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arxiv: 2604.12810 · v1 · submitted 2026-04-14 · ❄️ cond-mat.mes-hall

Recognition: unknown

Heating Dynamics of Mesoscopic Electron Baths at High Magnetic Field

F. Zanichelli , A. Veillon , C. Piquard , A. Aassime , Y. Sato , A. Cavanna , Y. Jin , J. Folk
show 3 more authors
U. Gennser A. Anthore F. Pierre
Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:22 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords mesoscopic thermalizationquantum Hall channelsnoise thermometrynuclear spinselectron heatinghigh magnetic fieldquantum thermodynamics
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The pith

Mesoscopic electron baths at high magnetic fields thermalize in two steps with a slow minute-scale rise.

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

The paper studies heat flow in a micrometer-scale metallic island connected to cold electron reservoirs through two to four ballistic quantum Hall channels. After an initial fast temperature jump, the electrons show a much slower continued rise that lasts minutes. This two-step process is explained by the competing heat flows through the quantum channels, to cold phonons, and to the nuclear spins inside the island. A reader would care because it shows that thermal timescales in small quantum devices can be far longer than bulk expectations, with direct consequences for how quickly such circuits can reach equilibrium.

Core claim

The central claim is that the heating of the mesoscopic electron bath follows a two-step thermalization: a rapid initial temperature increase followed by a much slower rise extending over minutes. This behavior is quantitatively accounted for by the balance between heat transport through the electronic quantum Hall channels, heat loss to cold phonons, and heat exchange with the nuclear spins in the metallic island.

What carries the argument

The balance of heat flows through ballistic quantum Hall channels to cold phonons and to nuclear spins in the metallic island, which produces the observed fast-then-slow temperature evolution.

Load-bearing premise

That the slow temperature rise over minutes is caused by heat flow to nuclear spins and phonons with no significant unaccounted experimental artifacts in the noise thermometry.

What would settle it

A measurement that shows the slow rise disappears when nuclear spin heat capacity is removed, for example by switching to a zero-spin isotope or by detuning the nuclear Zeeman splitting.

Figures

Figures reproduced from arXiv: 2604.12810 by A. Aassime, A. Anthore, A. Cavanna, A. Veillon, C. Piquard, F. Pierre, F. Zanichelli, J. Folk, U. Gennser, Y. Jin, Y. Sato.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: shows a representative observation of the time evolution of the electron temperature T measured in the 85 µm3 metallic island (0.34µm of AuGeNi de￾posited over an area of 250µm2 ). In contrast to the es￾timate above, the measured temperature clearly evolves on timescales much longer than the experimental time resolution. The continuous blue line in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: for the small island where the relative amplitude can be correspondingly smaller. Note also that a suffi￾ciently well-resolved slow stage amplitude is necessary to be able to extract τ from a T(t) fit. In practice, we re￾quire that the amplitude of the slow thermalization stage is twice as big as the standard error on T. This condi￾tion is always fulfilled for the data discussed in the main text; hence, th… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
read the original abstract

Quantum thermodynamics addresses the dynamics of heat flow in quantum devices driven out of equilibrium. Although mesoscopic circuits at low temperatures provide a flexible platform to explore this dynamics, experimental studies are wanting because thermal timescales in nanodevices are often too fast. Here we engineer and investigate with noise thermometry a mesoscopic thermal circuit where heat flows between electron, phonon and nuclear systems can occur on slower timescales. The central constituent of this device is a micrometer-scale metallic island electrically connected to large cold electron reservoirs through two to four ballistic quantum Hall channels, a component frequently used for exploring stationary thermal currents. We uncover a two-step thermalization process specific to the mesoscopic scale, involving a fast initial temperature step followed by a much slower rise extending over minutes. This observation is quantitatively accounted for by the balance between heat flows through electronic quantum channels, to cold phonons, and to the nuclear spins in the metallic island. The disclosed mesoscopic thermalization takes a step into the field of quantum thermo-\emph{dynamical} phenomena, highlighting their distinctive nature on a central constituent of quantum circuits. The implications for the thermal engineering of nanodevices include the thermal characterization of exotic states at high magnetic field.

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 / 2 minor

Summary. The manuscript reports an experimental investigation of heating dynamics in a micrometer-scale metallic island connected to cold electron reservoirs via 2-4 ballistic quantum Hall channels at high magnetic field. Using noise thermometry, the authors observe a two-step thermalization: a fast initial temperature step followed by a slow rise extending over minutes. This is claimed to be quantitatively accounted for by the balance of heat flows through the electronic quantum channels, coupling to cold phonons, and heat exchange with nuclear spins in the island.

Significance. If the quantitative model holds with the reported data, the result is significant for quantum thermodynamics: it demonstrates a mesoscopic-scale thermalization process on experimentally accessible (minute) timescales that involves nuclear spins as an additional heat reservoir, distinct from bulk behavior. This has implications for thermal engineering of nanodevices in the quantum Hall regime and highlights the role of multiple heat-flow channels in non-equilibrium dynamics.

major comments (2)
  1. [Results and Model] The central claim that the slow temperature rise is quantitatively explained by the three heat-flow paths (electronic channels, phonons, nuclear spins) requires explicit support. The model equations for the temperature evolution (including the nuclear spin contribution and its coupling strength), the values of all parameters, and a direct overlay of model predictions versus measured T(t) data with residuals or fit quality metrics are needed in the results/analysis section to verify the accounting.
  2. [Discussion] The weakest assumption—that the minutes-scale rise is dominated by nuclear spins rather than unaccounted artifacts in the noise thermometry or other slow mechanisms—needs stronger validation. Additional control data (e.g., varying island volume or magnetic field to modulate nuclear heat capacity) or bounds on possible systematic errors in the thermometry should be provided to rule out alternatives.
minor comments (2)
  1. [Abstract and Experimental Setup] The abstract states the device uses 'two to four' channels; the main text should clarify whether the number of channels primarily affects the fast electronic step or also influences the slow nuclear/phonon balance, with supporting data.
  2. [Figures] Figure captions and axis labels for the temperature-versus-time traces should explicitly indicate the time window of the slow rise and any averaging or filtering applied to the noise thermometry signal.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the detailed, constructive comments. We address each major point below and will revise the manuscript to improve clarity and strengthen the supporting evidence for our claims.

read point-by-point responses

  1. Referee: [Results and Model] The central claim that the slow temperature rise is quantitatively explained by the three heat-flow paths (electronic channels, phonons, nuclear spins) requires explicit support. The model equations for the temperature evolution (including the nuclear spin contribution and its coupling strength), the values of all parameters, and a direct overlay of model predictions versus measured T(t) data with residuals or fit quality metrics are needed in the results/analysis section to verify the accounting.

    Authors: We agree that the quantitative model should be presented more explicitly. In the revised manuscript we will add the full set of coupled differential equations for the electron temperature evolution, explicitly including the nuclear-spin heat-capacity term and the electron-nuclear coupling rate. All parameter values (electronic channel conductances, phonon coupling constant, nuclear heat capacity, and coupling strength) will be tabulated with their sources (literature values or fits). We will also add a figure panel overlaying the model prediction on the measured T(t) traces together with residuals and a fit-quality metric (e.g., reduced chi-squared). revision: yes

  2. Referee: [Discussion] The weakest assumption—that the minutes-scale rise is dominated by nuclear spins rather than unaccounted artifacts in the noise thermometry or other slow mechanisms—needs stronger validation. Additional control data (e.g., varying island volume or magnetic field to modulate nuclear heat capacity) or bounds on possible systematic errors in the thermometry should be provided to rule out alternatives.

    Authors: We acknowledge the need for stronger validation. New control experiments that vary island volume or magnetic field are not feasible within the present dataset and would require a new device fabrication run. However, we will expand the discussion to include quantitative bounds on possible systematic errors in the noise thermometry (e.g., amplifier drift, calibration uncertainty, and slow external heating). We will also show that the observed timescale and its dependence on the number of ballistic channels are inconsistent with typical artifact mechanisms and are instead consistent with the known nuclear-spin heat capacity and coupling strength in GaAs. These additions will be supported by order-of-magnitude estimates and references to prior literature on nuclear-spin relaxation in similar systems. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained experimental interpretation

full rationale

The paper reports an experimental observation of two-step thermalization in a mesoscopic device via noise thermometry, with the slow dynamics interpreted through standard heat-flow balance equations involving electronic channels, phonons, and nuclear spins. No derivation chain reduces by construction to its inputs, no fitted parameters are relabeled as predictions, and no load-bearing self-citations or imported uniqueness theorems are used. The central claim rests on direct comparison of measured temperature evolution to known physical mechanisms, making the analysis self-contained against external benchmarks without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on the abstract alone, the central claim rests on interpreting the observed temperature steps as a balance of heat flows to electronic channels, phonons, and nuclear spins; no explicit free parameters, new entities, or ad-hoc axioms are detailed.

axioms (1)
  • domain assumption Standard assumptions of ballistic transport in the quantum Hall regime and local thermal equilibrium within electron, phonon, and nuclear subsystems.
    Invoked implicitly when attributing the two temperature steps to specific heat-flow channels.

pith-pipeline@v0.9.0 · 5552 in / 1456 out tokens · 75973 ms · 2026-05-10T14:22:48.833995+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

68 extracted references · 3 canonical work pages

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    The 2DEG mesa is delimited by a wet etching approximately 100 nm deep with a H 3PO4/H2O2/H2O solution

    Nanofabrication The sample discussed in the main text (see Appendix H for the additional sample) is patterned by standard e- beam lithography on a GaAlAs heterostructure forming an electron gas 90 nm below the surface, with a density of 2.6×10 11 cm−2and a mobility of 0.5×10 6 cm2V−1s−1. The 2DEG mesa is delimited by a wet etching approximately 100 nm dee...

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    Noise mea- surements for the thermometry described below are per- formed near 1 MHz with homemade cryogenic amplifiers [11]

    Experimental setup The measurements are performed in a cryo-free dilu- tion refrigerator with extensive measurement lines filter- ing and thermalization (see [44] for details). Noise mea- surements for the thermometry described below are per- formed near 1 MHz with homemade cryogenic amplifiers [11]. The dc voltage source is realized by a dc current bias ...

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    Electronic temperature The electronic temperatureTis obtained from on-chip thermal noise measured on an ohmic contact. For the ν=1 data the conversion factor is calibrated from the linear slope of thermal noise vs temperature of the mix- ing chamber, at sufficiently high temperature where the 8 difference between electron and mixing chamber temper- atures...

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    5.Electronic temperature evolution of the small metallic is- land (Ω≃3.7µm 3,N=2 electronic channels,T b =9 mK)

    Extraction of the thermalization time 0.0 0.1 0.2 0.3 0.4 0.5 0 50 100 150 200 10 15 20 25 30 80 100 120 140 9.0 9.5 10.0 10.5 T (mK) t (s) T (mK) t (s) PJ (fW) FIG. 5.Electronic temperature evolution of the small metallic is- land (Ω≃3.7µm 3,N=2 electronic channels,T b =9 mK). Symbols areT(t)measurements following aP J step (see blue line and corre- spon...

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    4 is fitted using the least square method with individual weights associated with the stan- dard error on the measured relative temperature step

    Extraction of the nuclear spin parameters a) Ratioγ ns/K.The ensemble of slow stage ampli- tude data points in Fig. 4 is fitted using the least square method with individual weights associated with the stan- dard error on the measured relative temperature step. The fit function Eq. (8) is written explicitly as a func- tion of the relevant parameters in Eq...

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    The displayed value of∣gN∣µNB(=µB/I) atB=10.8 T corresponds to the magnetic energy splitting between nu- clear spin states, in mK, for each constitutive elements

    Nuclear spin parameters In Table I, we provide important nuclear spin charac- teristics of the atoms deposited to realize the metallic is- lands and composing the semiconductor heterojunction. The displayed value of∣gN∣µNB(=µB/I) atB=10.8 T corresponds to the magnetic energy splitting between nu- clear spin states, in mK, for each constitutive elements. H...

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    Test of high-temperature approximation In this section, we test whether, and at what accuracy, the use of predictions derived within the approximation µB/kBTns ≪1 remains justified even whenµB∼k BTns. As seen from the magnetic energy given in Table I for the highest B=10.8 T, the possible constitutive elements Ga, As and Al could approach this regime. (T-...

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    Thermalization time.We now turn to the time evo- lution during the second slow change. In this stage, the electron temperatureTevolves fromT step toT final as a function ofT ns according to the quasistationary heat bal- ance: PJ =J stat Q (T, Tb)+G ns Q(Tns)×(T−T ns).(16) Equations (16) and (14) involve both the sameP J, which gives T−Tns = Jstat Q (Tfina...

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    Ruling out instrumental bandwidth and filtering ar- tifacts.The characteristic time and relative amplitude of the slow thermalization stage depend strongly on the island hot temperature (Figs. 3 and 4). Most of the data points displayed with identical symbols are obtained se- quentially, for the same base temperature, with the same measurement protocol, a...

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    Ruling out thermal transients along measurement paths(including measurement lines and quantum Hall edge paths). Heating up/cooling down an island between the same base temperature and similarT hot, we find a strong reduction of the amplitude and characteristic time of the slow response for smaller islands (see violet circles vs green lozenges in Figs. 3 a...

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    Ruling out (transient and stationary) global chip heating.Two nominally identical implementation of the largest islands located 200µm away on the same chip (one shown in Fig. 1) were simultaneously measured through different noise measurement lines, and found to show identical thermal behaviors both in the stationary regime and on the dynamical response o...

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