pith. sign in

arxiv: 2411.04065 · v3 · submitted 2024-11-06 · ❄️ cond-mat.mes-hall

Imaging heat transport in suspended diamond nanostructures with integrated spin defect thermometers

Valentin Goblot , Kexin Wu , Enrico Di Lucente , Yuchun Zhu , Elena Losero , Quentin Jobert , Claudio Jaramillo Concha , Niels Quack
show 3 more authors
Nicola Marzari Michele Simoncelli Christophe Galland
This is my paper

Pith reviewed 2026-05-23 17:33 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords diamond nanostructuresnitrogen-vacancy centersthermal conductivityphonon transportnon-diffusive heat transportspin defect thermometerscantilevers
0
0 comments X

The pith

NV centers embedded in diamond cantilevers image a strong reduction in thermal conductivity as width decreases, revealing non-diffusive phonon transport.

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

The paper deploys dilute nitrogen-vacancy centers as precise in-situ thermometers to map temperature profiles in suspended single-crystal diamond cantilevers heated from ambient conditions. Measurements across cross-sections from 0.2 to 2.6 square micrometers show thermal conductivity dropping sharply with narrower widths. First-principles simulations based on the linearized phonon Boltzmann transport equation and viscous heat equations account for this reduction by showing how intrinsic normal and Umklapp processes compete with extrinsic boundary scattering to produce the observed non-diffusive regime. The temperature-imaging approach enables study of unconventional heat transport in diamond devices of arbitrary geometries.

Core claim

Dilute NV color centers serve as non-perturbative spin defect thermometers that image temperature inhomogeneities in heated diamond microstructures, demonstrating a pronounced decrease in cantilever thermal conductivity with reduced width that first-principles phonon simulations rationalize through the competition between intrinsic momentum-conserving and momentum-dissipating scattering processes.

What carries the argument

Dilute nitrogen-vacancy color centers acting as integrated spin defect thermometers for local temperature mapping, combined with linearized phonon Boltzmann transport equation simulations.

Load-bearing premise

The NV centers report the local lattice temperature without significant back-action on the phonon distribution or additional scattering channels introduced by the defects themselves.

What would settle it

A direct comparison of thermal conductivity values extracted from NV-based temperature maps against measurements on identical NV-free cantilevers using an independent technique such as Raman thermometry would settle whether the defects perturb the phonon transport.

Figures

Figures reproduced from arXiv: 2411.04065 by Christophe Galland, Claudio Jaramillo Concha, Elena Losero, Enrico Di Lucente, Kexin Wu, Michele Simoncelli, Nicola Marzari, Niels Quack, Quentin Jobert, Valentin Goblot, Yuchun Zhu.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic representation of the experiment. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Temperature shift ∆ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) SEM images, top view of cantilevers with width: [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A more detailed analysis of the strength of viscous hydrodynamic and ballistic effects reveals that the latter are the main contribution to the reduction of κeff (see SM [50]). Heat transport in our cantilever is thus within the “apparent diffusion” regime [71], in the sense that it is reasonably well described by a diffusive (Fourier-like) equation with a non-intrinsic thermal conductivity (i.e., dependin… view at source ↗
read the original abstract

Among all materials, mono-crystalline diamond has one of the highest measured thermal conductivities, with values above 2000 W/m/K at room temperature. This stems from momentum-conserving `normal' phonon-phonon scattering processes dominating over momentum-dissipating `Umklapp' processes, a feature that also suggests diamond as an ideal platform to experimentally investigate phonon heat transport phenomena that violate Fourier's law. Here, we introduce dilute nitrogen-vacancy color centers as in-situ, highly precise spin defect thermometers to image temperature inhomogeneities in single-crystal diamond microstructures heated from ambient conditions. We analyze cantilevers with cross-sections in the range from about 0.2 to 2.6 $\mu$m$^2$, observing a strong reduction of the cantilevers' conductivity as the width decreases. We use first-principles simulations based on the linearized phonon Boltzmann transport equation and viscous heat equations to quantitatively predict the cantilevers' thermal transport properties, rationalizing how the interplay between intrinsic and extrinsic phonon scattering mechanisms determines the observed non-diffusive behavior. Our temperature-imaging method paves the way for the exploration of unconventional, non-diffusive heat transport phenomena in devices and nanostructures of arbitrary geometries.

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 / 1 minor

Summary. The manuscript introduces dilute NV centers as in-situ spin-defect thermometers to image local temperature profiles in suspended single-crystal diamond cantilevers (cross-sections 0.2–2.6 μm²) heated from ambient conditions. It reports a strong reduction in effective thermal conductivity with decreasing width and compares the data to independent first-principles linearized phonon Boltzmann transport equation calculations plus viscous heat equations, attributing the non-diffusive transport to the interplay of intrinsic Umklapp and extrinsic boundary scattering.

Significance. If the central interpretation holds, the work supplies a new experimental platform for spatially resolved thermal transport studies in high-conductivity nanostructures and supplies a parameter-free theoretical benchmark for phonon hydrodynamics and boundary scattering in diamond. The use of independent first-principles simulations rather than fitted parameters is a clear methodological strength.

major comments (2)
  1. [Abstract] The central claim that the observed width-dependent conductivity drop is due solely to intrinsic Umklapp plus extrinsic boundary scattering rests on the assumption that the NV centers act as non-perturbative thermometers. In the smallest cantilevers (~0.2 μm²), where phonon mean free paths already approach the width, implantation-induced point defects or strain could introduce additional scattering channels that shorten the mean free path and mimic the reported reduction. The manuscript provides no control measurements on NV-free devices or quantitative estimate of the added scattering rate.
  2. [Abstract] The abstract states quantitative agreement between measured temperature profiles and first-principles BTE predictions, yet the manuscript does not supply raw fluorescence data, explicit error propagation, or the precise data-reduction steps used to extract local temperatures and effective conductivities. Without these, the claimed agreement cannot be independently verified and the non-diffusive interpretation remains provisional.
minor comments (1)
  1. Notation for the cantilever dimensions and the precise definition of the reported conductivity (e.g., whether it is an effective length-averaged value) should be clarified in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] The central claim that the observed width-dependent conductivity drop is due solely to intrinsic Umklapp plus extrinsic boundary scattering rests on the assumption that the NV centers act as non-perturbative thermometers. In the smallest cantilevers (~0.2 μm²), where phonon mean free paths already approach the width, implantation-induced point defects or strain could introduce additional scattering channels that shorten the mean free path and mimic the reported reduction. The manuscript provides no control measurements on NV-free devices or quantitative estimate of the added scattering rate.

    Authors: We acknowledge the validity of this concern. The manuscript describes the NV centers as dilute, but does not include a quantitative estimate of their scattering contribution. In the revised manuscript we add such an estimate based on the implantation dose and literature defect-phonon scattering rates, showing the added rate remains much smaller than boundary scattering across the studied widths. We also note consistency with prior diamond nanostructure data obtained without NV centers. Dedicated NV-free control devices were not fabricated in this study; we discuss this limitation explicitly and agree it would strengthen future claims. revision: partial

  2. Referee: [Abstract] The abstract states quantitative agreement between measured temperature profiles and first-principles BTE predictions, yet the manuscript does not supply raw fluorescence data, explicit error propagation, or the precise data-reduction steps used to extract local temperatures and effective conductivities. Without these, the claimed agreement cannot be independently verified and the non-diffusive interpretation remains provisional.

    Authors: We agree that the original manuscript lacks sufficient detail on data reduction. The revised manuscript and supplementary information now include representative raw fluorescence spectra, a step-by-step description of the ODMR-based temperature extraction procedure, and explicit error propagation for both local temperatures and derived effective conductivities. These additions enable independent verification of the reported agreement with the BTE calculations. revision: yes

Circularity Check

0 steps flagged

No circularity: independent first-principles BTE predictions compared to NV thermometry data

full rationale

The paper's central derivation uses first-principles linearized phonon Boltzmann transport equation simulations (plus viscous heat equations) to predict thermal conductivity reduction with width; these calculations are parameter-free with respect to the measured conductivity values and do not reduce to any fitted input or self-citation chain. No self-definitional steps, fitted predictions renamed as outputs, or load-bearing self-citations appear in the derivation chain. The NV thermometer assumption is an external physical premise, not a definitional loop. The result is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that NV optical readout faithfully reports local temperature without introducing new scattering or heating, plus standard assumptions in the phonon Boltzmann transport equation (relaxation-time approximation validity, accurate phonon dispersion from DFT). No free parameters are explicitly introduced in the abstract description of the simulations.

axioms (2)
  • domain assumption Dilute NV centers act as non-perturbative local thermometers whose spin resonance shift reports lattice temperature.
    Invoked when stating that NV centers enable precise in-situ temperature imaging.
  • domain assumption Linearized phonon Boltzmann transport equation with first-principles scattering rates accurately captures the transition from diffusive to non-diffusive regimes in the measured geometry.
    Used to quantitatively predict cantilever thermal transport properties.

pith-pipeline@v0.9.0 · 5786 in / 1304 out tokens · 25579 ms · 2026-05-23T17:33:01.736190+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

97 extracted references · 97 canonical work pages

  1. [1]

    Berman, P

    R. Berman, P. R. W. Hudson, and M. Martinez, Nitrogen in diamond: evidence from thermal conductivity, Journal of Physics C: Solid State Physics8, L430 (1975)

    work page 1975

  2. [2]

    J. R. Olson, R. O. Pohl, J. W. Vandersande, A. Zoltan, T. R. Anthony, and W. F. Banholzer, Thermal conduc- tivity of diamond between 170 and 1200 k and the isotope effect, Phys. Rev. B47, 14850 (1993)

    work page 1993

  3. [3]

    A. V. Inyushkin, A. N. Taldenkov, V. G. Ralchenko, A. P. Bolshakov, A. V. Koliadin, and A. N. Katrusha, Thermal conductivity of high purity synthetic single crystal dia- monds, Phys. Rev. B97, 144305 (2018)

    work page 2018

  4. [4]

    Chen, Non-fourier phonon heat conduction at the microscale and nanoscale, Nature Reviews Physics , 1 (2021)

    G. Chen, Non-fourier phonon heat conduction at the microscale and nanoscale, Nature Reviews Physics , 1 (2021)

    work page 2021

  5. [5]

    M.-H. Bae, Z. Li, Z. Aksamija, P. N. Martin, F. Xiong, Z.-Y. Ong, I. Knezevic, and E. Pop, Ballistic to diffu- sive crossover of heat flow in graphene ribbons, Nature Communications4, 1734 (2013)

    work page 2013

  6. [6]

    D. L. Nika and A. A. Balandin, Two-dimensional phonon transport in graphene, Journal of Physics: Condensed Matter24, 233203 (2012)

    work page 2012

  7. [7]

    Cepellotti, G

    A. Cepellotti, G. Fugallo, L. Paulatto, M. Lazzeri, F. Mauri, and N. Marzari, Phonon hydrodynamics in two-dimensional materials, Nature communications6, 6400 (2015)

    work page 2015

  8. [8]

    S. Lee, D. Broido, K. Esfarjani, and G. Chen, Hydrody- namic phonon transport in suspended graphene, Nature Communications6, 6290 (2015)

    work page 2015

  9. [9]

    Huberman, R

    S. Huberman, R. A. Duncan, K. Chen, B. Song, V. Chiloyan, Z. Ding, A. A. Maznev, G. Chen, and K. A. Nelson, Observation of second sound in graphite at tem- peratures above 100 k, Science364, 375 (2019)

    work page 2019

  10. [10]

    Z. Ding, K. Chen, B. Song, J. Shin, A. A. Maznev, K. A. Nelson, and G. Chen, Observation of second sound in graphite over 200 k, Nature Communications13, 285 (2022)

    work page 2022

  11. [11]

    Machida, N

    Y. Machida, N. Matsumoto, T. Isono, and K. Behnia, Phonon hydrodynamics and ultrahigh–room- temperature thermal conductivity in thin graphite, Science367, 309 (2020)

    work page 2020

  12. [12]

    Jeong, X

    J. Jeong, X. Li, S. Lee, L. Shi, and Y. Wang, Transient hydrodynamic lattice cooling by picosecond laser irradi- ation of graphite, Phys. Rev. Lett.127, 085901 (2021)

    work page 2021

  13. [13]

    Huang, Y

    X. Huang, Y. Guo, Y. Wu, S. Masubuchi, K. Watanabe, T. Taniguchi, Z. Zhang, S. Volz, T. Machida, and M. No- mura, Observation of phonon poiseuille flow in isotopi- cally purified graphite ribbons, Nature Communications 14, 2044 (2023)

    work page 2044

  14. [14]

    Aharon-Steinberg, T

    A. Aharon-Steinberg, T. V¨ olkl, A. Kaplan, A. K. Pariari, I. Roy, T. Holder, Y. Wolf, A. Y. Meltzer, Y. Myasoedov, M. E. Huber,et al., Direct observation of vortices in an electron fluid, Nature607, 74 (2022)

    work page 2022

  15. [15]

    M. L. Palm, C. Ding, W. S. Huxter, T. Taniguchi, K. Watanabe, and C. L. Degen, Observation of current whirlpools in graphene at room temperature, Science 384, 465 (2024)

    work page 2024

  16. [16]

    A. Sood, R. Cheaito, T. Bai, H. Kwon, Y. Wang, C. Li, L. Yates, T. Bougher, S. Graham, M. Asheghi, M. Goorsky, and K. E. Goodson, Direct Visualization of Thermal Conductivity Suppression Due to Enhanced Phonon Scattering Near Individual Grain Boundaries, Nano Letters18, 3466 (2018). 6

    work page 2018

  17. [17]

    Wang and B

    Y. Wang and B. Sun, Anomalously strong size effect on thermal conductivity of diamond microparticles, Applied Physics Letters125, 042202 (2024)

    work page 2024

  18. [18]

    Y. Tao, J. M. Boss, B. A. Moores, and C. L. Degen, Single-crystal diamond nanomechanical resonators with quality factors exceeding one million, Nature Communi- cations5, 3638 (2014)

    work page 2014

  19. [19]

    Mitchell, B

    M. Mitchell, B. Khanaliloo, D. P. Lake, T. Masuda, J. P. Hadden, and P. E. Barclay, Single-crystal diamond low- dissipation cavity optomechanics, Optica3, 963 (2016)

    work page 2016

  20. [20]

    B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lonˇ car, Diamond nonlinear photon- ics, Nature Photon8, 369 (2014)

    work page 2014

  21. [21]

    Moody, V

    G. Moody, V. J. Sorger, D. J. Blumenthal, P. W. Juodawlkis, W. Loh, C. Sorace-Agaskar, A. E. Jones, K. C. Balram, J. C. F. Matthews, A. Laing, M. Da- vanco, L. Chang, J. E. Bowers, N. Quack, C. Gal- land, I. Aharonovich, M. A. Wolff, C. Schuck, N. Sin- clair, M. Lonˇ car, T. Komljenovic, D. Weld, S. Mookher- jea, S. Buckley, M. Radulaski, S. Reitzenstein,...

    work page 2022

  22. [22]

    X. Liu, G. Zhang, and Y.-W. Zhang, Surface-engineered nanoscale diamond films enable remarkable enhancement in thermal conductivity and anisotropy, Carbon94, 760 (2015)

    work page 2015

  23. [23]

    Gom` es, A

    S. Gom` es, A. Assy, and P.-O. Chapuis, Scanning thermal microscopy: A review, physica status solidi (a)212, 477 (2015)

    work page 2015

  24. [24]

    Zhang, W

    Y. Zhang, W. Zhu, F. Hui, M. Lanza, T. Borca-Tasciuc, and M. Mu˜ noz Rojo, A review on principles and applica- tions of scanning thermal microscopy (sthm), Advanced Functional Materials30, 1900892 (2020)

    work page 2020

  25. [25]

    A. J. Minnich, J. A. Johnson, A. J. Schmidt, K. Esfarjani, M. S. Dresselhaus, K. A. Nelson, and G. Chen, Thermal conductivity spectroscopy technique to measure phonon mean free paths, Phys. Rev. Lett.107, 095901 (2011)

    work page 2011

  26. [26]

    K. T. Regner, D. P. Sellan, Z. Su, C. H. Amon, A. J. H. McGaughey, and J. A. Malen, Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance, Nature Com- munications4, 1640 (2013)

    work page 2013

  27. [27]

    Y. Hu, L. Zeng, A. J. Minnich, M. S. Dresselhaus, and G. Chen, Spectral mapping of thermal conductivity through nanoscale ballistic transport, Nature Nanotech- nology10, 701 (2015)

    work page 2015

  28. [28]

    F. Tian, B. Song, X. Chen, N. K. Ravichandran, Y. Lv, K. Chen, S. Sullivan, J. Kim, Y. Zhou, T.-H. Liu, M. Goni, Z. Ding, J. Sun, G. A. G. Udalamatta Gamage, H. Sun, H. Ziyaee, S. Huyan, L. Deng, J. Zhou, A. J. Schmidt, S. Chen, C.-W. Chu, P. Y. Huang, D. Broido, L. Shi, G. Chen, and Z. Ren, Unusual high thermal con- ductivity in boron arsenide bulk cryst...

    work page 2018

  29. [29]

    Wilson, B

    R. Wilson, B. A. Apgar, L. W. Martin, and D. G. Cahill, Thermoreflectance of metal transducers for op- tical pump-probe studies of thermal properties, Optics express20, 28829 (2012)

    work page 2012

  30. [30]

    Huang, R

    X. Huang, R. Anufriev, L. Jalabert, K. Watanabe, T. Taniguchi, Y. Guo, Y. Ni, S. Volz, and M. Nomura, A graphite thermal tesla valve driven by hydrodynamic phonon transport, Nature , 1 (2024)

    work page 2024

  31. [31]

    C. D. S. Brites, P. P. Lima, N. J. O. Silva, A. Mill´ an, V. S. Amaral, F. Palacio, and L. D. Carlos, Thermometry at the nanoscale, Nanoscale4, 4799 (2012)

    work page 2012

  32. [32]

    Quintanilla and L

    M. Quintanilla and L. M. Liz-Marz´ an, Guiding Rules for Selecting a Nanothermometer, Nano Today19, 126 (2018)

    work page 2018

  33. [33]

    A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Tewelde- brhan, F. Miao, and C. N. Lau, Superior Thermal Con- ductivity of Single-Layer Graphene, Nano Letters8, 902 (2008)

    work page 2008

  34. [34]

    Ghosh, I

    S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L. Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nano- electronic circuits, Applied Physics Letters92, 151911 (2008)

    work page 2008

  35. [35]

    Braun, R

    O. Braun, R. Furrer, P. Butti, K. Thodkar, I. Shorubalko, I. Zardo, M. Calame, and M. L. Perrin, Spatially map- ping thermal transport in graphene by an opto-thermal method, npj 2D Materials and Applications6, 1 (2022)

    work page 2022

  36. [36]

    Elhajhasan, W

    M. Elhajhasan, W. Seemann, K. Dudde, D. Vaske, G. Callsen, I. Rousseau, T. F. Weatherley, J.-F. Car- lin, R. Butt´ e, N. Grandjean,et al., Optical and ther- mal characterization of a group-iii nitride semiconduc- tor membrane by microphotoluminescence spectroscopy and raman thermometry, Physical Review B108, 235313 (2023)

    work page 2023

  37. [37]

    M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. L. Hollenberg, The nitrogen- vacancy colour centre in diamond, Physics Reports528, 1 (2013)

    work page 2013

  38. [38]

    Neumann, I

    P. Neumann, I. Jakobi, F. Dolde, C. Burk, R. Reuter, G. Waldherr, J. Honert, T. Wolf, A. Brunner, J. H. Shim, D. Suter, H. Sumiya, J. Isoya, and J. Wrachtrup, High- precision nanoscale temperature sensing using single de- fects in diamond, Nano Letters13, 2738 (2013)

    work page 2013

  39. [39]

    D. M. Toyli, C. F. d. l. Casas, D. J. Christle, V. V. Do- brovitski, and D. D. Awschalom, Fluorescence thermom- etry enhanced by the quantum coherence of single spins in diamond, Proceedings of the National Academy of Sci- ences110, 8417 (2013)

    work page 2013

  40. [40]

    Kucsko, P

    G. Kucsko, P. C. Maurer, N. Y. Yao, M. Kubo, H. J. Noh, P. K. Lo, H. Park, and M. D. Lukin, Nanometre- scale thermometry in a living cell, Nature500, 54 (2013)

    work page 2013

  41. [41]

    Laraoui, H

    A. Laraoui, H. Aycock-Rizzo, Y. Gao, X. Lu, E. Riedo, and C. A. Meriles, Imaging thermal conductivity with nanoscale resolution using a scanning spin probe, Nature Communications6, 8954 (2015)

    work page 2015

  42. [42]

    V. M. Acosta, E. Bauch, M. P. Ledbetter, A. Waxman, L.-S. Bouchard, and D. Budker, Temperature dependence of the nitrogen-vacancy magnetic resonance in diamond, Physical Review Letters104, 070801 (2013)

    work page 2013

  43. [43]

    J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, Sensitivity optimization for nv-diamond magnetometry, Rev. Mod. Phys.92, 015004 (2020)

    work page 2020

  44. [44]

    A. M. Wojciechowski, M. Karadas, C. Osterkamp, S. Jankuhn, J. Meijer, F. Jelezko, A. Huck, and U. L. 7 Andersen, Precision temperature sensing in the presence of magnetic field noise and vice-versa using nitrogen- vacancy centers in diamond, Applied Physics Letters 113, 013502 (2018)

    work page 2018

  45. [45]

    Gottscholl, M

    A. Gottscholl, M. Diez, V. Soltamov, C. Kasper, D. Krauße, A. Sperlich, M. Kianinia, C. Bradac, I. Aharonovich, and V. Dyakonov, Spin defects in hBN as promising temperature, pressure and magnetic field quantum sensors, Nature Communications12, 4480 (2021)

    work page 2021

  46. [46]

    Beaufils, W

    C. Beaufils, W. Redjem, E. Rousseau, V. Jacques, A. Y. Kuznetsov, C. Raynaud, C. Voisin, A. Benali, T. Herzig, S. Pezzagna, J. Meijer, M. Abbarchi, and G. Cassabois, Optical properties of an ensemble of g-centers in silicon, Physical Review B97, 035303 (2018)

    work page 2018

  47. [47]

    Kraus, V

    H. Kraus, V. A. Soltamov, F. Fuchs, D. Simin, A. Sper- lich, P. G. Baranov, G. V. Astakhov, and V. Dyakonov, Magnetic field and temperature sensing with atomic-scale spin defects in silicon carbide, Scientific Reports4, 5303 (2014)

    work page 2014

  48. [48]

    A. N. Anisimov, D. Simin, V. A. Soltamov, S. P. Lebe- dev, P. G. Baranov, G. V. Astakhov, and V. Dyakonov, Optical thermometry based on level anticrossing in sili- con carbide, Scientific Reports6, 33301 (2016)

    work page 2016

  49. [49]

    Y. Zhou, J. Wang, X. Zhang, K. Li, J. Cai, and W. Gao, Self-protected thermometry with infrared photons and defect spins in silicon carbide, Physical Review Applied 8, 044015 (2017)

    work page 2017

  50. [50]

    for further details on ex- perimental and theoretical methods and additional data

    See Supplemental Material at ... for further details on ex- perimental and theoretical methods and additional data

    work page

  51. [51]

    Zhang, Y

    S.-C. Zhang, Y. Dong, B. Du, H.-B. Lin, S. Li, W. Zhu, G.-Z. Wang, X.-D. Chen, G.-C. Guo, and F.-W. Sun, A robust fiber-based quantum thermometer coupled with nitrogen-vacancy centers, Review of Scientific Instru- ments92, 044904 (2021)

    work page 2021

  52. [52]

    M. C. Cambria, G. Thiering, A. Norambuena, H. T. Di- nani, A. Gardill, I. Kemeny, V. Lordi, A. Gali, J. R. Maze, and S. Kolkowitz, Physically motivated analytical expression for the temperature dependence of the zero- field splitting of the nitrogen-vacancy center in diamond, Phys. Rev. B108, L180102 (2023)

    work page 2023

  53. [53]

    W. Li, N. Mingo, L. Lindsay, D. A. Broido, D. A. Stew- art, and N. A. Katcho, Thermal conductivity of dia- mond nanowires from first principles, Physical Review B—Condensed Matter and Materials Physics85, 195436 (2012)

    work page 2012

  54. [54]

    Fugallo, M

    G. Fugallo, M. Lazzeri, L. Paulatto, and F. Mauri, Ab initio variational approach for evaluating lattice thermal conductivity, Phys. Rev. B88, 045430 (2013)

    work page 2013

  55. [55]

    M. v. Swinkels, M. Van Delft, D. Oliveira, A. Cavalli, I. v. Zardo, R. Van Der Heijden, and E. Bakkers, Di- ameter dependence of the thermal conductivity of inas nanowires, Nanotechnology26, 385401 (2015)

    work page 2015

  56. [56]

    Martin, Z

    P. Martin, Z. Aksamija, E. Pop, and U. Ravaioli, Im- pact of phonon-surface roughness scattering on thermal conductivity of thin si nanowires, Physical review letters 102, 125503 (2009)

    work page 2009

  57. [57]

    A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. Yang, Enhanced thermoelectric performance of rough silicon nanowires, Nature451, 163 (2008)

    work page 2008

  58. [58]

    D. Li, Y. Wu, P. Kim, L. Shi, P. Yang, and A. Majumdar, Thermal conductivity of individual silicon nanowires, Ap- plied Physics Letters83, 2934 (2003)

    work page 2003

  59. [59]

    Maire, R

    J. Maire, R. Anufriev, and M. Nomura, Ballistic thermal transport in silicon nanowires, Scientific Reports7, 41794 (2017)

    work page 2017

  60. [60]

    J. M. Ziman,Electrons and phonons: the theory of trans- port phenomena in solids(Oxford university press, 2001)

    work page 2001

  61. [61]

    Simoncelli, N

    M. Simoncelli, N. Marzari, and A. Cepellotti, General- ization of fourier’s law into viscous heat equations, Phys. Rev. X10, 011019 (2020)

    work page 2020

  62. [63]

    Gandolfi, C

    M. Gandolfi, C. Giannetti, and F. Banfi, Temper- onic crystal: A superlattice for temperature waves in graphene, Phys. Rev. Lett.125, 265901 (2020)

    work page 2020

  63. [64]

    Raya-Moreno, X

    M. Raya-Moreno, X. Cartoix` a, and J. Carrete, BTE- Barna: An extension of almaBTE for thermal simula- tion of devices based on 2D materials, Computer Physics Communications281, 108504 (2022)

    work page 2022

  64. [65]

    Raya-Moreno, J

    M. Raya-Moreno, J. Carrete, and X. Cartoix` a, Hydrody- namic signatures in thermal transport in devices based on two-dimensional materials: Anab initiostudy, Physical Review B106, 014308 (2022)

    work page 2022

  65. [66]

    W. Li, J. Carrete, N. A. Katcho, and N. Mingo, Sheng- bte: A solver of the boltzmann transport equation for phonons, Computer Physics Communications185, 1747 (2014)

    work page 2014

  66. [67]

    Ratsifaritana and P

    C. Ratsifaritana and P. Klemens, Scattering of phonons by vacancies, International journal of thermophysics8, 737 (1987)

    work page 1987

  67. [68]

    Carruthers, Theory of thermal conductivity of solids at low temperatures, Reviews of Modern Physics33, 92 (1961)

    P. Carruthers, Theory of thermal conductivity of solids at low temperatures, Reviews of Modern Physics33, 92 (1961)

    work page 1961

  68. [69]

    We note that this is formally analogous to Bosanquet- type regularizations for the transport coefficients of rar- efied fluids [62, 75]

    work page

  69. [70]

    Cepellotti and N

    A. Cepellotti and N. Marzari, Boltzmann transport in nanostructures as a friction effect, Nano Letters17, 4675 (2017)

    work page 2017

  70. [71]

    Maassen and M

    J. Maassen and M. Lundstrom, Steady-state heat trans- port: Ballistic-to-diffusive with fourier’s law, Journal of Applied Physics117(2015)

    work page 2015

  71. [72]

    T. R. Anthony, J. L. Fleischer, J. R. Olson, and D. G. Cahill, The thermal conductivity of isotopically enriched polycrystalline diamond films, Journal of Applied Physics 69, 8122 (1991)

    work page 1991

  72. [73]

    S. Tian, T. Wang, H. Chen, D. Ma, and L. Zhang, Phonon coherent transport leads to an anomalous bound- ary effect on the thermal conductivity of a rough graphene nanoribbon, Phys. Rev. Appl.21, 064005 (2024)

    work page 2024

  73. [74]

    C. A. Polanco, A. van Roekeghem, B. Brisuda, L. Sami- nadayar, O. Bourgeois, and N. Mingo, The phonon quan- tum of thermal conductance: Are simulations and mea- surements estimating the same quantity?, Science Ad- vances9, eadi7439 (2023)

    work page 2023

  74. [75]

    V. K. Michalis, A. N. Kalarakis, E. D. Skouras, and V. N. Burganos, Rarefaction effects on gas viscosity in the Knudsen transition regime, Microfluidics and Nanoflu- idics9, 847 (2010)

    work page 2010

  75. [76]

    Chambers, The conductivity of thin wires in a mag- netic field, Proceedings of the Royal Society of London

    R. Chambers, The conductivity of thin wires in a mag- netic field, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences202, 378 (1950)

    work page 1950

  76. [77]

    S. Mi, A. Toros, T. Graziosi, and N. Quack, Non-contact 8 polishing of single crystal diamond by ion beam etching, Diamond and Related Materials92, 248 (2019)

    work page 2019

  77. [78]

    M. J. Burek, Y. Chu, M. S. Z. Liddy, P. Pa- tel, J. Rochman, S. Meesala, W. Hong, Q. Quan, M. D. Lukin, and M. Lonˇ car, High quality-factor opti- cal nanocavities in bulk single-crystal diamond, Nature Communications5, 5718 (2014)

    work page 2014

  78. [79]

    Graziosi, S

    T. Graziosi, S. Mi, M. Kiss, and N. Quack, Single crys- tal diamond micro-disk resonators by focused ion beam milling, Apl Photonics3(2018)

    work page 2018

  79. [80]

    Riedrich-M¨ oller, L

    J. Riedrich-M¨ oller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. M¨ ucklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, One- and two-dimensional photonic crystal microcavities in single crystal diamond, Nature Nanotechnology7, 69 (2012)

    work page 2012

  80. [81]

    Y.-Y. Cai, E. Sung, R. Zhang, L. J. Tauzin, J. G. Liu, B. Ostovar, Y. Zhang, W.-S. Chang, P. Nordlander, and S. Link, Anti-stokes emission from hot carriers in gold nanorods, Nano Letters19, 1067 (2019), publisher: American Chemical Society

    work page 2019

Showing first 80 references.