A lower bound to the thermal diffusivity of insulators
Abstract
It has been known for decades that thermal conductivity of insulating crystals becomes proportional to the inverse of temperature when the latter is comparable to, or higher than, the Debye temperature. This behavior has been understood as resulting from Umklapp scattering among phonons. We put under scrutiny the magnitude of the thermal diffusion constant in this regime and find that it does not fall below a threshold set by the square of sound velocity times the Planckian time (τp = h/kBT). The conclusion, based on scrutinizing the ratio in cubic crystals with high thermal resistivity, appears to hold even in glasses where Umklapp events are not conceivable. Furthermore, explaining this boundary, reminiscent of a recently-noticed limit for charge transport in metals, is a challenge to theory.
- Authors:
-
[1];
- PSL Research Univ., Paris (France); Univ. zu Köln, Koln (Germany)
- Stanford Univ., Stanford, CA (United States)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1576517
- Grant/Contract Number:
- AC02-76SF00515
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Physics. Condensed Matter
- Additional Journal Information:
- Journal Volume: 31; Journal Issue: 40; Journal ID: ISSN 0953-8984
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Behnia, Kamran, and Kapitulnik, Aharon. A lower bound to the thermal diffusivity of insulators. United States: N. p., 2019.
Web. doi:10.1088/1361-648x/ab2db6.
Behnia, Kamran, & Kapitulnik, Aharon. A lower bound to the thermal diffusivity of insulators. United States. doi:10.1088/1361-648x/ab2db6.
Behnia, Kamran, and Kapitulnik, Aharon. Thu .
"A lower bound to the thermal diffusivity of insulators". United States. doi:10.1088/1361-648x/ab2db6. https://www.osti.gov/servlets/purl/1576517.
@article{osti_1576517,
title = {A lower bound to the thermal diffusivity of insulators},
author = {Behnia, Kamran and Kapitulnik, Aharon},
abstractNote = {It has been known for decades that thermal conductivity of insulating crystals becomes proportional to the inverse of temperature when the latter is comparable to, or higher than, the Debye temperature. This behavior has been understood as resulting from Umklapp scattering among phonons. We put under scrutiny the magnitude of the thermal diffusion constant in this regime and find that it does not fall below a threshold set by the square of sound velocity times the Planckian time (τp = h/kBT). The conclusion, based on scrutinizing the ratio in cubic crystals with high thermal resistivity, appears to hold even in glasses where Umklapp events are not conceivable. Furthermore, explaining this boundary, reminiscent of a recently-noticed limit for charge transport in metals, is a challenge to theory.},
doi = {10.1088/1361-648x/ab2db6},
journal = {Journal of Physics. Condensed Matter},
number = 40,
volume = 31,
place = {United States},
year = {2019},
month = {7}
}
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Works referenced in this record:
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journal, January 2018
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Sound Wave Propagation in Molten Silver Halides
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Interpretation of the Thermal Conductivity of Glasses
journal, March 1949
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Pressure Dependence of the Structural Phase Transition Temperature in SrTiO 3 and KMnF 3
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Lattice Thermal Conductivity
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- Dugdale, J. S.; MacDonald, D. K. C.
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Ab initio phonon dispersions for PbTe
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Thermal conductivity of perovskite ferroelectrics
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Lead telluride alloy thermoelectrics
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Model for Lattice Thermal Conductivity at Low Temperatures
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Universal Charge Diffusion and the Butterfly Effect in Holographic Theories
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Quantum chaos on a critical Fermi surface
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Normal-state transport properties of crystals
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- Physical Review B, Vol. 41, Issue 1
Theory of Diffusive Fluctuations
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- Chen-Lin, Xinyi; Delacrétaz, Luca V.; Hartnoll, Sean A.
- Physical Review Letters, Vol. 122, Issue 9
The crystal structure of IV-VI compounds. I. Classification and description
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Three-phonon phase space and lattice thermal conductivity in semiconductors
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- Journal of Physics: Condensed Matter, Vol. 20, Issue 16
Low-temperature thermal conductivity and acoustic attenuation in amorphous solids
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Lattice Thermal Conductivity
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- Ranninger, Julius
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The heat capacity and Gruneisen parameter of KTaO 3
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Intrinsically Minimal Thermal Conductivity in Cubic Semiconductors
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Theory of universal incoherent metallic transport
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Large thermoelectric response of metallic perovskites:
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- Okuda, T.; Nakanishi, K.; Miyasaka, S.
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First Principles Peierls-Boltzmann Phonon Thermal Transport: A Topical Review
journal, April 2016
- Lindsay, Lucas
- Nanoscale and Microscale Thermophysical Engineering, Vol. 20, Issue 2
Anomalous thermal diffusivity in underdoped YBa 2 Cu 3 O 6+x
journal, May 2017
- Zhang, Jiecheng; Levenson-Falk, Eli M.; Ramshaw, B. J.
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Thermal Conductivity and Specific Heat of Noncrystalline Solids
journal, September 1971
- Zeller, R. C.; Pohl, R. O.
- Physical Review B, Vol. 4, Issue 6
Improved Callaway model for lattice thermal conductivity
journal, October 2013
- Allen, Philip B.
- Physical Review B, Vol. 88, Issue 14
Large Anisotropy of the Electrical Conductivity of Graphite
journal, October 1939
- Krishnan, K. S.; Ganguli, N.
- Nature, Vol. 144, Issue 3650
The Molar Heats of Lead Sulphide, Selenide and Telluride in the Temperature Range 20 K to 260 K
journal, July 1954
- Parkinson, D. H.; Quarrington, J. E.
- Proceedings of the Physical Society. Section A, Vol. 67, Issue 7
Competition and cooperation between antiferrodistortive and ferroelectric instabilities in the model perovskite SrTiO 3
journal, March 2014
- Aschauer, Ulrich; Spaldin, Nicola A.
- Journal of Physics: Condensed Matter, Vol. 26, Issue 12
Anisotropic Thermal Conductivity of Pyrolytic Graphite
journal, August 1962
- Slack, Glen A.
- Physical Review, Vol. 127, Issue 3
Resonant bonding leads to low lattice thermal conductivity
journal, April 2014
- Lee, Sangyeop; Esfarjani, Keivan; Luo, Tengfei
- Nature Communications, Vol. 5, Issue 1
Phase-Change Materials: Vibrational Softening upon Crystallization and Its Impact on Thermal Properties
journal, April 2011
- Matsunaga, Toshiyuki; Yamada, Noboru; Kojima, Rie
- Advanced Functional Materials, Vol. 21, Issue 12
Thermophysical properties of polycrystalline PbS, PbSe, and PbTe in the temperature range 300?700 K
journal, September 1983
- El-Sharkawy, A. A.; Abou El-Azm, A. M.; Kenawy, M. I.
- International Journal of Thermophysics, Vol. 4, Issue 3
Some aspects of the thermal conductivity of isotopically enriched diamond single crystals
journal, May 1992
- Onn, D. G.; Witek, A.; Qiu, Y. Z.
- Physical Review Letters, Vol. 68, Issue 18
Enhancement of Thermoelectric Efficiency in PbTe by Distortion of the Electronic Density of States
journal, July 2008
- Heremans, J. P.; Jovovic, V.; Toberer, E. S.
- Science, Vol. 321, Issue 5888, p. 554-557
Theory of Heat Conduction in Rare-Gas Crystals
journal, January 1965
- Julian, Carl L.
- Physical Review, Vol. 137, Issue 1A
Ultrasonic propagation velocity in KTaO3
journal, February 1968
- Barrett, H. H.
- Physics Letters A, Vol. 26, Issue 6
Thermal diffusivity of oxide perovskite compounds at elevated temperature
journal, May 2010
- Hofmeister, Anne M.
- Journal of Applied Physics, Vol. 107, Issue 10
Nonmetallic crystals with high thermal conductivity
journal, January 1973
- Slack, G. A.
- Journal of Physics and Chemistry of Solids, Vol. 34, Issue 2
SnSe: a remarkable new thermoelectric material
journal, January 2016
- Zhao, Li-Dong; Chang, Cheng; Tan, Gangjian
- Energy & Environmental Science, Vol. 9, Issue 10
Sound velocities of PbTe to 14 GPa: evidence for coupling between acoustic and optic phonons
journal, August 2013
- Jacobsen, Matthew K.; Liu, Wei; Li, Baosheng
- Journal of Physics: Condensed Matter, Vol. 25, Issue 36
Thermal diffusivity of Bi2Sr2CaCu2O8 single crystals
journal, December 1993
- Wu, X. D.; Fanton, J. G.; Kino, G. S.
- Physica C: Superconductivity, Vol. 218, Issue 3-4
History and challenges of barium titanate: Part I
journal, January 2008
- Vijatovic, M. M.; Bobic, J. D.; Stojanovic, B. D.
- Science of Sintering, Vol. 40, Issue 2
Thermal Transport and Phonon Hydrodynamics in Strontium Titanate
journal, March 2018
- Martelli, Valentina; Jiménez, Julio Larrea; Continentino, Mucio
- Physical Review Letters, Vol. 120, Issue 12
Thermal conductivity of disordered harmonic solids
journal, November 1993
- Allen, Philip B.; Feldman, Joseph L.
- Physical Review B, Vol. 48, Issue 17
Similarity of Scattering Rates in Metals Showing T-Linear Resistivity
journal, February 2013
- Bruin, J. A. N.; Sakai, H.; Perry, R. S.
- Science, Vol. 339, Issue 6121
The thermal conductivity of insulators and semiconductors
journal, March 1986
- Vandersande, J. W.; Wood, C.
- Contemporary Physics, Vol. 27, Issue 2
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
journal, November 1990
- Bouchaud, Jean-Philippe; Georges, Antoine
- Physics Reports, Vol. 195, Issue 4-5
Superconductivity in Bad Metals
journal, April 1995
- Emery, V. J.; Kivelson, S. A.
- Physical Review Letters, Vol. 74, Issue 16
Dissecting holographic conductivities
journal, September 2015
- Davison, Richard A.; Goutéraux, Blaise
- Journal of High Energy Physics, Vol. 2015, Issue 9
Anisotropy of the elastic and nonlinear acoustic properties of dense textured
journal, April 1994
- Saunders, G. A.
- Physical Review B, Vol. 49, Issue 14
Ultrasonic Velocities in BaTiO 3
journal, April 1973
- Kashida, Shoji; Hatta, Ichiro; Ikushima, Akira
- Journal of the Physical Society of Japan, Vol. 34, Issue 4
Works referencing / citing this record:
Some aspects of the thermal conductivity of isotopically enriched diamond single crystals
journal, May 1992
- Onn, D. G.; Witek, A.; Qiu, Y. Z.
- Physical Review Letters, Vol. 68, Issue 18
Ultrasonic propagation velocity in KTaO3
journal, February 1968
- Barrett, H. H.
- Physics Letters A, Vol. 26, Issue 6
Thermal conductivity of disordered harmonic solids
journal, November 1993
- Allen, Philip B.; Feldman, Joseph L.
- Physical Review B, Vol. 48, Issue 17
Nonmetallic crystals with high thermal conductivity
journal, January 1973
- Slack, G. A.
- Journal of Physics and Chemistry of Solids, Vol. 34, Issue 2
Thermophysical properties of polycrystalline PbS, PbSe, and PbTe in the temperature range 300?700 K
journal, September 1983
- El-Sharkawy, A. A.; Abou El-Azm, A. M.; Kenawy, M. I.
- International Journal of Thermophysics, Vol. 4, Issue 3
The heat capacity and Gruneisen parameter of KTaO 3
journal, October 1987
- White, G. K.; Collocott, S. J.
- Journal of Physics C: Solid State Physics, Vol. 20, Issue 30
Ultrasonic Velocities in BaTiO 3
journal, April 1973
- Kashida, Shoji; Hatta, Ichiro; Ikushima, Akira
- Journal of the Physical Society of Japan, Vol. 34, Issue 4
The thermal conductivity of insulators and semiconductors
journal, March 1986
- Vandersande, J. W.; Wood, C.
- Contemporary Physics, Vol. 27, Issue 2
Phase-Change Materials: Vibrational Softening upon Crystallization and Its Impact on Thermal Properties
journal, April 2011
- Matsunaga, Toshiyuki; Yamada, Noboru; Kojima, Rie
- Advanced Functional Materials, Vol. 21, Issue 12
Anisotropic Thermal Conductivity of Pyrolytic Graphite
journal, August 1962
- Slack, Glen A.
- Physical Review, Vol. 127, Issue 3
Thermal diffusivity of oxide perovskite compounds at elevated temperature
journal, May 2010
- Hofmeister, Anne M.
- Journal of Applied Physics, Vol. 107, Issue 10
The crystal structure of IV-VI compounds. I. Classification and description
journal, September 1980
- Littlewood, P. B.
- Journal of Physics C: Solid State Physics, Vol. 13, Issue 26
Theory of Heat Conduction in Rare-Gas Crystals
journal, January 1965
- Julian, Carl L.
- Physical Review, Vol. 137, Issue 1A
Thermalization and possible signatures of quantum chaos in complex crystalline materials
journal, September 2019
- Zhang, Jiecheng; Kountz, Erik D.; Behnia, Kamran
- Proceedings of the National Academy of Sciences, Vol. 116, Issue 40
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
journal, November 1990
- Bouchaud, Jean-Philippe; Georges, Antoine
- Physics Reports, Vol. 195, Issue 4-5
Thermal Transport and Phonon Hydrodynamics in Strontium Titanate
journal, March 2018
- Martelli, Valentina; Jiménez, Julio Larrea; Continentino, Mucio
- Physical Review Letters, Vol. 120, Issue 12
Sound Wave Propagation in Molten Silver Halides
journal, February 1989
- Takesawa, Koh-ichi; Takeda, Shin'ichi; Harada, zi
- Journal of the Physical Society of Japan, Vol. 58, Issue 2
The Molar Heats of Lead Sulphide, Selenide and Telluride in the Temperature Range 20 K to 260 K
journal, July 1954
- Parkinson, D. H.; Quarrington, J. E.
- Proceedings of the Physical Society. Section A, Vol. 67, Issue 7
Large Anisotropy of the Electrical Conductivity of Graphite
journal, October 1939
- Krishnan, K. S.; Ganguli, N.
- Nature, Vol. 144, Issue 3650
Intrinsically Minimal Thermal Conductivity in Cubic Semiconductors
journal, July 2008
- Morelli, D. T.; Jovovic, V.; Heremans, J. P.
- Physical Review Letters, Vol. 101, Issue 3, Article No. 035901
Heat capacity and thermodynamic properties of lead selenide and lead telluride
journal, November 2009
- Pashinkin, A. S.; Mikhailova, M. S.; Malkova, A. S.
- Inorganic Materials, Vol. 45, Issue 11
Interpretation of the Thermal Conductivity of Glasses
journal, March 1949
- Kittel, Charles
- Physical Review, Vol. 75, Issue 6
Lead telluride alloy thermoelectrics
journal, November 2011
- LaLonde, Aaron D.; Pei, Yanzhong; Wang, Heng
- Materials Today, Vol. 14, Issue 11
Resonant bonding leads to low lattice thermal conductivity
journal, April 2014
- Lee, Sangyeop; Esfarjani, Keivan; Luo, Tengfei
- Nature Communications, Vol. 5, Issue 1
Pressure Dependence of the Structural Phase Transition Temperature in SrTiO 3 and KMnF 3
journal, July 1975
- Okai, Bin; Yoshimoto, Jiichiro
- Journal of the Physical Society of Japan, Vol. 39, Issue 1
Universal Charge Diffusion and the Butterfly Effect in Holographic Theories
journal, August 2016
- Blake, Mike
- Physical Review Letters, Vol. 117, Issue 9
Lattice Thermal Conductivity
journal, June 1955
- Dugdale, J. S.; MacDonald, D. K. C.
- Physical Review, Vol. 98, Issue 6
Ab initio phonon dispersions for PbTe
journal, December 2008
- An, Jiming; Subedi, Alaska; Singh, D. J.
- Solid State Communications, Vol. 148, Issue 9-10
Improved Callaway model for lattice thermal conductivity
journal, October 2013
- Allen, Philip B.
- Physical Review B, Vol. 88, Issue 14
Superconductivity in Bad Metals
journal, April 1995
- Emery, V. J.; Kivelson, S. A.
- Physical Review Letters, Vol. 74, Issue 16
Thermal diffusivity above the Mott-Ioffe-Regel limit
journal, December 2019
- Zhang, Jiecheng; Kountz, Erik D.; Levenson-Falk, Eli M.
- Physical Review B, Vol. 100, Issue 24
Thermal conductivity of perovskite ferroelectrics
journal, September 2008
- Tachibana, Makoto; Kolodiazhnyi, Taras; Takayama-Muromachi, Eiji
- Applied Physics Letters, Vol. 93, Issue 9
Thermal Conductivity and Specific Heat of Noncrystalline Solids
journal, September 1971
- Zeller, R. C.; Pohl, R. O.
- Physical Review B, Vol. 4, Issue 6
Competition and cooperation between antiferrodistortive and ferroelectric instabilities in the model perovskite SrTiO 3
journal, March 2014
- Aschauer, Ulrich; Spaldin, Nicola A.
- Journal of Physics: Condensed Matter, Vol. 26, Issue 12
Model for Lattice Thermal Conductivity at Low Temperatures
journal, February 1959
- Callaway, Joseph
- Physical Review, Vol. 113, Issue 4
Large thermoelectric response of metallic perovskites:
journal, March 2001
- Okuda, T.; Nakanishi, K.; Miyasaka, S.
- Physical Review B, Vol. 63, Issue 11
Normal-state transport properties of crystals
journal, January 1990
- Martin, S.; Fiory, A. T.; Fleming, R. M.
- Physical Review B, Vol. 41, Issue 1
History and challenges of barium titanate: Part I
journal, January 2008
- Vijatovic, M. M.; Bobic, J. D.; Stojanovic, B. D.
- Science of Sintering, Vol. 40, Issue 2
Anisotropy of the elastic and nonlinear acoustic properties of dense textured
journal, April 1994
- Saunders, G. A.
- Physical Review B, Vol. 49, Issue 14
Dissecting holographic conductivities
journal, September 2015
- Davison, Richard A.; Goutéraux, Blaise
- Journal of High Energy Physics, Vol. 2015, Issue 9
Theory of Diffusive Fluctuations
journal, March 2019
- Chen-Lin, Xinyi; Delacrétaz, Luca V.; Hartnoll, Sean A.
- Physical Review Letters, Vol. 122, Issue 9
Theory of universal incoherent metallic transport
journal, December 2014
- Hartnoll, Sean A.
- Nature Physics, Vol. 11, Issue 1
Enhancement of Thermoelectric Efficiency in PbTe by Distortion of the Electronic Density of States
journal, July 2008
- Heremans, J. P.; Jovovic, V.; Toberer, E. S.
- Science, Vol. 321, Issue 5888, p. 554-557
Thermal diffusivity of Bi2Sr2CaCu2O8 single crystals
journal, December 1993
- Wu, X. D.; Fanton, J. G.; Kino, G. S.
- Physica C: Superconductivity, Vol. 218, Issue 3-4
First Principles Peierls-Boltzmann Phonon Thermal Transport: A Topical Review
journal, April 2016
- Lindsay, Lucas
- Nanoscale and Microscale Thermophysical Engineering, Vol. 20, Issue 2
Similarity of Scattering Rates in Metals Showing T-Linear Resistivity
journal, February 2013
- Bruin, J. A. N.; Sakai, H.; Perry, R. S.
- Science, Vol. 339, Issue 6121
Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles
journal, January 2018
- Ribeiro, Guilherme A. S.; Paulatto, Lorenzo; Bianco, Raffaello
- Physical Review B, Vol. 97, Issue 1
Anomalous thermal diffusivity in underdoped YBa 2 Cu 3 O 6+x
journal, May 2017
- Zhang, Jiecheng; Levenson-Falk, Eli M.; Ramshaw, B. J.
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 21
Low-temperature thermal conductivity and acoustic attenuation in amorphous solids
journal, October 2002
- Pohl, Robert O.; Liu, Xiao; Thompson, EunJoo
- Reviews of Modern Physics, Vol. 74, Issue 4
SnSe: a remarkable new thermoelectric material
journal, January 2016
- Zhao, Li-Dong; Chang, Cheng; Tan, Gangjian
- Energy & Environmental Science, Vol. 9, Issue 10
Sound velocities of PbTe to 14 GPa: evidence for coupling between acoustic and optic phonons
journal, August 2013
- Jacobsen, Matthew K.; Liu, Wei; Li, Baosheng
- Journal of Physics: Condensed Matter, Vol. 25, Issue 36
Quantum chaos on a critical Fermi surface
journal, February 2017
- Patel, Aavishkar A.; Sachdev, Subir
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 8
Three-phonon phase space and lattice thermal conductivity in semiconductors
journal, March 2008
- Lindsay, L.; Broido, D. A.
- Journal of Physics: Condensed Matter, Vol. 20, Issue 16