous to the shift observed in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a): Plots of the functions in the integral defining [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Thermopower dependence on [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Thermopower density plots in the ( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Thermopower density plots in the ( [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Thermopower density plots in the ( [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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Forward citations

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  1. Bipolar Thermoelectric Superconducting Quantum Devices

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Reference graph

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