skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
ORCiD logo [1];  [2]
  1. PSL Research Univ., Paris (France); Univ. zu Köln, Koln (Germany)
  2. 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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
  • DOI: 10.1103/PhysRevB.97.014306

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
  • DOI: 10.1143/JPSJ.58.538

Finding merit in dividing neighbors
journal, January 2016


Interpretation of the Thermal Conductivity of Glasses
journal, March 1949


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
  • DOI: 10.1143/JPSJ.39.162

Lattice Thermal Conductivity
journal, June 1955


Ab initio phonon dispersions for PbTe
journal, December 2008


Thermal conductivity of perovskite ferroelectrics
journal, September 2008

  • Tachibana, Makoto; Kolodiazhnyi, Taras; Takayama-Muromachi, Eiji
  • Applied Physics Letters, Vol. 93, Issue 9
  • DOI: 10.1063/1.2978072

Lead telluride alloy thermoelectrics
journal, November 2011


Heat capacity and thermodynamic properties of lead selenide and lead telluride
journal, November 2009


Model for Lattice Thermal Conductivity at Low Temperatures
journal, February 1959


Universal Charge Diffusion and the Butterfly Effect in Holographic Theories
journal, August 2016


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
  • DOI: 10.1073/pnas.1618185114

Normal-state transport properties of Bi 2 + x Sr 2 y CuO 6 + δ crystals
journal, January 1990


Theory of Diffusive Fluctuations
journal, March 2019


The crystal structure of IV-VI compounds. I. Classification and description
journal, September 1980


Three-phonon phase space and lattice thermal conductivity in semiconductors
journal, March 2008


Why the temperature is high
journal, July 2004


Low-temperature thermal conductivity and acoustic attenuation in amorphous solids
journal, October 2002


Lattice Thermal Conductivity
journal, December 1965


The heat capacity and Gruneisen parameter of KTaO 3
journal, October 1987


Intrinsically Minimal Thermal Conductivity in Cubic IVVI2 Semiconductors
journal, July 2008


Theory of universal incoherent metallic transport
journal, December 2014


Large thermoelectric response of metallic perovskites: Sr 1 x La x TiO 3 ( 0 <~ x <~ 0 . 1 )
journal, March 2001


First Principles Peierls-Boltzmann Phonon Thermal Transport: A Topical Review
journal, April 2016


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
  • DOI: 10.1073/pnas.1703416114

Thermal Conductivity and Specific Heat of Noncrystalline Solids
journal, September 1971


Improved Callaway model for lattice thermal conductivity
journal, October 2013


Large Anisotropy of the Electrical Conductivity of Graphite
journal, October 1939

  • Krishnan, K. S.; Ganguli, N.
  • Nature, Vol. 144, Issue 3650
  • DOI: 10.1038/144667a0

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
  • DOI: 10.1088/0370-1298/67/7/301

Competition and cooperation between antiferrodistortive and ferroelectric instabilities in the model perovskite SrTiO 3
journal, March 2014


Anisotropic Thermal Conductivity of Pyrolytic Graphite
journal, August 1962


Resonant bonding leads to low lattice thermal conductivity
journal, April 2014

  • Lee, Sangyeop; Esfarjani, Keivan; Luo, Tengfei
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms4525

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
  • DOI: 10.1002/adfm.201002274

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
  • DOI: 10.1007/BF00502357

Some aspects of the thermal conductivity of isotopically enriched diamond single crystals
journal, May 1992


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
  • DOI: 10.1126/science.1159725

Theory of Heat Conduction in Rare-Gas Crystals
journal, January 1965


Ultrasonic propagation velocity in KTaO3
journal, February 1968


Thermal diffusivity of oxide perovskite compounds at elevated temperature
journal, May 2010

  • Hofmeister, Anne M.
  • Journal of Applied Physics, Vol. 107, Issue 10
  • DOI: 10.1063/1.3371815

Nonmetallic crystals with high thermal conductivity
journal, January 1973


SnSe: a remarkable new thermoelectric material
journal, January 2016

  • Zhao, Li-Dong; Chang, Cheng; Tan, Gangjian
  • Energy & Environmental Science, Vol. 9, Issue 10
  • DOI: 10.1039/C6EE01755J

Sound velocities of PbTe to 14 GPa: evidence for coupling between acoustic and optic phonons
journal, August 2013


Thermal diffusivity of Bi2Sr2CaCu2O8 single crystals
journal, December 1993


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
  • DOI: 10.2298/SOS0802155V

Thermal Transport and Phonon Hydrodynamics in Strontium Titanate
journal, March 2018


Thermal conductivity of disordered harmonic solids
journal, November 1993


Similarity of Scattering Rates in Metals Showing T-Linear Resistivity
journal, February 2013


The thermal conductivity of insulators and semiconductors
journal, March 1986


Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
journal, November 1990


Superconductivity in Bad Metals
journal, April 1995


Dissecting holographic conductivities
journal, September 2015

  • Davison, Richard A.; Goutéraux, Blaise
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)090

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
  • DOI: 10.1143/JPSJ.34.997

    Works referencing / citing this record:

    Some aspects of the thermal conductivity of isotopically enriched diamond single crystals
    journal, May 1992


    Ultrasonic propagation velocity in KTaO3
    journal, February 1968


    Thermal conductivity of disordered harmonic solids
    journal, November 1993


    Nonmetallic crystals with high thermal conductivity
    journal, January 1973


    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
    • DOI: 10.1007/bf00502357

    The heat capacity and Gruneisen parameter of KTaO 3
    journal, October 1987


    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
    • DOI: 10.1143/jpsj.34.997

    The thermal conductivity of insulators and semiconductors
    journal, March 1986


    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
    • DOI: 10.1002/adfm.201002274

    Anisotropic Thermal Conductivity of Pyrolytic Graphite
    journal, August 1962


    Thermal diffusivity of oxide perovskite compounds at elevated temperature
    journal, May 2010

    • Hofmeister, Anne M.
    • Journal of Applied Physics, Vol. 107, Issue 10
    • DOI: 10.1063/1.3371815

    The crystal structure of IV-VI compounds. I. Classification and description
    journal, September 1980


    Theory of Heat Conduction in Rare-Gas Crystals
    journal, January 1965


    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
    • DOI: 10.1073/pnas.1910131116

    Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
    journal, November 1990


    Thermal Transport and Phonon Hydrodynamics in Strontium Titanate
    journal, March 2018


    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
    • DOI: 10.1143/jpsj.58.538

    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
    • DOI: 10.1088/0370-1298/67/7/301

    Large Anisotropy of the Electrical Conductivity of Graphite
    journal, October 1939

    • Krishnan, K. S.; Ganguli, N.
    • Nature, Vol. 144, Issue 3650
    • DOI: 10.1038/144667a0

    Intrinsically Minimal Thermal Conductivity in Cubic IVVI2 Semiconductors
    journal, July 2008


    Heat capacity and thermodynamic properties of lead selenide and lead telluride
    journal, November 2009


    Interpretation of the Thermal Conductivity of Glasses
    journal, March 1949


    Lead telluride alloy thermoelectrics
    journal, November 2011


    Resonant bonding leads to low lattice thermal conductivity
    journal, April 2014

    • Lee, Sangyeop; Esfarjani, Keivan; Luo, Tengfei
    • Nature Communications, Vol. 5, Issue 1
    • DOI: 10.1038/ncomms4525

    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
    • DOI: 10.1143/jpsj.39.162

    Universal Charge Diffusion and the Butterfly Effect in Holographic Theories
    journal, August 2016


    Lattice Thermal Conductivity
    journal, June 1955


    Ab initio phonon dispersions for PbTe
    journal, December 2008


    Improved Callaway model for lattice thermal conductivity
    journal, October 2013


    Superconductivity in Bad Metals
    journal, April 1995


    Thermal diffusivity above the Mott-Ioffe-Regel limit
    journal, December 2019


    Thermal conductivity of perovskite ferroelectrics
    journal, September 2008

    • Tachibana, Makoto; Kolodiazhnyi, Taras; Takayama-Muromachi, Eiji
    • Applied Physics Letters, Vol. 93, Issue 9
    • DOI: 10.1063/1.2978072

    Thermal Conductivity and Specific Heat of Noncrystalline Solids
    journal, September 1971


    Competition and cooperation between antiferrodistortive and ferroelectric instabilities in the model perovskite SrTiO 3
    journal, March 2014


    Model for Lattice Thermal Conductivity at Low Temperatures
    journal, February 1959


    Large thermoelectric response of metallic perovskites: Sr 1 x La x TiO 3 ( 0 <~ x <~ 0 . 1 )
    journal, March 2001


    Why the temperature is high
    journal, July 2004


    Normal-state transport properties of Bi 2 + x Sr 2 y CuO 6 + δ crystals
    journal, January 1990


    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
    • DOI: 10.2298/sos0802155v

    Dissecting holographic conductivities
    journal, September 2015

    • Davison, Richard A.; Goutéraux, Blaise
    • Journal of High Energy Physics, Vol. 2015, Issue 9
    • DOI: 10.1007/jhep09(2015)090

    Finding merit in dividing neighbors
    journal, January 2016


    Theory of Diffusive Fluctuations
    journal, March 2019


    Theory of universal incoherent metallic transport
    journal, December 2014


    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
    • DOI: 10.1126/science.1159725

    Thermal diffusivity of Bi2Sr2CaCu2O8 single crystals
    journal, December 1993


    First Principles Peierls-Boltzmann Phonon Thermal Transport: A Topical Review
    journal, April 2016


    Similarity of Scattering Rates in Metals Showing T-Linear Resistivity
    journal, February 2013


    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
    • DOI: 10.1103/physrevb.97.014306

    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
    • DOI: 10.1073/pnas.1703416114

    Low-temperature thermal conductivity and acoustic attenuation in amorphous solids
    journal, October 2002


    SnSe: a remarkable new thermoelectric material
    journal, January 2016

    • Zhao, Li-Dong; Chang, Cheng; Tan, Gangjian
    • Energy & Environmental Science, Vol. 9, Issue 10
    • DOI: 10.1039/c6ee01755j

    Sound velocities of PbTe to 14 GPa: evidence for coupling between acoustic and optic phonons
    journal, August 2013


    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
    • DOI: 10.1073/pnas.1618185114

    Three-phonon phase space and lattice thermal conductivity in semiconductors
    journal, March 2008