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arxiv: 2603.18922 · v1 · submitted 2026-03-19 · ❄️ cond-mat.mes-hall

Recognition: 2 theorem links

· Lean Theorem

Peltier cooling in Corbino-geometry quantum Hall systems

Akira Endo , Yoshiaki Hashimoto
Authors on Pith no claims yet

Pith reviewed 2026-05-15 08:23 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Peltier effectCorbino geometryquantum Hall effectLandau levelsthermoelectric transportself-consistent Born approximation
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The pith

The radial Peltier coefficient in Corbino-geometry quantum Hall systems reaches large negative or positive values just above or below integer Landau-level fillings.

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

The paper derives an analytic formula for the radial Peltier coefficient Π_rr from the spectral conductivity obtained in the self-consistent Born approximation. Π_rr takes large negative values just above an integer filling factor and large positive values just below it, with the absolute magnitude growing as temperature or disorder strength is lowered. In the clean limit the coefficient approaches the sawtooth form determined by the energy of the highest occupied Landau level relative to the chemical potential. When a radial dc current is passed through a real Corbino disk the measured temperature at the outer perimeter rises or falls exactly as the sign of Π_rr requires, including cooling below the bath temperature.

Core claim

The radial Peltier coefficient Π_rr exhibits large negative (positive) values just above (below) integer Landau-level filling factors. Its absolute magnitude increases with decreasing temperature or disorder strength and converges to the saw-tooth profile −(E_{N_F σ_F} − ζ)/e when disorder vanishes. Application of a radial dc current in a real Corbino device produces corresponding heating or cooling at the outer edge, with the electron temperature falling below the bath temperature when the current direction matches the sign of Π_rr.

What carries the argument

The radial Peltier coefficient Π_rr, obtained from the spectral conductivity calculated in the self-consistent Born approximation, which sets the thermoelectric response to radial current between concentric electrodes in Corbino geometry.

If this is right

  • Temperature at the outer perimeter changes in the direction required by the sign of Π_rr when radial current is applied.
  • The magnitude of the temperature change grows as temperature or disorder is reduced.
  • In the vanishing-disorder limit Π_rr recovers the exact sawtooth dependence on chemical potential set by the highest occupied Landau level.
  • Observable cooling below bath temperature occurs for appropriate current directions near integer fillings.

Where Pith is reading between the lines

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

  • This mechanism could enable localized cooling at the edges of mesoscopic quantum Hall devices without additional refrigeration stages.
  • The same radial-current geometry might be used to probe Landau-level spectral properties through thermoelectric response.
  • Analogous Peltier effects may appear in other two-dimensional systems that support Landau levels under perpendicular magnetic fields.

Load-bearing premise

The measured temperature change at the outer perimeter is produced solely by the radial Peltier effect and is not contaminated by Joule heating, contact resistance, or phonon contributions.

What would settle it

No temperature drop below the bath temperature when a radial outward current is applied in the filling-factor region where Π_rr is predicted negative would falsify the central claim.

read the original abstract

Quantum Hall systems having Corbino geometry are expected to have a large Peltier coefficient $\Pi_{rr}$ in the quantum Hall plateau region. We present an analytic formula for $\Pi_{rr}$ calculated employing the spectral conductivity obtained based on the self-consistent Born approximation. The coefficient $\Pi_{rr}$ is shown to have a large negative (positive) value just above (below) an integer Landau-level filling, with the absolute value $|\Pi_{rr}|$ increasing with decreasing temperature or decreasing disorder, and approaching the saw-tooth shape $- (E_{N_\mathrm{F} \sigma_\mathrm{F}}-\zeta)/e$ in the limit of vanishing disorder, where $E_{N_\mathrm{F} \sigma_\mathrm{F}}$ is the highest occupied Landau level and $\zeta$ is the chemical potential. As an initial attempt to experimentally observe the effect of the large $|\Pi_{rr}|$, we measure the electron temperature $T_\mathrm{out}$ near the outer perimeter of a Corbino disk, applying a radial dc current $I_\mathrm{dc}$. The temperature $T_\mathrm{out}$ is observed to increase or decrease depending on the direction of $I_\mathrm{dc}$ and the sign of $\Pi_{rr}$ as expected from the Peltier effect. Notably, $T_\mathrm{out}$ becomes lower than the bath temperature for outward (inward) $I_\mathrm{dc}$ in the region where $\Pi_{rr} < 0$ ($\Pi_{rr} > 0$).

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 derives an analytic formula for the radial Peltier coefficient Π_rr in Corbino-geometry quantum Hall systems using spectral conductivity from the self-consistent Born approximation (SCBA). It predicts that Π_rr takes large negative (positive) values just above (below) integer Landau-level fillings, with |Π_rr| growing as temperature or disorder decreases and approaching the saw-tooth form −(E_{N_F σ_F}−ζ)/e in the clean limit. Experimentally, the authors apply radial DC current I_dc to a Corbino disk and report that the outer-perimeter electron temperature T_out drops below the bath temperature precisely where the calculated Π_rr < 0 (or rises where Π_rr > 0), interpreting this as direct evidence of radial Peltier cooling.

Significance. If the observed temperature changes are shown to arise solely from the radial Peltier term without appreciable contamination, the work would establish a new, geometrically tunable thermoelectric effect in the quantum Hall regime. The closed-form SCBA expression supplies a concrete, parameter-light prediction that can be tested quantitatively, and the Corbino geometry isolates the radial thermoelectric response from edge-state complications.

major comments (3)
  1. [Experimental results] Experimental results (section describing T_out measurements): the reported cooling T_out < T_bath lacks error bars, quantitative fits to the expected Π_rr I_r magnitude, or any subtraction of possible Joule-heating backgrounds from finite σ_rr or contacts; without these, the central claim that the sign change is produced by the Peltier effect remains only qualitative.
  2. [Theory / SCBA derivation] Theory section deriving Π_rr via SCBA: the analytic formula assumes the SCBA spectral conductivity remains accurate throughout the experimental density and temperature window, yet SCBA is known to overestimate extended-state conductivity near integer fillings where localization dominates; this directly affects the predicted |Π_rr| and its temperature dependence.
  3. [Experimental methods and results] Experimental section: no control data are shown at exact integer filling factors (where Π_rr should vanish) or with zero radial current, nor is a radial temperature profile presented that would localize the cooling to the expected Corbino edge rather than contacts or bulk heating.
minor comments (2)
  1. [Theory] Notation: the definition of the chemical potential ζ and its relation to the Fermi level in the saw-tooth limit should be stated explicitly in the theory section to avoid ambiguity with the Landau-level index N_F.
  2. [Figures] Figure captions: the experimental traces of T_out vs. filling factor should include the corresponding theoretical Π_rr curve on the same plot for direct visual comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and constructive suggestions. We address each major comment below and will revise the manuscript to incorporate clarifications and additional data where feasible.

read point-by-point responses

  1. Referee: Experimental results (section describing T_out measurements): the reported cooling T_out < T_bath lacks error bars, quantitative fits to the expected Π_rr I_r magnitude, or any subtraction of possible Joule-heating backgrounds from finite σ_rr or contacts; without these, the central claim that the sign change is produced by the Peltier effect remains only qualitative.

    Authors: We agree that the current experimental presentation is qualitative, consistent with the manuscript's description of this as an 'initial attempt.' In the revised manuscript we will add error bars to the T_out data points, include order-of-magnitude quantitative comparisons between the observed ΔT and the expected Peltier cooling magnitude using the calculated Π_rr and the applied I_r (accounting for the thermal conductance of the device), and explicitly discuss subtraction of Joule-heating contributions arising from finite σ_rr and contact resistances. These additions will make the evidence for the Peltier origin more quantitative. revision: yes

  2. Referee: Theory section deriving Π_rr via SCBA: the analytic formula assumes the SCBA spectral conductivity remains accurate throughout the experimental density and temperature window, yet SCBA is known to overestimate extended-state conductivity near integer fillings where localization dominates; this directly affects the predicted |Π_rr| and its temperature dependence.

    Authors: The referee correctly identifies a known limitation of the SCBA. Our derivation is performed entirely within the SCBA, which yields the closed-form analytic expression for Π_rr. We will revise the theory section to add an explicit discussion of the SCBA's regime of validity, noting that it tends to overestimate the extended-state conductivity near integer fillings where localization effects become important, and that the predicted |Π_rr| should therefore be viewed as an upper bound in those regions. We will also emphasize that the clean-limit sawtooth form −(E_{N_F σ_F}−ζ)/e is recovered independently of the SCBA details. revision: partial

  3. Referee: Experimental section: no control data are shown at exact integer filling factors (where Π_rr should vanish) or with zero radial current, nor is a radial temperature profile presented that would localize the cooling to the expected Corbino edge rather than contacts or bulk heating.

    Authors: We acknowledge that the present manuscript does not include these control measurements or a radial temperature profile. In the revised version we will add data taken at exact integer filling factors and with I_dc = 0 to demonstrate the absence of temperature excursions, and we will include (or describe) a radial temperature profile that localizes the observed cooling to the outer perimeter, consistent with the Corbino geometry and the radial Peltier term. revision: yes

Circularity Check

0 steps flagged

No significant circularity; Π_rr formula derived independently via SCBA and experiment is separate observable

full rationale

The analytic expression for Π_rr is obtained by direct application of the self-consistent Born approximation to the spectral conductivity, yielding the stated sign changes, temperature/disorder dependence, and clean-limit saw-tooth form −(E_{N_F σ_F}−ζ)/e. This is a standard theoretical calculation whose output is not equivalent to its inputs by construction. The Corbino-disk temperature measurements are reported as an independent experimental check whose sign matches the calculated Π_rr; no parameter fitting, background subtraction, or self-citation chain reduces the observed T_out behavior to the theoretical input. No load-bearing self-citations, self-definitional steps, or fitted-input predictions appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the self-consistent Born approximation for the spectral conductivity and on the assumption that the measured temperature change is produced by the Peltier effect alone.

axioms (1)
  • domain assumption Self-consistent Born approximation accurately describes the spectral conductivity in disordered quantum Hall systems
    Invoked to obtain the conductivity used in the Peltier-coefficient formula

pith-pipeline@v0.9.0 · 5578 in / 1278 out tokens · 51845 ms · 2026-05-15T08:23:46.501018+00:00 · methodology

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Reference graph

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