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

This content will become publicly available on July 11, 2020

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 (τ p = h/ k B T). 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.
@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
This content will become publicly available on July 11, 2020
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Improved Callaway model for lattice thermal conductivity
journal, October 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

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

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


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


Interpretation of the Thermal Conductivity of Glasses
journal, March 1949


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

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

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

Lattice Thermal Conductivity
journal, June 1955


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


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


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


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


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

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

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


Theory of Diffusive Fluctuations
journal, March 2019


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


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


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


Thermal conductivity of disordered harmonic solids
journal, November 1993


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


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


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


Theory of universal incoherent metallic transport
journal, December 2014


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

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

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

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