A lower bound to the thermal diffusivity of insulators

Behnia, Kamran; Kapitulnik, Aharon

doi:10.1088/1361-648x/ab2db6

A lower bound to the thermal diffusivity of insulators

Journal Article · Thu Jul 11 00:00:00 EDT 2019 · Journal of Physics. Condensed Matter

DOI:https://doi.org/10.1088/1361-648x/ab2db6· OSTI ID:1576517

^[1]; Kapitulnik, Aharon ^[2]

PSL Research Univ., Paris (France); Univ. zu Köln, Koln (Germany)
Stanford Univ., Stanford, CA (United States)

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_BT). 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.

View Accepted Manuscript (DOE)

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1576517

Alternate ID(s):: OSTI ID: 23009270

Journal Information:: Journal of Physics. Condensed Matter, Journal Name: Journal of Physics. Condensed Matter Journal Issue: 40 Vol. 31; ISSN 0953-8984

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (62)

Phase-Change Materials: Vibrational Softening upon Crystallization and Its Impact on Thermal Properties Matsunaga, Toshiyuki; Yamada, Noboru; Kojima, Rie Advanced Functional Materials, Vol. 21, Issue 12 https://doi.org/10.1002/adfm.201002274	journal	April 2011
Thermophysical properties of polycrystalline PbS, PbSe, and PbTe in the temperature range 300?700 K El-Sharkawy, A. A.; Abou El-Azm, A. M.; Kenawy, M. I. International Journal of Thermophysics, Vol. 4, Issue 3 https://doi.org/10.1007/BF00502357	journal	September 1983
Dissecting holographic conductivities Davison, Richard A.; Goutéraux, Blaise Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)090	journal	September 2015
Nonmetallic crystals with high thermal conductivity Slack, G. A. Journal of Physics and Chemistry of Solids, Vol. 34, Issue 2 https://doi.org/10.1016/0022-3697(73)90092-9	journal	January 1973
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications Bouchaud, Jean-Philippe; Georges, Antoine Physics Reports, Vol. 195, Issue 4-5 https://doi.org/10.1016/0370-1573(90)90099-N	journal	November 1990
Ultrasonic propagation velocity in KTaO3 Barrett, H. H. Physics Letters A, Vol. 26, Issue 6 https://doi.org/10.1016/0375-9601(68)90609-9	journal	February 1968
Thermal diffusivity of Bi2Sr2CaCu2O8 single crystals Wu, X. D.; Fanton, J. G.; Kino, G. S. Physica C: Superconductivity, Vol. 218, Issue 3-4 https://doi.org/10.1016/0921-4534(93)90044-Q	journal	December 1993
The Thermal Conductivity of Nonmetallic Crystals Slack, Glen A. Solid State Physics https://doi.org/10.1016/S0081-1947(08)60359-8	book	January 1979
Lead telluride alloy thermoelectrics LaLonde, Aaron D.; Pei, Yanzhong; Wang, Heng Materials Today, Vol. 14, Issue 11 https://doi.org/10.1016/S1369-7021(11)70278-4	journal	November 2011
Ab initio phonon dispersions for PbTe An, Jiming; Subedi, Alaska; Singh, D. J. Solid State Communications, Vol. 148, Issue 9-10 https://doi.org/10.1016/j.ssc.2008.09.027	journal	December 2008
Quantum Phase Transitions Sachdev, Subir https://doi.org/10.1017/CBO9780511973765	book	January 2011
Quantum Phase Transitions Sachdev, Subir Cambridge University Press https://doi.org/10.1017/cbo9780511622540	book	January 2012
Large Anisotropy of the Electrical Conductivity of Graphite Krishnan, K. S.; Ganguli, N. Nature, Vol. 144, Issue 3650 https://doi.org/10.1038/144667a0	journal	October 1939
Why the temperature is high Zaanen, Jan Nature, Vol. 430, Issue 6999 https://doi.org/10.1038/430512a	journal	July 2004
Resonant bonding leads to low lattice thermal conductivity Lee, Sangyeop; Esfarjani, Keivan; Luo, Tengfei Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms4525	journal	April 2014
Theory of universal incoherent metallic transport Hartnoll, Sean A. Nature Physics, Vol. 11, Issue 1 https://doi.org/10.1038/nphys3174	journal	December 2014
SnSe: a remarkable new thermoelectric material Zhao, Li-Dong; Chang, Cheng; Tan, Gangjian Energy & Environmental Science, Vol. 9, Issue 10 https://doi.org/10.1039/C6EE01755J	journal	January 2016
Thermal conductivity of perovskite ferroelectrics Tachibana, Makoto; Kolodiazhnyi, Taras; Takayama-Muromachi, Eiji Applied Physics Letters, Vol. 93, Issue 9 https://doi.org/10.1063/1.2978072	journal	September 2008
Thermal diffusivity of oxide perovskite compounds at elevated temperature Hofmeister, Anne M. Journal of Applied Physics, Vol. 107, Issue 10 https://doi.org/10.1063/1.3371815	journal	May 2010
Quantum chaos on a critical Fermi surface Patel, Aavishkar A.; Sachdev, Subir Proceedings of the National Academy of Sciences, Vol. 114, Issue 8 https://doi.org/10.1073/pnas.1618185114	journal	February 2017
Anomalous thermal diffusivity in underdoped YBa ₂ Cu ₃ O _6+x Zhang, Jiecheng; Levenson-Falk, Eli M.; Ramshaw, B. J. Proceedings of the National Academy of Sciences, Vol. 114, Issue 21 https://doi.org/10.1073/pnas.1703416114	journal	May 2017
The thermal conductivity of insulators and semiconductors Vandersande, J. W.; Wood, C. Contemporary Physics, Vol. 27, Issue 2 https://doi.org/10.1080/00107518608211003	journal	March 1986
First Principles Peierls-Boltzmann Phonon Thermal Transport: A Topical Review Lindsay, Lucas Nanoscale and Microscale Thermophysical Engineering, Vol. 20, Issue 2 https://doi.org/10.1080/15567265.2016.1218576	journal	April 2016
The crystal structure of IV-VI compounds. I. Classification and description Littlewood, P. B. Journal of Physics C: Solid State Physics, Vol. 13, Issue 26 https://doi.org/10.1088/0022-3719/13/26/009	journal	September 1980
The heat capacity and Gruneisen parameter of KTaO ₃ White, G. K.; Collocott, S. J. Journal of Physics C: Solid State Physics, Vol. 20, Issue 30 https://doi.org/10.1088/0022-3719/20/30/003	journal	October 1987
The Molar Heats of Lead Sulphide, Selenide and Telluride in the Temperature Range 20 K to 260 K Parkinson, D. H.; Quarrington, J. E. Proceedings of the Physical Society. Section A, Vol. 67, Issue 7 https://doi.org/10.1088/0370-1298/67/7/301	journal	July 1954
Three-phonon phase space and lattice thermal conductivity in semiconductors Lindsay, L.; Broido, D. A. Journal of Physics: Condensed Matter, Vol. 20, Issue 16 https://doi.org/10.1088/0953-8984/20/16/165209	journal	March 2008
Sound velocities of PbTe to 14 GPa: evidence for coupling between acoustic and optic phonons Jacobsen, Matthew K.; Liu, Wei; Li, Baosheng Journal of Physics: Condensed Matter, Vol. 25, Issue 36 https://doi.org/10.1088/0953-8984/25/36/365402	journal	August 2013
Competition and cooperation between antiferrodistortive and ferroelectric instabilities in the model perovskite SrTiO ₃ Aschauer, Ulrich; Spaldin, Nicola A. Journal of Physics: Condensed Matter, Vol. 26, Issue 12 https://doi.org/10.1088/0953-8984/26/12/122203	journal	March 2014
Model for Lattice Thermal Conductivity at Low Temperatures Callaway, Joseph Physical Review, Vol. 113, Issue 4 https://doi.org/10.1103/PhysRev.113.1046	journal	February 1959
Anisotropic Thermal Conductivity of Pyrolytic Graphite Slack, Glen A. Physical Review, Vol. 127, Issue 3 https://doi.org/10.1103/PhysRev.127.694	journal	August 1962
Theory of Heat Conduction in Rare-Gas Crystals Julian, Carl L. Physical Review, Vol. 137, Issue 1A https://doi.org/10.1103/PhysRev.137.A128	journal	January 1965
Interpretation of the Thermal Conductivity of Glasses Kittel, Charles Physical Review, Vol. 75, Issue 6 https://doi.org/10.1103/PhysRev.75.972	journal	March 1949
Lattice Thermal Conductivity Dugdale, J. S.; MacDonald, D. K. C. Physical Review, Vol. 98, Issue 6 https://doi.org/10.1103/PhysRev.98.1751	journal	June 1955
Thermal Conductivity and Specific Heat of Noncrystalline Solids Zeller, R. C.; Pohl, R. O. Physical Review B, Vol. 4, Issue 6 https://doi.org/10.1103/PhysRevB.4.2029	journal	September 1971
Thermal conductivity of disordered harmonic solids Allen, Philip B.; Feldman, Joseph L. Physical Review B, Vol. 48, Issue 17 https://doi.org/10.1103/PhysRevB.48.12581	journal	November 1993
Anisotropy of the elastic and nonlinear acoustic properties of dense textured Bi 2 Sr 2 CaCu 2 O 8 + y Saunders, G. A. Physical Review B, Vol. 49, Issue 14 https://doi.org/10.1103/PhysRevB.49.9862	journal	April 1994
Large thermoelectric response of metallic perovskites: Sr 1 − x La x TiO 3 ( 0 <~ x <~ 0 . 1 ) Okuda, T.; Nakanishi, K.; Miyasaka, S. Physical Review B, Vol. 63, Issue 11 https://doi.org/10.1103/PhysRevB.63.113104	journal	March 2001
Improved Callaway model for lattice thermal conductivity Allen, Philip B. Physical Review B, Vol. 88, Issue 14 https://doi.org/10.1103/PhysRevB.88.144302	journal	October 2013
Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles Ribeiro, Guilherme A. S.; Paulatto, Lorenzo; Bianco, Raffaello Physical Review B, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevB.97.014306	journal	January 2018
Intrinsically Minimal Thermal Conductivity in Cubic I−V−VI2 Semiconductors Morelli, D. T.; Jovovic, V.; Heremans, J. P. Physical Review Letters, Vol. 101, Issue 3, Article No. 035901 https://doi.org/10.1103/PhysRevLett.101.035901	journal	July 2008
Universal Charge Diffusion and the Butterfly Effect in Holographic Theories Blake, Mike Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.091601	journal	August 2016
Thermal Transport and Phonon Hydrodynamics in Strontium Titanate Martelli, Valentina; Jiménez, Julio Larrea; Continentino, Mucio Physical Review Letters, Vol. 120, Issue 12 https://doi.org/10.1103/PhysRevLett.120.125901	journal	March 2018
Theory of Diffusive Fluctuations Chen-Lin, Xinyi; Delacrétaz, Luca V.; Hartnoll, Sean A. Physical Review Letters, Vol. 122, Issue 9 https://doi.org/10.1103/PhysRevLett.122.091602	journal	March 2019
Some aspects of the thermal conductivity of isotopically enriched diamond single crystals Onn, D. G.; Witek, A.; Qiu, Y. Z. Physical Review Letters, Vol. 68, Issue 18 https://doi.org/10.1103/PhysRevLett.68.2806	journal	May 1992
Superconductivity in Bad Metals Emery, V. J.; Kivelson, S. A. Physical Review Letters, Vol. 74, Issue 16 https://doi.org/10.1103/PhysRevLett.74.3253	journal	April 1995
Low-temperature thermal conductivity and acoustic attenuation in amorphous solids Pohl, Robert O.; Liu, Xiao; Thompson, EunJoo Reviews of Modern Physics, Vol. 74, Issue 4 https://doi.org/10.1103/RevModPhys.74.991	journal	October 2002
Normal-state transport properties of Bi 2 + x Sr 2 − y CuO 6 + δ crystals Martin, S.; Fiory, A. T.; Fleming, R. M. Physical Review B, Vol. 41, Issue 1 https://doi.org/10.1103/physrevb.41.846	journal	January 1990
Enhancement of Thermoelectric Efficiency in PbTe by Distortion of the Electronic Density of States Heremans, J. P.; Jovovic, V.; Toberer, E. S. Science, Vol. 321, Issue 5888, p. 554-557 https://doi.org/10.1126/science.1159725	journal	July 2008
Similarity of Scattering Rates in Metals Showing T-Linear Resistivity Bruin, J. A. N.; Sakai, H.; Perry, R. S. Science, Vol. 339, Issue 6121 https://doi.org/10.1126/science.1227612	journal	February 2013
Finding merit in dividing neighbors Behnia, K. Science, Vol. 351, Issue 6269 https://doi.org/10.1126/science.aad8688	journal	January 2016
Heat capacity and thermodynamic properties of lead selenide and lead telluride Pashinkin, A. S.; Mikhailova, M. S.; Malkova, A. S. Inorganic Materials, Vol. 45, Issue 11 https://doi.org/10.1134/S0020168509110065	journal	November 2009
Ultrasonic Velocities in BaTiO ₃ Kashida, Shoji; Hatta, Ichiro; Ikushima, Akira Journal of the Physical Society of Japan, Vol. 34, Issue 4 https://doi.org/10.1143/JPSJ.34.997	journal	April 1973
Pressure Dependence of the Structural Phase Transition Temperature in SrTiO ₃ and KMnF ₃ Okai, Bin; Yoshimoto, Jiichiro Journal of the Physical Society of Japan, Vol. 39, Issue 1 https://doi.org/10.1143/JPSJ.39.162	journal	July 1975
Sound Wave Propagation in Molten Silver Halides Takesawa, Koh-ichi; Takeda, Shin'ichi; Harada, zi Journal of the Physical Society of Japan, Vol. 58, Issue 2 https://doi.org/10.1143/JPSJ.58.538	journal	February 1989
History and challenges of barium titanate: Part I Vijatovic, M. M.; Bobic, J. D.; Stojanovic, B. D. Science of Sintering, Vol. 40, Issue 2 https://doi.org/10.2298/SOS0802155V	journal	January 2008
Ab Initio Phonon Dispersions for PbTe An, Jiming; Subedi, Alaska; Singh, David J. arXiv https://doi.org/10.48550/arxiv.0806.2727	text	January 2008
Theory of universal incoherent metallic transport Hartnoll, Sean A. arXiv https://doi.org/10.48550/arxiv.1405.3651	text	January 2014
Anomalous Thermal Diffusivity in Underdoped YBa$_2$Cu$_3$O$_{6+x}$ Zhang, J. -C.; Levenson-Falk, E. M.; Ramshaw, B. J. arXiv https://doi.org/10.48550/arxiv.1610.05845	text	January 2016
Quantum chaos on a critical Fermi surface Patel, Aavishkar A.; Sachdev, Subir arXiv https://doi.org/10.48550/arxiv.1611.00003	text	January 2016
Theory of diffusive fluctuations Chen-Lin, Xinyi; Delacrétaz, Luca V.; Hartnoll, Sean A. arXiv https://doi.org/10.48550/arxiv.1811.12540	text	January 2018
Competition and cooperation between antiferrodistortive and ferroelectric instabilities in the model perovskite SrTiO₃ Spaldin, Nicola A.; Aschauer, Ulrich Johannes Institute of Physics Publishing IOP https://doi.org/10.7892/boris.72983	text	January 2014

Cited By (8)

Holographic axion model: A simple gravitational tool for quantum matter Baggioli, Matteo; Kim, Keun-Young; Li, Li Science China Physics, Mechanics & Astronomy, Vol. 64, Issue 7 https://doi.org/10.1007/s11433-021-1681-8	journal	June 2021
On the Planckian bound for heat diffusion in insulators Mousatov, Connie H.; Hartnoll, Sean A. Nature Physics, Vol. 16, Issue 5 https://doi.org/10.1038/s41567-020-0828-6	journal	March 2020
Classical model for sub-Planckian thermal diffusivity in complex crystals Wu, Huan-Kuang; Sau, Jay D. Physical Review B, Vol. 103, Issue 18 https://doi.org/10.1103/physrevb.103.184305	journal	May 2021
Thermalization and Possible Signatures of Quantum Chaos in Complex Crystalline Materials Zhang, Jiecheng; Kountz, Erik D.; Behnia, Kamran arXiv https://doi.org/10.48550/arxiv.2001.03805	text	January 2020
Phonons, electrons and thermal transport in Planckian high T$_c$ materials Mousatov, Connie H.; Hartnoll, Sean A. arXiv https://doi.org/10.48550/arxiv.2011.10466	preprint	January 2020
Thermalization and possible signatures of quantum chaos in complex crystalline materials Zhang, Jiecheng; Kountz, Erik D.; Behnia, Kamran Proceedings of the National Academy of Sciences, Vol. 116, Issue 40 https://doi.org/10.1073/pnas.1910131116	journal	September 2019
Thermal diffusivity above the Mott-Ioffe-Regel limit Zhang, Jiecheng; Kountz, Erik D.; Levenson-Falk, Eli M. Physical Review B, Vol. 100, Issue 24 https://doi.org/10.1103/physrevb.100.241114	journal	December 2019
Thermal Diffusivity Above Mott-Ioffe-Regel Limit Zhang, Jiecheng; Kountz, Erik D.; Levenson-Falk, Eli M. arXiv https://doi.org/10.48550/arxiv.1808.07564	text	January 2018