Skip to main content
SpringerLink
Log in

Phonon anharmonicity: a pertinent review of recent progress and perspective

  • Invited Review
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

Anharmonic lattice vibrations play pivotal roles in the thermal dynamics in condense matters and affect how the atoms interact and conduct heat. An in-depth understanding of the microscopic mechanism of phonon anharmonicity in condensed systems is critical for developing better functional and energy materials. In recent years, various novel behaviors in condense matters driven by phonon anharmonic effects were discovered, such as soft mode phase transition, negative thermal expansion (NTE), multiferroicity, ultralow thermal conductivity (κ), high thermal resistance, and high-temperature superconductivity. These properties have endowed anharmonicity with many promising applications and provided remarkable opportunities for developing “Anharmonicity Engineering”—regulating heat transport towards excellent performance in materials. In this work, we review the recent development of studies on phonon anharmonic effect and summarize its origin, mechanism, research methods, and applications. Besides, the remaining challenges, future trends, and prospects of phonon anharmonicity are also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. Monserrat, N. D. Drummond, and R. J. Needs, Phys. Rev. B 87, 144302 (2013), arXiv: 1303.0745.

    Article  ADS  Google Scholar 

  2. D. C. Wallace, Thermodynamics of Crystals (Wiley, New York, 1972).

    Book  Google Scholar 

  3. I. P. Ipatova, A. A. Maradudin, E. W. Montroll, and G. H. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation (2nd ed) (Academic Press, New York, 1971).

    Google Scholar 

  4. B. Fultz, Prog. Mater. Sci. 55, 247 (2010).

    Article  Google Scholar 

  5. B. Fultz, T. Kelley, J. Lin, J. D. Lee, O. Delaire, M. Kresch, M. McKerns, and H. Smith, Experimental Inelastic Neutron Scattering with a Chopper Spectrometer (Springer, Heidelberg, 2018).

    Google Scholar 

  6. M. Born, and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, Oxford, 1954).

    MATH  Google Scholar 

  7. G. P. Srivastava, The Physics of Phonons (CRC Press, Boca Raton, 1990).

    Google Scholar 

  8. G. Mie, Ann. Physik 316, 657 (1903).

    Article  ADS  Google Scholar 

  9. E. Grüneisen, Ann. Physik 331, 393 (1908).

    Article  ADS  Google Scholar 

  10. M. Born, J. Chem. Phys. 7, 591 (1939).

    Article  ADS  Google Scholar 

  11. M. Born, Math. Proc. Camb. Phil. Soc. 36, 160 (1940).

    Article  ADS  Google Scholar 

  12. R. D. Misra, and M. Born, Math. Proc. Camb. Phil. Soc. 36, 173 (1940).

    Article  ADS  Google Scholar 

  13. M. Born, and R. D. Misra, Math. Proc. Camb. Phil. Soc. 36, 466 (1940).

    Article  ADS  Google Scholar 

  14. M. Born, and E. Brody, Z. Physik 6, 132 (1921).

    Article  ADS  Google Scholar 

  15. G. Leibfried, and W. Ludwig, Solid State Phys. 12, 275 (1961).

    Article  Google Scholar 

  16. L. Wilk, Anharmonic Helmholtz Free Energy to O(λ4) in the Non-leading Term Approximation, Dissertation for Master’s Degree (Brock University, Ontario, 1972).

    Google Scholar 

  17. G. Leibfried. Gittertheorie der Mechanischen und Thermischen Eigenschaften der Kristalle (Springer, Berlin, Heidelberg, 1955).

    Book  Google Scholar 

  18. M. Born, and M. Blackman, Z. Physik 82, 551 (1933).

    Article  ADS  Google Scholar 

  19. M. Blackman, Z. Physik 86, 421 (1933).

    Article  ADS  Google Scholar 

  20. S. K. Joshi, and A. K. Rajagopal, Solid State Phys. 22, 159 (1969).

    Article  Google Scholar 

  21. A. D. B. Woods, W. Cochran, and B. N. Brockhouse, Phys. Rev. 119, 980 (1960).

    Article  ADS  Google Scholar 

  22. A. D. B. Woods, B. N. Brockhouse, R. A. Cowley, and W. Cochran, Phys. Rev. 131, 1025 (1963).

    Article  ADS  Google Scholar 

  23. R. A. Cowley, W. Cochran, B. N. Brockhouse, and A. D. B. Woods, Phys. Rev. 131, 1030 (1963).

    Article  ADS  Google Scholar 

  24. R. A. Cowley, Rep. Prog. Phys. 31, 123 (1968).

    Article  ADS  Google Scholar 

  25. K. N. Pathak, Phys. Rev. 139, 1569 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  26. H. J. Maris, Phys. Lett. 17, 228 (1965).

    Article  ADS  Google Scholar 

  27. W. Cochran, C R C Crit. Rev. Solid State Sci. 2, 1 (1971).

    Article  Google Scholar 

  28. W. Cochran, and R. A. Cowley, Phonons in perfect crystals, in Light and Matter Ia (Springer, Berlin, 1967).

    Google Scholar 

  29. C. G. Rodrigues, J. N. Teixeira Rabelo, and V. I. Zubov, Braz. J. Phys. 36, 592 (2006).

    Article  ADS  Google Scholar 

  30. T. Feng, and L. Ruan, J. Nanomater. 2014, 1 (2014).

    Google Scholar 

  31. T. Paszkiewicz, Physics of Phonons (Springer, Berlin, 1987).

    Book  Google Scholar 

  32. G. Dolling, The Calculation of Phonon Frequencies (Academic Press, New York, 1976).

    Book  Google Scholar 

  33. H. Bilz, D. Strauch, and R. K. Wehner, Light and Matter Id (Springer, Berlin, 1984).

    Book  Google Scholar 

  34. K. Esfarjani, and Y. Liang, Nanoscale Energy Transport 7, 1 (2019).

    Google Scholar 

  35. T. Tadano, and S. Tsuneyuki, J. Phys. Soc. Jpn. 87, 041015 (2018), arXiv: 1706.04744.

    Article  ADS  Google Scholar 

  36. T. Feng, and X. Ruan, Nanoscale Energy Transport 2, 1 (2020).

    Google Scholar 

  37. O. L. Krivanek, N. Dellby, J. A. Hachtel, J. C. Idrobo, M. T. Hotz, B. Plotkin-Swing, N. J. Bacon, A. L. Bleloch, G. J. Corbin, M. V. Hoffman, C. E. Meyer, and T. C. Lovejoy, Ultramicroscopy 203, 60 (2019).

    Article  Google Scholar 

  38. R. Mittal, M. K. Gupta, and S. L. Chaplot, Prog. Mater. Sci. 92, 360 (2018).

    Article  Google Scholar 

  39. C. W. Li, J. Hong, A. F. May, D. Bansal, S. Chi, T. Hong, G. Ehlers, and O. Delaire, Nat. Phys. 11, 1063 (2015).

    Article  Google Scholar 

  40. D. S. Kim, H. L. Smith, J. L. Niedziela, C. W. Li, D. L. Abernathy, and B. Fultz, Phys. Rev. B 91, 014307 (2015).

    Article  ADS  Google Scholar 

  41. D. Bansal, J. Hong, C. W. Li, A. F. May, W. Porter, M. Y. Hu, D. L. Abernathy, and O. Delaire, Phys. Rev. B 94, 054307 (2016), arXiv: 1608.01883.

    Article  ADS  Google Scholar 

  42. J. He, M. Amsler, Y. Xia, S. S. Naghavi, V. I. Hegde, S. Hao, S. Goedecker, V. Ozoliņš, and C. Wolverton, Phys. Rev. Lett. 117, 046602 (2016), arXiv: 1604.03827.

    Article  ADS  Google Scholar 

  43. D. M. Juraschek, M. Fechner, A. V. Balatsky, and N. A. Spaldin, Phys. Rev. Mater. 1, 014401 (2017), arXiv: 1612.06331.

    Article  Google Scholar 

  44. J. P. Heremans, Nat. Phys. 11, 990 (2015).

    Article  Google Scholar 

  45. W. Kim, J. Mater. Chem. C 3, 10336 (2015).

    Article  Google Scholar 

  46. Z. Tian, S. Lee, and G. Chen, Annu. Rev. Heat Transfer. 17, 425 (2014).

    Article  Google Scholar 

  47. E. S. Toberer, A. Zevalkink, and G. J. Snyder, J. Mater. Chem. 21, 15843 (2011).

    Article  Google Scholar 

  48. J. Hong, and O. Delaire, Mater. Today Phys. 10, 100093 (2019).

    Article  Google Scholar 

  49. M. Sist, K. F. F. Fischer, H. Kasai, and B. B. Iversen, Angew. Chem. 129, 3679 (2017).

    Article  ADS  Google Scholar 

  50. B. Wei, X. Yu, C. Yang, X. Rao, X. Wang, S. Chi, X. Sun, and J. Hong, Phys. Rev. B 99, 184301 (2019).

    Article  ADS  Google Scholar 

  51. M. P. Jiang, M. Trigo, I. Savić, S. Fahy, É. D. Murray, C. Bray, J. Clark, T. Henighan, M. Kozina, M. Chollet, J. M. Glownia, M. C. Hoffmann, D. Zhu, O. Delaire, A. F. May, B. C. Sales, A. M. Lindenberg, P. Zalden, T. Sato, R. Merlin, and D. A. Reis, Nat. Commun. 7, 12291 (2016).

    Article  ADS  Google Scholar 

  52. C. Stock, P. M. Gehring, R. A. Ewings, G. Xu, J. Li, D. Viehland, and H. Luo, Phys. Rev. Mater. 2, 024404 (2018), arXiv: 1802.03780.

    Article  Google Scholar 

  53. M. Lejman, C. Paillard, V. Juvé, G. Vaudel, N. Guiblin, L. Bellaiche, M. Viret, V. E. Gusev, B. Dkhil, and P. Ruello, Phys. Rev. B 99, 104103 (2019), arXiv: 1812.03666.

    Article  ADS  Google Scholar 

  54. D. Bansal, J. L. Niedziela, R. Sinclair, V. O. Garlea, D. L. Abernathy, S. Chi, Y. Ren, H. Zhou, and O. Delaire, Nat. Commun. 9, 15 (2018).

    Article  ADS  Google Scholar 

  55. J. Young, A. Stroppa, S. Picozzi, and J. M. Rondinelli, J. Phys.-Condens. Matter. 27, 283202 (2015).

    Article  Google Scholar 

  56. M. Borinaga, P. Riego, A. Leonardo, M. Calandra, F. Mauri, A. Bergara, and I. Errea, J. Phys.-Condens. Matter. 28, 494001 (2016).

    Article  Google Scholar 

  57. Y. S. Ponosov, and S. V. Streltsov, Phys. Rev. B 96, 214503 (2017).

    Article  ADS  Google Scholar 

  58. R. Yang, Y. Dai, B. Xu, W. Zhang, Z. Qiu, Q. Sui, C. C. Homes, and X. Qiu, Phys. Rev. B 95, 064506 (2017).

    Article  ADS  Google Scholar 

  59. J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids (Clarendon Press, Oxford, 2001).

    Book  MATH  Google Scholar 

  60. M. T. Dove, Introduction to Lattice Dynamics (Cambridge Univiersity Press, Cambridge, 1993).

    Book  Google Scholar 

  61. D. Wallace, Thermodynamics of Crystals (Wiley, New York, 1972).

    Book  Google Scholar 

  62. A. M. Bratkovsky, V. G. Vaks, and A. V. Trefilov, Phys. Lett. A 103, 75 (1984).

    Article  ADS  Google Scholar 

  63. M. I. Katsnelson, and A. V. Trefilov, AIP Conf. Proc. 708, 727 (2004).

    Article  ADS  Google Scholar 

  64. Y. Chen, K. M. Ho, and B. N. Harmon, Phys. Rev. B 37, 283 (1988).

    Article  ADS  Google Scholar 

  65. P. S. Landa, Nonlinear Oscillations and Waves in Dynamical Systems (Kluwer Academic Publishers, Dordrecht, 1996).

    Book  MATH  Google Scholar 

  66. R. A. Cowley, J. Phys. France 26, 659 (1965).

    Article  Google Scholar 

  67. F. Gervais, Solid State Commun. 13, 1211 (1973).

    Article  ADS  Google Scholar 

  68. M. I. Katsnelson, Lattice Dynamics: Anharmonic Effect (Academic Press, Massachusetts, 2005).

    Google Scholar 

  69. J. Kulda, A. Debernardi, M. Cardona, F. de Geuser, and E. E. Haller, Phys. Rev. B 69, 045209 (2004).

    Article  ADS  Google Scholar 

  70. C. A. Bryant, and P. H. Keesom, Phys. Rev. 124, 698 (1961).

    Article  ADS  Google Scholar 

  71. A. A. Maradudin, and A. E. Fein, Phys. Rev. 128, 2589 (1962).

    Article  ADS  Google Scholar 

  72. T. Lan, C. W. Li, and B. Fultz, Phys. Rev. B 86, 134302 (2012).

    Article  ADS  Google Scholar 

  73. T. Lan, and Z. Zhu, Adv. Cond. Matter Phys. 2016, 2714592 (2016).

    Google Scholar 

  74. T. Feng, and X. Ruan, Phys. Rev. B 93, 045202 (2016), arXiv: 1510.00706.

    Article  ADS  Google Scholar 

  75. T. Feng, L. Lindsay, and X. Ruan, Phys. Rev. B 96, 161201 (2017).

    Article  ADS  Google Scholar 

  76. 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, Science 361, 582 (2018).

    Article  ADS  Google Scholar 

  77. T. Feng, and X. Ruan, Phys. Rev. B 97, 045202 (2018).

    Article  ADS  Google Scholar 

  78. G. L. Squires, Introduction to the Theory of Thermal Neutron Scattering (Cambridge University Press, Cambridge, 2012).

    Book  Google Scholar 

  79. A. Furrer, and T. StrÃ, Neutron Scattering in Condensed Matter Physics (World Scientific Publishing Company, Singapore, 2009).

    Book  MATH  Google Scholar 

  80. T. Koyanagi, M. J. Lance, and Y. Katoh, Script. Mater. 125, 58 (2016).

    Article  Google Scholar 

  81. J. Zhu, R. Rao, A. M. Rao, and R. Podila, Recent Patents Mater. Sci. 11, 24 (2018).

    Article  Google Scholar 

  82. B. Wei, Q. Cai, Q. Sun, Y. Su, A. H. Said, D. L. Abernathy, J. Hong, and C. Li, arXiv: 2106.10922.

  83. S. M. Shapiro, J. M. Tranquada, and G. Shirane, Neutron Scattering with a Triple-Axis Spectrometer: Basic Techniques (Cambridge University Press, Cambridge, 2006).

    Google Scholar 

  84. B. Dorner, Coherent Inelastic Neutron Scattering in Lattice Dynamics (Springer, Berlin, 2013).

    Google Scholar 

  85. C. W. Li, O. Hellman, J. Ma, A. F. May, H. B. Cao, X. Chen, A. D. Christianson, G. Ehlers, D. J. Singh, B. C. Sales, and O. Delaire, Phys. Rev. Lett. 112, 175501 (2014), arXiv: 1312.7467.

    Article  ADS  Google Scholar 

  86. M. Christensen, A. B. Abrahamsen, N. B. Christensen, F. Juranyi, N. H. Andersen, K. Lefmann, J. Andreasson, C. R. H. Bahl, and B. B. Iversen, Nat. Mater. 7, 811 (2008).

    Article  ADS  Google Scholar 

  87. H. L. Smith, Y. Shen, D. S. Kim, F. C. Yang, C. P. Adams, C. W. Li, D. L. Abernathy, M. B. Stone, and B. Fultz, Phys. Rev. Mater. 2, 103602 (2018).

    Article  Google Scholar 

  88. J. D. Budai, J. Hong, M. E. Manley, E. D. Specht, C. W. Li, J. Z. Tischler, D. L. Abernathy, A. H. Said, B. M. Leu, L. A. Boatner, R. J. McQueeney, and O. Delaire, Nature 515, 535 (2014).

    Article  ADS  Google Scholar 

  89. H. Uchiyama, Y. Oshima, R. Patterson, S. Iwamoto, J. Shiomi, and K. Shimamura, Phys. Rev. Lett. 120, 235901 (2018).

    Article  ADS  Google Scholar 

  90. B. K. Ridley, J. Phys.-Condens. Matter 8, L511 (1996).

    Article  ADS  Google Scholar 

  91. P. G. Klemens, Phys. Rev. 148, 845 (1966).

    Article  ADS  Google Scholar 

  92. H. N. Liu, X. Cong, M. L. Lin, and P. H. Tan, Carbon 152, 451 (2019).

    Article  Google Scholar 

  93. X. Cong, Q. Q. Li, X. Zhang, M. L. Lin, J. B. Wu, X. L. Liu, P. Venezuela, and P. H. Tan, Carbon 149, 19 (2019).

    Article  Google Scholar 

  94. M. Yang, X. Cheng, Y. Li, Y. Ren, M. Liu, and Z. Qi, Appl. Phys. Lett. 110, 093108 (2017).

    Article  ADS  Google Scholar 

  95. B. Poojitha, K. Rubi, S. Sarkar, R. Mahendiran, T. Venkatesan, and S. Saha, Phys. Rev. Mater. 3, 024412 (2019).

    Article  Google Scholar 

  96. A. M. Pugachev, I. V. Zaytseva, N. V. Surovtsev, and A. S. Krylov, Ceram. Int. 46, 22619 (2020).

    Article  Google Scholar 

  97. K. Shportko, P. Zalden, A. M. Lindenberg, R. Rückamp, and M. Grüninger, Vib. Spectr. 95, 51 (2018).

    Article  Google Scholar 

  98. L. C. Chen, Z. Y. Cao, H. Yu, B. B. Jiang, L. Su, X. Shi, L. D. Chen, and X. J. Chen, Appl. Phys. Lett. 113, 022105 (2018).

    Article  ADS  Google Scholar 

  99. Y. Su, J. Guo, X. Cheng, S. Feng, and Y. Yang, J. Alloys Compd. 805, 489 (2019).

    Article  Google Scholar 

  100. M. Maczka, M. Ptak, K. Hermanowicz, A. Majchrowski, A. Pikul, and J. Hanuza, Phys. Rev. B 83, 174439 (2011).

    Article  ADS  Google Scholar 

  101. U. Schade, L. Puskar, M. Berg, E. Ritter, I. Efthimiopoulos, A. Marcelli, M. Ortolani, W. Xu, Y. Liu, and L. Zhao, Phase Transitions in SnSe probed by Far Infrared Spectroscopy, in IRMMW-THz (IEEE, Nagoya, 2018), pp. 1–2.

    Google Scholar 

  102. F. Liu, P. Parajuli, R. Rao, P. C. Wei, A. Karunarathne, S. Bhattacharya, R. Podila, J. He, B. Maruyama, G. Priyadarshan, J. R. Gladden, Y. Y. Chen, and A. M. Rao, Phys. Rev. B 98, 224309 (2018).

    Article  ADS  Google Scholar 

  103. X. Xu, Q. Song, H. Wang, P. Li, K. Zhang, Y. Wang, K. Yuan, Z. Yang, Y. Ye, and L. Dai, ACS Appl. Mater. Interfaces 9, 12601 (2017).

    Article  Google Scholar 

  104. Y. Lu, T. Sun, and D. B. Zhang, Phys. Rev. B 97, 174304 (2018).

    Article  ADS  Google Scholar 

  105. C. A. Young, and A. L. Goodwin, J. Mater. Chem. 21, 6464 (2011).

    Article  Google Scholar 

  106. E. S. Božin, C. D. Malliakas, P. Souvatzis, T. Proffen, N. A. Spaldin, M. G. Kanatzidis, and S. J. L. Billinge, Science 330, 1660 (2010).

    Article  ADS  Google Scholar 

  107. S. Kastbjerg, N. Bindzus, M. Søndergaard, S. Johnsen, N. Lock, M. Christensen, M. Takata, M. A. Spackman, and B. Brummerstedt Iversen, Adv. Funct. Mater. 23, 5477 (2013).

    Article  Google Scholar 

  108. D. S. Yang, and S. K. Joo, Solid State Commun. 105, 595 (1998).

    Article  ADS  Google Scholar 

  109. N. Van Hung, N. Ba Duc, and R. R. Frahm, J. Phys. Soc. Jpn. 72, 1254 (2003).

    Article  ADS  Google Scholar 

  110. L. Hu, J. Chen, A. Sanson, H. Wu, C. Guglieri Rodriguez, L. Olivi, Y. Ren, L. Fan, J. Deng, and X. Xing, J. Am. Chem. Soc. 138, 8320 (2016).

    Article  Google Scholar 

  111. K. W. Hipps, and U. Mazur. Inelastic electron tunneling spectroscopy, in Handbook of Vibrational Spectroscopy (John Wiley & Sons Ltd, Chichester, 2002).

    Google Scholar 

  112. X. Yan, C. Liu, C. A. Gadre, L. Gu, T. Aoki, T. C. Lovejoy, N. Dellby, O. L. Krivanek, D. G. Schlom, R. Wu, and X. Pan, Nature 589, 65 (2021).

    Article  ADS  Google Scholar 

  113. O. Delaire, and C. Stassis, Phonon Study in Characterization of Materials (John Wiley & Sons, Inc., Chichester, 2012).

    Google Scholar 

  114. A. Q. R. Baron, High-Resolution Inelastic X-Ray Scattering II: Scattering Theory, Harmonic Phonons, and Calculations (Springer, Cham, 2016).

    Google Scholar 

  115. R. R. Jones, D. C. Hooper, L. Zhang, D. Wolverson, and V. K. Valev, Nanoscale Res. Lett. 14, 231 (2019).

    Article  ADS  Google Scholar 

  116. S. Baroni, S. de Gironcoli, A. dal Corso, and P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001), arXiv: cond-mat/0012092.

    Article  ADS  Google Scholar 

  117. P. Souvatzis, O. Eriksson, M. I. Katsnelson, and S. P. Rudin, Phys. Rev. Lett. 100, 095901 (2008), arXiv: 0803.1325.

    Article  ADS  Google Scholar 

  118. I. Errea, M. Calandra, and F. Mauri, Phys. Rev. B 89, 064302 (2014), arXiv: 1311.3083.

    Article  ADS  Google Scholar 

  119. J. M. Bowman, J. Chem. Phys. 68, 608 (1978).

    Article  ADS  Google Scholar 

  120. O. Hellman, I. A. Abrikosov, and S. I. Simak, Phys. Rev. B 84, 180301 (2011), arXiv: 1103.5590.

    Article  ADS  Google Scholar 

  121. O. Hellman, and I. A. Abrikosov, Phys. Rev. B 88, 144301 (2013), arXiv: 1308.5436.

    Article  ADS  Google Scholar 

  122. O. Hellman, and D. A. Broido, Phys. Rev. B 90, 134309 (2014).

    Article  ADS  Google Scholar 

  123. J. Klarbring, O. Hellman, I. A. Abrikosov, and S. I. Simak, Phys. Rev. Lett. 125, 045701 (2020), arXiv: 1912.05351.

    Article  ADS  Google Scholar 

  124. X. Gonze, and C. Lee, Phys. Rev. B 55, 10355 (1997).

    Article  ADS  Google Scholar 

  125. M. T. Dove, Collect SFN 12, 123 (2011).

    Article  Google Scholar 

  126. P. Lazar, J. Martincová, and M. Otyepka, Phys. Rev. B 92, 224104 (2015).

    Article  ADS  Google Scholar 

  127. A. Rohskopf, S. Wyant, K. Gordiz, H. Reza Seyf, M. Gopal Muraleedharan, and A. Henry, Comput. Mater. Sci. 184, 109884 (2020).

    Article  Google Scholar 

  128. C. W. Li, X. Tang, J. A. Muñoz, J. B. Keith, S. J. Tracy, D. L. Abernathy, and B. Fultz, Phys. Rev. Lett. 107, 195504 (2011).

    Article  ADS  Google Scholar 

  129. W. Qiu, L. Xi, P. Wei, X. Ke, J. Yang, and W. Zhang, Proc. Natl. Acad. Sci. USA 111, 15031 (2014).

    Article  ADS  Google Scholar 

  130. K. Parlinski, Phys. Rev. B 98, 054305 (2018).

    Article  ADS  Google Scholar 

  131. S. S. Naghavi, J. He, Y. Xia, and C. Wolverton, Chem. Mater. 30, 5639 (2018).

    Article  Google Scholar 

  132. A. Cepellotti, G. Fugallo, L. Paulatto, M. Lazzeri, F. Mauri, and N. Marzari, Nat. Commun. 6, 6400 (2015).

    Article  ADS  Google Scholar 

  133. T. Sun, D. B. Zhang, and R. M. Wentzcovitch, Phys. Rev. B 89, 094109 (2014).

    Article  ADS  Google Scholar 

  134. D. B. Zhang, T. Sun, and R. M. Wentzcovitch, Phys. Rev. Lett. 112, 058501 (2014), arXiv: 1312.7490.

    Article  ADS  Google Scholar 

  135. J. J. Zhou, O. Hellman, and M. Bernardi, Phys. Rev. Lett. 121, 226603 (2018), arXiv: 1806.05775.

    Article  ADS  Google Scholar 

  136. Y. Xia, Appl. Phys. Lett. 113, 073901 (2018).

    Article  ADS  Google Scholar 

  137. J. S. Kang, H. Wu, M. Li, and Y. Hu, Nano Lett. 19, 4941 (2019).

    Article  ADS  Google Scholar 

  138. C. Kwon, Y. Xia, F. Zhou, and B. Han, Phys. Rev. B 102, 184309 (2020).

    Article  ADS  Google Scholar 

  139. Y. Xia, K. Pal, J. He, V. Ozoliņš, and C. Wolverton, Phys. Rev. Lett. 124, 065901 (2020).

    Article  ADS  Google Scholar 

  140. D. S. Kim, Silicon Revisited: Understanding Pure Phonon Anharmonicity and the Effects on Thermophysical Properties, Dissertation for Doctoral Degree (California Institute of Technology, Pasadena, 2018).

    Google Scholar 

  141. L. Lindsay, A. Katre, A. Cepellotti, and N. Mingo, J. Appl. Phys. 126, 050902 (2019).

    Article  ADS  Google Scholar 

  142. E. J. Skoug, and D. T. Morelli, Phys. Rev. Lett. 107, 235901 (2011).

    Article  ADS  Google Scholar 

  143. Y. Oba, T. Tadano, R. Akashi, and S. Tsuneyuki, Phys. Rev. Mater. 3, 033601 (2019), arXiv: 1810.08800.

    Article  Google Scholar 

  144. Y. Luo, L. Sun, J. Wang, Z. Tian, H. Nian, and J. Wang, J. Eur. Ceram. Soc. 38, 2043 (2018).

    Article  Google Scholar 

  145. A. Walsh, D. J. Payne, R. G. Egdell, and G. W. Watson, Chem. Soc. Rev. 40, 4455 (2011).

    Article  Google Scholar 

  146. M. K. Jana, and K. Biswas, ACS Energy Lett. 3, 1315 (2018).

    Article  Google Scholar 

  147. D. T. Morelli, V. Jovovic, and J. P. Heremans, Phys. Rev. Lett. 101, 035901 (2008).

    Article  ADS  Google Scholar 

  148. M. D. Nielsen, V. Ozolins, and J. P. Heremans, Energy Environ. Sci. 6, 570 (2013).

    Article  Google Scholar 

  149. M. K. Jana, K. Pal, U. V. Waghmare, and K. Biswas, Angew. Chem. 128, 7923 (2016).

    Article  ADS  Google Scholar 

  150. A. E. Whitten, B. Dittrich, M. A. Spackman, P. Turner, and T. C. Brown, Dalton Trans. 1, 23 (2004).

    Article  Google Scholar 

  151. W. Wan, Y. Ge, and Y. Liu, Appl. Phys. Lett. 114, 031901 (2019), arXiv: 1809.11124.

    Article  ADS  Google Scholar 

  152. A. Walsh, and G. W. Watson, J. Solid State Chem. 178, 1422 (2005).

    Article  ADS  Google Scholar 

  153. S. Lee, K. Esfarjani, T. Luo, J. Zhou, Z. Tian, and G. Chen, Nat. Commun. 5, 3525 (2014).

    Article  ADS  Google Scholar 

  154. M. K. Jana, K. Pal, U. V. Waghmare, and K. Biswas, Angew. Chem. Int. Ed. 55, 7792 (2016).

    Article  Google Scholar 

  155. W. G. Zeier, A. Zevalkink, Z. M. Gibbs, G. Hautier, M. G. Kanatzidis, and G. J. Snyder, Angew. Chem. Int. Ed. 55, 6826 (2016).

    Article  Google Scholar 

  156. A. F. U. Islam, M. N. H. Liton, H. M. T. Islam, M. A. Helal, and M. Kamruzzaman, Chin. Phys. B 26, 036301 (2017).

    Article  ADS  Google Scholar 

  157. A. Salamat, A. L. Hector, P. F. McMillan, and C. Ritter, Inorg. Chem. 50, 11905 (2011).

    Article  Google Scholar 

  158. C. Chang, and L. D. Zhao, Mater. Today Phys. 4, 50 (2018).

    Article  Google Scholar 

  159. B. Du, K. Chen, H. Yan, and M. J. Reece, Script. Mater. 111, 49 (2016).

    Article  Google Scholar 

  160. L. Pauling, Nature of Chemical Bond (Cornell University Press, New York, 1939).

    MATH  Google Scholar 

  161. Y. Yu, M. Cagnoni, O. Cojocaru-Mirédin, and M. Wuttig, Adv. Funct. Mater. 30, 1904862 (2019).

    Article  Google Scholar 

  162. K. Shportko, S. Kremers, M. Woda, D. Lencer, J. Robertson, and M. Wuttig, Nat. Mater. 7, 653 (2008).

    Article  ADS  Google Scholar 

  163. C. Koch, G. Schienke, M. Paulsen, D. Meyer, M. Wimmer, H. Volker, M. Wuttig, and W. Bensch, Chem. Mater. 29, 9320 (2017).

    Article  Google Scholar 

  164. Y. Zhang, X. Ke, P. R. C. Kent, J. Yang, and C. Chen, Phys. Rev. Lett. 107, 175503 (2011).

    Article  ADS  Google Scholar 

  165. K. M. Rabe, and J. D. Joannopoulos, Phys. Rev. B 32, 2302 (1985).

    Article  ADS  Google Scholar 

  166. O. Delaire, J. Ma, K. Marty, A. F. May, M. A. McGuire, M. H. Du, D. J. Singh, A. Podlesnyak, G. Ehlers, M. D. Lumsden, and B. C. Sales, Nat. Mater. 10, 614 (2011), arXiv: 1103.2564.

    Article  ADS  Google Scholar 

  167. J. An, A. Subedi, and D. J. Singh, Solid State Commun. 148, 417 (2008), arXiv: 0806.2727.

    Article  ADS  Google Scholar 

  168. T. Shiga, J. Shiomi, J. Ma, O. Delaire, T. Radzynski, A. Lusakowski, K. Esfarjani, and G. Chen, Phys. Rev. B 85, 155203 (2012), arXiv: 1204.0592.

    Article  ADS  Google Scholar 

  169. A. J. Sievers, and S. Takeno, Phys. Rev. 140, A1030 (1965).

    Article  ADS  Google Scholar 

  170. G. A. Slack, New materials and performance limits for thermoelectric cooling, in CRC Handbook of Thermoelectrics (Boca Raton, CRC Press, 1995).

    Google Scholar 

  171. M. A. Avila, K. Suekuni, K. Umeo, H. Fukuoka, S. Yamanaka, and T. Takabatake, Appl. Phys. Lett. 92, 041901 (2008).

    Article  ADS  Google Scholar 

  172. J. Dong, O. F. Sankey, and C. W. Myles, Phys. Rev. Lett. 86, 2361 (2001).

    Article  ADS  Google Scholar 

  173. J. S. Tse, and M. A. White, J. Phys. Chem. 92, 5006 (1988).

    Article  Google Scholar 

  174. J. S. Tse, D. D. Klug, J. Y. Zhao, W. Sturhahn, E. E. Alp, J. Baumert, C. Gutt, M. R. Johnson, and W. Press, Nat. Mater. 4, 917 (2005).

    Article  ADS  Google Scholar 

  175. Y. Takasu, T. Hasegawa, N. Ogita, M. Udagawa, M. A. Avila, and T. Takabatake, Phys. B-Condensed Matter. 383, 134 (2006).

    Article  ADS  Google Scholar 

  176. T. Takabatake, K. Suekuni, T. Nakayama, and E. Kaneshita, Rev. Mod. Phys. 86, 669 (2014), arXiv: 1402.5756.

    Article  ADS  Google Scholar 

  177. T. Nakayama, and E. Kaneshita, J. Phys. Soc. Jpn. 80, 104604 (2011), arXiv: 1103.1441.

    Article  ADS  Google Scholar 

  178. B. C. Sales, D. Mandrus, B. C. Chakoumakos, V. Keppens, and J. R. Thompson, Phys. Rev. B 56, 15081 (1997).

    Article  ADS  Google Scholar 

  179. W. Lee, H. Li, A. B. Wong, D. Zhang, M. Lai, Y. Yu, Q. Kong, E. Lin, J. J. Urban, J. C. Grossman, and P. Yang, Proc. Natl. Acad. Sci. USA 114, 8693 (2017).

    Article  ADS  Google Scholar 

  180. W. Lai, Y. Wang, D. T. Morelli, and X. Lu, Adv. Funct. Mater. 25, 3648 (2015).

    Article  Google Scholar 

  181. W. Peng, G. Petretto, G. M. Rignanese, G. Hautier, and A. Zevalkink, Joule 2, 1879 (2018).

    Article  Google Scholar 

  182. M. Christensen, S. Johnsen, and B. B. Iversen, Dalton Trans. 39, 978 (2010).

    Article  Google Scholar 

  183. M. Christensen, N. Lock, J. Overgaard, and B. B. Iversen, J. Am. Chem. Soc. 128, 15657 (2006).

    Article  Google Scholar 

  184. D. Cao, F. Bridges, P. Chesler, S. Bushart, E. D. Bauer, and M. B. Maple, Phys. Rev. B 70, 094109 (2004).

    Article  ADS  Google Scholar 

  185. D. J. Voneshen, K. Refson, E. Borissenko, M. Krisch, A. Bosak, A. Piovano, E. Cemal, M. Enderle, M. J. Gutmann, M. Hoesch, M. Roger, L. Gannon, A. T. Boothroyd, S. Uthayakumar, D. G. Porter, and J. P. Goff, Nat. Mater. 12, 1028 (2013).

    Article  ADS  Google Scholar 

  186. C. Gutt, J. Baumert, W. Press, J. S. Tse, and S. Janssen, J. Chem. Phys. 116, 3795 (2002).

    Article  ADS  Google Scholar 

  187. K. Suekuni, C. H. Lee, H. I. Tanaka, E. Nishibori, A. Nakamura, H. Kasai, H. Mori, H. Usui, M. Ochi, T. Hasegawa, M. Nakamura, S. Ohira-Kawamura, T. Kikuchi, K. Kaneko, H. Nishiate, K. Hashikuni, Y. Kosaka, K. Kuroki, and T. Takabatake, Adv. Mater. 30, 1706230 (2018).

    Article  Google Scholar 

  188. S. Mukhopadhyay, D. S. Parker, B. C. Sales, A. A. Puretzky, M. A. McGuire, and L. Lindsay, Science 360, 1455 (2018).

    Article  ADS  Google Scholar 

  189. T. Mori, S. Goshima, K. Iwamoto, S. Kushibiki, H. Matsumoto, N. Toyota, K. Suekuni, M. A. Avila, T. Takabatake, T. Hasegawa, N. Ogita, and M. Udagawa, Phys. Rev. B 79, 212301 (2009), arXiv: 0905.3610.

    Article  ADS  Google Scholar 

  190. J. Wu, J. Xu, and K. Tanigaki, arXiv: 1802.09228.

  191. V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B 67, 094203 (2003), arXiv: cond-mat/0203165.

    Article  ADS  Google Scholar 

  192. T. Chatterji, P. G. Freeman, M. Jimenez-Ruiz, R. Mittal, and S. L. Chaplot, Phys. Rev. B 79, 184302 (2009).

    Article  ADS  Google Scholar 

  193. A. Pramanick, S. O. Diallo, O. Delaire, S. Calder, A. D. Christianson, X. L. Wang, and J. A. Fernandez-Baca, Phys. Rev. B 88, 180101 (2013), arXiv: 1306.4745.

    Article  ADS  Google Scholar 

  194. Z. Dabiri, A. Kazempour, and M. A. Sadeghzadeh, Phys. B-Condensed Matter. 501, 95 (2016).

    Article  ADS  Google Scholar 

  195. A. Mialitsin, B. S. Dennis, N. D. Zhigadlo, J. Karpinski, and G. Blumberg, Phys. Rev. B 75, 020509 (2007), arXiv: cond-mat/0701085.

    Article  ADS  Google Scholar 

  196. M. Yoshida, K. Arai, R. Kaido, M. Takigawa, S. Yonezawa, Y. Muraoka, and Z. Hiroi, Phys. Rev. Lett. 98, 197002 (2007), arXiv: cond-mat/0610760.

    Article  ADS  Google Scholar 

  197. A. A. Olvera, N. A. Moroz, P. Sahoo, P. Ren, T. P. Bailey, A. A. Page, C. Uher, and P. F. P. Poudeu, Energy Environ. Sci. 10, 1668 (2017).

    Article  Google Scholar 

  198. M. U. Farooq, S. Butt, K. Gao, X. Sun, X. L. Pang, S. U. Khan, W. Xu, F. Mohmed, A. Mahmood, and N. Mahmood, Ceram. Int. 42, 8395 (2016).

    Article  Google Scholar 

  199. F. Gascoin, and A. Maignan, Chem. Mater. 23, 2510 (2011).

    Article  Google Scholar 

  200. S. Bhattacharya, R. Basu, R. Bhatt, S. Pitale, A. Singh, D. K. Aswal, S. K. Gupta, M. Navaneethan, and Y. Hayakawa, J. Mater. Chem. A 1, 11289 (2013).

    Article  Google Scholar 

  201. K. Wakamura, K. Hirokawa, and K. Orita, J. Phys. Chem. Solids 57, 75 (1996).

    Article  ADS  Google Scholar 

  202. R. A. Yakshibayev, V. N. Zabolotsky, and R. F. Almukhametov, Solid State Ion. 31, 1 (1988).

    Article  Google Scholar 

  203. S. Roychowdhury, M. K. Jana, J. Pan, S. N. Guin, D. Sanyal, U. V. Waghmare, and K. Biswas, Angew. Chem. Int. Ed. 57, 4043 (2018).

    Article  Google Scholar 

  204. S. N. Guin, J. Pan, A. Bhowmik, D. Sanyal, U. V. Waghmare, and K. Biswas, J. Am. Chem. Soc. 136, 12712 (2014).

    Article  Google Scholar 

  205. J. B. Boyce, and B. A. Huberman, Phys. Rep. 51, 189 (1979).

    Article  ADS  Google Scholar 

  206. J. Frenkel. Kinetic Theory of Liquids (Oxford University Press, London, 1946).

    MATH  Google Scholar 

  207. F. Damay, S. Petit, S. Rols, M. Braendlein, R. Daou, E. Elkaïm, F. Fauth, F. Gascoin, C. Martin, and A. Maignan, Sci. Rep. 6, 23415 (2016).

    Article  ADS  Google Scholar 

  208. D. Wu, S. Huang, D. Feng, B. Li, Y. Chen, J. Zhang, and J. He, Phys. Chem. Chem. Phys. 18, 23872 (2016).

    Article  Google Scholar 

  209. D. J. Voneshen, H. C. Walker, K. Refson, and J. P. Goff, Phys. Rev. Lett. 118, 145901 (2017).

    Article  ADS  Google Scholar 

  210. K. Wakamura, F. Miura, A. Kojima, and T. Kanashiro, Phys. Rev. B 41, 2758 (1990).

    Article  ADS  Google Scholar 

  211. J. L. Niedziela, D. Bansal, A. F. May, J. Ding, T. Lanigan-Atkins, G. Ehlers, D. L. Abernathy, A. Said, and O. Delaire, Nat. Phys. 15, 73 (2019).

    Article  Google Scholar 

  212. A. Gagor, D. Gnida, and A. Pietraszko, Mater. Chem. Phys. 146, 283 (2014).

    Article  Google Scholar 

  213. R. Mittal, M. Zbiri, H. Schober, E. Marelli, S. J. Hibble, A. M. Chippindale, and S. L. Chaplot, Phys. Rev. B 83, 024301 (2011), arXiv: 1009.5540.

    Article  ADS  Google Scholar 

  214. C. Ulrich, E. Anastassakis, K. Syassen, A. Debernardi, and M. Cardona, Phys. Rev. Lett. 78, 1283 (1997).

    Article  ADS  Google Scholar 

  215. G. A. Kourouklis, and E. Anastassakis, Phys. Stat. Sol. (B) 152, 89 (1989).

    Article  ADS  Google Scholar 

  216. Y. S. Raptis, G. A. Kourouklis, E. Anastassakis, E. Haro-Poniatowski, and M. Balkanski, J. Phys. France 48, 239 (1987).

    Article  Google Scholar 

  217. G. Lucazeau, J. Raman Spectrosc. 34, 478 (2003).

    Article  ADS  Google Scholar 

  218. G. A. Samara, and P. S. Peercy, Phys. Rev. B 7, 1131 (1973).

    Article  ADS  Google Scholar 

  219. M. Balkanski, R. F. Wallis, and E. Haro, Phys. Rev. B 28, 1928 (1983).

    Article  ADS  Google Scholar 

  220. R. A. Cowley, S. N. Gvasaliya, and B. Roessli, Ferroelectrics 378, 53 (2009).

    Article  Google Scholar 

  221. K. McCash, The Soft Mode Driven Dynamics of Ferroelectric Perovskites at the Nanoscale: An Atomistic Study, Dissertation for Doctoral Degree (University of South Florida, Florida, 2014).

    Google Scholar 

  222. M. T. Dove, and H. Fang, Rep. Prog. Phys. 79, 066503 (2016).

    Article  ADS  Google Scholar 

  223. T. H. K. Barron, J. G. Collins, and G. K. White, Adv. Phys. 29, 609 (1980).

    Article  ADS  Google Scholar 

  224. J. W. Gibbs, Elementary Principles in Statistical Mechanics (Charles Scribner’s Sons, New York, 1902).

    MATH  Google Scholar 

  225. C. Lind, Materials 5, 1125 (2012).

    Article  ADS  Google Scholar 

  226. T. A. Mary, J. S. O. Evans, T. Vogt, and A. W. Sleight, Science 272, 90 (1996).

    Article  ADS  Google Scholar 

  227. V. Korthuis, N. Khosrovani, A. W. Sleight, N. Roberts, R. Dupree, and W. W. J. Warren, Chem. Mater. 7, 412 (1995).

    Article  Google Scholar 

  228. A. K. Tyagi, S. N. Achary, and M. D. Mathews, J. Alloys Compd. 339, 207 (2002).

    Article  Google Scholar 

  229. J. N. Grima, R. Gatt, and V. Zammit, Xjenza 11, 17 (2006).

    Google Scholar 

  230. L. E. Cross, Ferroelectric Ceramics: Materials and Application Issues (No. CONF-941199) (American Ceramic Society, Westerville, 1996).

    Google Scholar 

  231. V. Garcia, and M. Bibes, Nat. Commun. 5, 1 (2014).

    Article  Google Scholar 

  232. L. E. Cross, Mater. Chem. Phys. 43, 108 (1996).

    Article  Google Scholar 

  233. A. M. Glass, Appl. Phys. Lett. 13, 147 (1968).

    Article  ADS  Google Scholar 

  234. J. Hlinka, T. Ostapchuk, D. Nuzhnyy, J. Petzelt, P. Kuzel, C. Kadlec, P. Vanek, I. Ponomareva, and L. Bellaiche, Phys. Rev. Lett. 101, 167402 (2008).

    Article  ADS  Google Scholar 

  235. G. Andersson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, and B. Stebler, Ferroelectrics 84, 285 (1988).

    Article  Google Scholar 

  236. B. Xu, O. Hellman, and L. Bellaiche, Phys. Rev. B 100, 020102 (2019), arXiv: 1902.08880.

    Article  ADS  Google Scholar 

  237. J. M. Wesselinowa, and S. Kovachev, Phys. Rev. B 75, 045411 (2007).

    Article  ADS  Google Scholar 

  238. W. Cochran, Phys. Rev. Lett. 3, 412 (1959).

    Article  ADS  Google Scholar 

  239. P. W. Anderson, in Fisika Dielektrikov, edited by G. I. Skanav (Academic Nauk SSSR, Moscow, 1960).

  240. E. E. McCabe, E. Bousquet, C. P. J. Stockdale, C. A. Deacon, T. T. Tran, P. S. Halasyamani, M. C. Stennett, and N. C. Hyatt, Chem. Mater. 27, 8298 (2015).

    Article  Google Scholar 

  241. H. Yin, C. Liu, G. P. Zheng, Y. Wang, and F. Ren, Appl. Phys. Lett. 114, 192903 (2019).

    Article  ADS  Google Scholar 

  242. C. Yang, Y. Liu, G. Tang, X. Wang, and J. Hong, Appl. Phys. Lett. 113, 082905 (2018).

    Article  ADS  Google Scholar 

  243. G. Dolino, Phase Trans. 21, 59 (1990).

    Article  Google Scholar 

  244. P. A. Fleury, J. F. Scott, and J. M. Worlock, Phys. Rev. Lett. 21, 16 (1968).

    Article  ADS  Google Scholar 

  245. M. T. Dove, I. U. Heilmann, J. K. Kjems, J. Kurittu, and G. S. Pawley, Phys. Stat. Sol. (B) 120, 173 (1983).

    Article  ADS  Google Scholar 

  246. L. E. Bell, Science 321, 1457 (2008).

    Article  ADS  Google Scholar 

  247. G. J. Snyder, and E. S. Toberer, Nat. Mater. 7, 105 (2008).

    Article  ADS  Google Scholar 

  248. H. J. Goldsmid, Introduction to Thermoelectricity (Springer, Berlin, 2010).

    Book  Google Scholar 

  249. C. Wood, Rep. Prog. Phys. 51, 459 (1988).

    Article  ADS  Google Scholar 

  250. J. Yang, L. Xi, W. Qiu, L. Wu, X. Shi, L. Chen, J. Yang, W. Zhang, C. Uher, and D. J. Singh, npj Comput. Mater. 2, 15015 (2016).

    Article  ADS  Google Scholar 

  251. T. Hori, and J. Shiomi, Sci. Tech. Adv. Mater. 20, 10 (2019).

    Article  Google Scholar 

  252. T. M. Tritt, Thermal Conductivity: Theory, Properties, and Applications (Kluwer Academic/Plenum Publishers, New York, 2004).

    Book  Google Scholar 

  253. P. Ying, X. Li, Y. Wang, J. Yang, C. Fu, W. Zhang, X. Zhao, and T. Zhu, Adv. Funct. Mater. 27, 1604145 (2017).

    Article  Google Scholar 

  254. Z. Liu, Y. Zhang, J. Mao, W. Gao, Y. Wang, J. Shuai, W. Cai, J. Sui, and Z. Ren, Acta Mater. 128, 227 (2017).

    Article  ADS  Google Scholar 

  255. Z. Liu, J. Mao, J. Sui, and Z. Ren, Energy Environ. Sci. 11, 23 (2018).

    Article  Google Scholar 

  256. X. Li, P. F. Liu, E. Zhao, Z. Zhang, T. Guidi, M. D. Le, M. Avdeev, K. Ikeda, T. Otomo, M. Kofu, K. Nakajima, J. Chen, L. He, Y. Ren, X. L. Wang, B. T. Wang, Z. Ren, H. Zhao, and F. Wang, Nat. Commun. 11, 942 (2020), arXiv: 2001.07070.

    Article  ADS  Google Scholar 

  257. G. A. Slack, CRC Handbook of Thermoelectrics (CRC Press, New York, 1995).

    Google Scholar 

  258. H. Liu, X. Shi, F. Xu, L. Zhang, W. Zhang, L. Chen, Q. Li, C. Uher, T. Day, and G. J. Snyder, Nat. Mater. 11, 422 (2012).

    Article  ADS  Google Scholar 

  259. M. Zhao, D. Kim, V. L. Nguyen, J. Jiang, L. Sun, Y. H. Lee, and H. Yang, Nano Lett. 19, 61 (2019).

    Article  ADS  Google Scholar 

  260. M. G. Kanatzidis, Semiconduct. Semimet. 69, 51 (2001).

    Article  Google Scholar 

  261. Y. Zhu, B. Wei, J. Liu, N. Z. Koocher, Y. Li, L. Hu, W. He, G. Deng, W. Xu, X. Wang, J. M. Rondinelli, L. D. Zhao, G. J. Snyder, and J. Hong, Mater. Today Phys. 19, 100428 (2021).

    Article  Google Scholar 

  262. C. Uher, Semiconduct. Semimet. 69, 139 (2001).

    Article  Google Scholar 

  263. G. J. Poon, Semiconduct. Semimet. 70, 37 (2001).

    Article  Google Scholar 

  264. I. Terasaki, Y. Ishii, D. Tanaka, K. Takahata, and Y. Iguchi, Jpn. J. Appl. Phys. 40, L65 (2001).

    Article  ADS  Google Scholar 

  265. S. Sarkar, I. Maity, H. L. Pradeepa, G. Nayak, L. Marty, J. Renard, J. Coraux, N. Bendiab, V. Bouchiat, S. Das, K. Majumdar, M. Jain, and A. Bid, Phys. Rev. B 101, 205302 (2020), arXiv: 2009.04206.

    Article  ADS  Google Scholar 

  266. E. Granado, P. G. Pagliuso, J. A. Sanjurjo, C. Rettori, M. A. Subramanian, S. W. Cheong, and S. B. Oseroff, Phys. Rev. B 60, 6513 (1999).

    Article  ADS  Google Scholar 

  267. V. S. Bhadram, B. Rajeswaran, A. Sundaresan, and C. Narayana, Europhys. Lett. 101, 17008 (2013), arXiv: 1205.3551.

    Article  ADS  Google Scholar 

  268. D. Reznik, L. Pintschovius, M. Ito, S. Iikubo, M. Sato, H. Goka, M. Fujita, K. Yamada, G. D. Gu, and J. M. Tranquada, Nature 440, 1170 (2006), arXiv: cond-mat/0512063.

    Article  ADS  Google Scholar 

  269. H. Liu, C. Yang, B. Wei, L. Jin, A. Alatas, A. Said, S. Tongay, F. Yang, A. Javey, J. Hong, and J. Wu, Adv. Sci. 7, 1902071 (2020).

    Article  Google Scholar 

  270. B. Xu, Y. M. Dai, L. X. Zhao, K. Wang, R. Yang, W. Zhang, J. Y. Liu, H. Xiao, G. F. Chen, S. A. Trugman, J. X. Zhu, A. J. Taylor, D. A. Yarotski, R. P. Prasankumar, and X. G. Qiu, Nat. Commun. 8, 14933 (2017), arXiv: 1608.08160.

    Article  ADS  Google Scholar 

  271. A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar, D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J. I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, and Z. X. Shen, Nature 412, 510 (2001), arXiv: cond-mat/0102227.

    Article  ADS  Google Scholar 

  272. C. Cazorla, O. Diéguez, and J. Íñiguez, Sci. Adv. 3, e1700288 (2017), arXiv: 1612.04356.

    Article  ADS  Google Scholar 

  273. C. Li, N. K. Ravichandran, L. Lindsay, and D. Broido, Phys. Rev. Lett. 121, 175901 (2018).

    Article  ADS  Google Scholar 

  274. S. Petit, F. Moussa, M. Hennion, S. Pailhès, L. Pinsard-Gaudart, and A. Ivanov, Phys. Rev. Lett. 99, 266604 (2007).

    Article  ADS  Google Scholar 

  275. R. Pradip, P. Piekarz, A. Bosak, D. G. Merkel, O. Waller, A. Seiler, A. I. Chumakov, R. Rüffer, A. M. Oleś, K. Parlinski, M. Krisch, T. Baumbach, and S. Stankov, Phys. Rev. Lett. 116, 185501 (2016).

    Article  ADS  Google Scholar 

  276. K. Y. Bliokh, and V. D. Freilikher, Phys. Rev. B 74, 174302 (2006), arXiv: cond-mat/0604248.

    Article  ADS  Google Scholar 

  277. B. S. Kandemir, and D. Akay, Philos. Mag. 97, 2225 (2017).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Henan Key Laboratory of Materials on Deep-Earth Engineering, School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000, China

    Bin Wei

  2. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Bin Wei & Jiawang Hong

  3. Department of Mechanical Engineering, University of California, Riverside, Riverside, CA, 92521, USA

    Qiyang Sun & Chen Li

  4. Materials Science and Engineering, University of California, Riverside, Riverside, CA, 92521, USA

    Chen Li

Authors
  1. Bin Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiyang Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiawang Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiawang Hong.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 12172047), Beijing Natural Science Foundation (Grant No. Z190011), and Beijing Institute of Technology Research Fund Program for Young Scholars. Bin Wei thanks the Doctoral Foundation of Henan Polytechnic University (Natural Science). Chen Li thanks the Initial Complement of University of California, Riverside.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, B., Sun, Q., Li, C. et al. Phonon anharmonicity: a pertinent review of recent progress and perspective. Sci. China Phys. Mech. Astron. 64, 117001 (2021). https://doi.org/10.1007/s11433-021-1748-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-021-1748-7

PACS number(s)

Search

Navigation