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arxiv: 2604.13527 · v1 · submitted 2026-04-15 · ❄️ cond-mat.mes-hall

Coherent control of thermal transport with pillar-based phononic crystals

Tatu A. S. Korkiam\"aki , Tuomas A. Puurtinen , Mikko Kivek\"as , Teemu Loippo , Adam Krysztofik , Bartlomiej Graczykowski , Ilari J. Maasilta This is my paper

Pith reviewed 2026-05-10 12:59 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords phononic crystalsthermal conductancecoherent controlpillar arrayssilicon nitride membranelow temperaturephonon dispersionsurface scattering
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The pith

Periodic arrays of aluminum pillars on intact silicon nitride membranes reduce thermal conductance by up to an order of magnitude at sub-Kelvin temperatures through coherent phonon control.

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

This paper demonstrates that phononic crystals formed by placing a periodic array of aluminum pillars on an uncut silicon nitride membrane can coherently control thermal transport at low temperatures. Measurements and simulations across lattice constants from 0.3 to 5 micrometers show conductance reductions reaching a factor of ten relative to a plain membrane. This pillar-based method achieves effects similar to earlier hole-drilled structures while avoiding membrane perforation. For lattices larger than 1 micrometer the data deviate from coherent predictions, which the work links to increased diffusive scattering at rough pillar surfaces.

Core claim

Pillar-based phononic crystals formed by a periodic array of Al pillars on an uncut SiN membrane achieve coherent control of thermal conductance at sub-Kelvin temperatures, yielding up to an order of magnitude reduction in thermal conductance compared to an unaltered membrane, with coherence breaking down for lattice constants larger than 1 micrometer due to diffusive scattering from surface roughness.

What carries the argument

The periodic array of aluminum pillars on the silicon nitride membrane, which alters phonon dispersion, group velocities, and density of states to enable coherent thermal transport control.

Load-bearing premise

The reduction in thermal conductance at small lattice constants arises primarily from coherent phonon mode modification rather than from other scattering processes.

What would settle it

Fabricating pillar arrays with significantly smoother surfaces and measuring whether thermal conductance for lattice constants above 1 micrometer then matches the fully coherent simulation predictions.

Figures

Figures reproduced from arXiv: 2604.13527 by Adam Krysztofik, Bartlomiej Graczykowski, Ilari J. Maasilta, Mikko Kivek\"as, Tatu A. S. Korkiam\"aki, Teemu Loippo, Tuomas A. Puurtinen.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

Two-dimensional phononic crystals (PnCs) formed by a periodic array of holes in a suspended membrane have previously been used to coherently control thermal conductance at low temperatures by modifying the phonon dispersion, thereby altering the phonon group velocities and the density of states. Here, in contrast, we demonstrate that PnCs formed by a periodic array of Al pillars on an uncut \SiN membrane can also be used to achieve similar coherent control. We have measured and simulated the thermal conductance of four pillar-based PnCs with different lattice constants ranging from 0.3 to 5 $\mu$m at sub-Kelvin temperatures, showing a strong up to an order of magnitude reduction in thermal conductance compared to an unaltered membrane. For the larger lattice constants $> 1 $ $\mu$m, however, the experiments do not agree with the coherent theory simulations, which we interpret as a breakdown of coherence induced by increasingly effective diffusive scattering due to the roughness of the Al pillar surfaces.

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 demonstrates that phononic crystals formed by periodic arrays of aluminum pillars on uncut suspended SiN membranes can achieve coherent control of thermal transport at sub-Kelvin temperatures. Thermal conductance measurements on four devices with lattice constants a = 0.3–5 μm show reductions of up to an order of magnitude relative to a bare membrane. Finite-element simulations assuming coherent phonon propagation match the data for the smallest lattice constants but diverge for a > 1 μm; the authors interpret the mismatch as a coherence breakdown caused by diffusive scattering from roughness on the Al pillar surfaces.

Significance. If the coherence interpretation holds, the work establishes pillar-based PnCs as a viable alternative to hole-based structures for phonon dispersion engineering, with the advantage of leaving the membrane intact. The experimental reduction in conductance is clearly demonstrated and the simulations provide supporting evidence for small periods, strengthening the case for coherent phonon control in low-temperature mesoscopic systems.

major comments (2)
  1. [Abstract and discussion] Abstract and discussion of results for a > 1 μm: the attribution of the experimental–simulation mismatch to roughness-induced loss of coherence is load-bearing for the claim of coherent control across the studied range, yet no surface-roughness statistics (AFM, SEM, or otherwise), no calculated scattering rates, and no quantitative model showing that roughness becomes dominant precisely above 1 μm are provided. Without these, alternative explanations (fabrication variation in pillar geometry, incomplete coherent model, or incoherent scattering already present at small a) cannot be ruled out.
  2. [Results] Comparison of experiment and coherent simulations (results section): the manuscript states that simulations match for small lattices but does not report the precise lattice constants at which agreement holds, the magnitude of the deviation (e.g., factor by which measured G falls below simulated G), or any error analysis on the measured conductances. This quantitative detail is required to assess whether the small-a agreement securely demonstrates coherent control or could arise from other factors.
minor comments (2)
  1. [Abstract] The abstract phrase “strong up to an order of magnitude reduction” should be replaced by the actual measured reduction factors for each of the four lattice constants.
  2. [Figures] Figure captions and legends should explicitly label which curves correspond to which lattice constant and include experimental error bars.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each of the major comments below and have revised the manuscript to incorporate additional details and clarifications.

read point-by-point responses

  1. Referee: [Abstract and discussion] Abstract and discussion of results for a > 1 μm: the attribution of the experimental–simulation mismatch to roughness-induced loss of coherence is load-bearing for the claim of coherent control across the studied range, yet no surface-roughness statistics (AFM, SEM, or otherwise), no calculated scattering rates, and no quantitative model showing that roughness becomes dominant precisely above 1 μm are provided. Without these, alternative explanations (fabrication variation in pillar geometry, incomplete coherent model, or incoherent scattering already present at small a) cannot be ruled out.

    Authors: We agree that the manuscript would benefit from more direct evidence supporting the roughness interpretation. Unfortunately, quantitative surface roughness statistics from AFM or detailed scattering rate calculations are not available in our current dataset. In the revised manuscript, we have expanded the discussion to explicitly consider alternative explanations such as fabrication variations in pillar geometry and possible limitations in the coherent model. We have also included available SEM images of the pillars to provide qualitative information on surface morphology. We maintain that the systematic increase in discrepancy with larger lattice constants is consistent with roughness effects becoming more prominent as phonon wavelengths become comparable to feature sizes, but we have softened the language to present this as a plausible interpretation rather than a definitive conclusion. revision: partial

  2. Referee: [Results] Comparison of experiment and coherent simulations (results section): the manuscript states that simulations match for small lattices but does not report the precise lattice constants at which agreement holds, the magnitude of the deviation (e.g., factor by which measured G falls below simulated G), or any error analysis on the measured conductances. This quantitative detail is required to assess whether the small-a agreement securely demonstrates coherent control or could arise from other factors.

    Authors: We agree that additional quantitative details are necessary. In the revised manuscript, we have updated the results section to report the specific lattice constants at which the simulations match the experimental data, the magnitude of any deviations for each device, and an error analysis on the measured thermal conductances, including uncertainties from membrane thickness and temperature measurements. This provides a clearer basis for evaluating the demonstration of coherent control at small lattice constants. revision: yes

standing simulated objections not resolved
  • Quantitative AFM or SEM-based surface roughness statistics and a calculated model of roughness scattering rates to demonstrate dominance above 1 μm

Circularity Check

0 steps flagged

No significant circularity; experimental comparison to independent simulations

full rationale

The paper presents direct measurements of thermal conductance in fabricated pillar-based PnCs across multiple lattice constants, benchmarked against unaltered membranes and against coherent phonon simulations performed with standard finite-element methods. No derivation chain reduces a claimed prediction to a fitted parameter by the paper's own equations, nor does any central result depend on a self-citation whose content is itself unverified or defined in terms of the target claim. The interpretation of mismatch at large lattice constants as roughness-induced decoherence is an auxiliary assumption, not a load-bearing step that forces the main conclusion of coherent control at small periods. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that phonon transport remains coherent at sub-Kelvin temperatures for small lattice constants and that surface roughness induces diffusive scattering for larger ones; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Coherent phonon transport model based on modified dispersion applies for lattice constants below 1 μm at sub-Kelvin temperatures
    Invoked to explain agreement between experiment and simulation for small lattices.

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