Approaching the strongly anharmonic limit with ab initio calculations of materials’ vibrational properties – a colloquium*

Colloquium
Part of the following topical collections:
  1. Topical issue: Ψk Volker Heine Young Investigator Award – 2015 Finalists

Abstract

Despite ab initio computational techniques have opened new possibilities to interpret experimental results and predict the properties of new materials, their applications are limited by the adopted approximative schemes. Consequently, the first-principles calculation of many physical properties and phenomena is hindered and ab initio methods need to be further developed to overcome such limits. For example, the standard harmonic approximation used to assess the vibrational properties of materials often completely breaks down, so that the vibrational properties need to be calculated including strong anharmonic effects. The harmonic approximation has also intrinsic failures as it cannot estimate the lattice thermal conductivity of materials nor the temperature dependence of the phonon frequencies, crucial to account for temperature driven second-order phase transitions. Several methods developed in the last years to account for anharmonicity in the non-perturbative regime and overcome such difficulties are briefly reviewed in this colloquium paper. In particular, the stochastic self-consistent harmonic approximation, a variational method that allows calculating vibrational properties in strongly anharmonic systems, is described in further detail. Applications of the latter method to superconducting palladium, platinum, and sulfur hydrides are discussed, where anharmonicity has a huge impact on their vibrational and superconducting properties.

References

  1. 1.
    G. Onida, L. Reining, A. Rubio, Rev. Mod. Phys. 74, 601 (2002)ADSCrossRefGoogle Scholar
  2. 2.
    J. Taylor, H. Guo, J. Wang, Phys. Rev. B 63, 245407 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    T. Frederiksen, M. Paulsson, M. Brandbyge, A.P. Jauho, Phys. Rev. B 75, 205413 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    D.A. Broido, M. Malorny, G. Birner, N. Mingo, D.A. Stewart, Appl. Phys. Lett. 91, 231922 (2007)ADSCrossRefGoogle Scholar
  5. 5.
    G. Fugallo, M. Lazzeri, L. Paulatto, F. Mauri, Phys. Rev. B 88, 045430 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    A.Y. Liu, A.A. Quong, Phys. Rev. B 53, R7575 (1996)ADSCrossRefGoogle Scholar
  7. 7.
    F. Mauri, O. Zakharov, S. de Gironcoli, S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 77, 1151 (1996)ADSCrossRefGoogle Scholar
  8. 8.
    S. Curtarolo, G.L.W. Hart, M.B. Nardelli, N. Mingo, S. Sanvito, O. Levy, Nat. Mater. 12, 191 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)ADSCrossRefGoogle Scholar
  12. 12.
    M. Petersilka, U.J. Gossmann, E.K.U. Gross, Phys. Rev. Lett. 76, 1212 (1996)ADSCrossRefGoogle Scholar
  13. 13.
    G. Mahan, B. Sales, J. Sharp, Phys. Today 50, 42 (1997)CrossRefGoogle Scholar
  14. 14.
    F.J. DiSalvo, Science 285, 703 (1999)CrossRefGoogle Scholar
  15. 15.
    L.D. Zhao, S.H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Nature 508, 373 (2014)ADSCrossRefGoogle Scholar
  16. 16.
    G.K.H. Madsen, J. Am. Chem. Soc. 128, 12140 (2006)CrossRefGoogle Scholar
  17. 17.
    G.S. Pawley, W. Cochran, R.A. Cowley, G. Dolling, Phys. Rev. Lett. 17, 753 (1966)ADSCrossRefGoogle Scholar
  18. 18.
    O. Delaire et al., Nat. Mater. 10, 614 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    Y. Luspin, J.L. Servoin, F. Gervais, J. Phys. C 13, 3761 (1980)ADSCrossRefGoogle Scholar
  20. 20.
    F. Weber, S. Rosenkranz, J.P. Castellan, R. Osborn, R. Hott, R. Heid, K.P. Bohnen, T. Egami, A.H. Said, D. Reznik, Phys. Rev. Lett. 107, 107403 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    M. Leroux, I. Errea, M. Le Tacon, S.M. Souliou, G. Garbarino, L. Cario, A. Bosak, F. Mauri, M. Calandra, P. Rodière, Phys. Rev. B 92, 140303 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    M. Holt, P. Zschack, H. Hong, M.Y. Chou, T.C. Chiang, Phys. Rev. Lett. 86, 3799 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    M. Leroux, M. Le Tacon, M. Calandra, L. Cario, M.A. Méasson, P. Diener, E. Borrissenko, A. Bosak, P. Rodière, Phys. Rev. B 86, 155125 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    P.H. Ghosez, X. Gonze, J.P. Michenaud, Ferroelectrics 206, 205 (1998)CrossRefGoogle Scholar
  25. 25.
    M. Calandra, I.I. Mazin, F. Mauri, Phys. Rev. B 80, 241108 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    M. Calandra, F. Mauri, Phys. Rev. Lett. 106, 196406 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    A.A. Maradudin, A.E. Fein, Phys. Rev. 128, 2589 (1962)ADSCrossRefGoogle Scholar
  28. 28.
    M. Calandra, M. Lazzeri, F. Mauri, Physica C 456, 38 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    L. Paulatto, F. Mauri, M. Lazzeri, Phys. Rev. B 87, 214303 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    D.A. Broido, T.L. Reinecke, Phys. Rev. B 70, 081310 (2004)ADSCrossRefGoogle Scholar
  31. 31.
    D.A. Broido, A. Ward, N. Mingo, Phys. Rev. B 72, 014308 (2005)ADSCrossRefGoogle Scholar
  32. 32.
    A. Ward, D.A. Broido, D.A. Stewart, G. Deinzer, Phys. Rev. B 80, 125203 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    I. Errea, M. Calandra, F. Mauri, Phys. Rev. Lett. 111, 177002 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    I. Errea, M. Calandra, F. Mauri, Phys. Rev. B 89, 064302 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    I. Errea, M. Calandra, C.J. Pickard, J. Nelson, R.J. Needs, Y. Li, H. Liu, Y. Zhang, Y. Ma, F. Mauri, Phys. Rev. Lett. 114, 157004 (2015)ADSCrossRefGoogle Scholar
  36. 36.
    I. Errea, M. Calandra, F. Mauri, Phys. Stat. Sol. B 251, 2556 (2014)ADSCrossRefGoogle Scholar
  37. 37.
    I. Errea, M. Calandra, C.J. Pickard, J. Nelson, R.J. Needs, Y. Li, H. Liu, Y. Zhang, Y. Ma, F. Mauri, Nature 532, 81 (2016)ADSCrossRefGoogle Scholar
  38. 38.
    S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001)ADSCrossRefGoogle Scholar
  39. 39.
    X. Gonze, C. Lee, Phys. Rev. B 55, 10355 (1997)ADSCrossRefGoogle Scholar
  40. 40.
    G. Kresse, J. Furthmüller, J. Hafner, Europhys. Lett. 32, 729 (1995)ADSCrossRefGoogle Scholar
  41. 41.
    B. Fultz, Prog. Mater. Sci. 55, 247 (2010)CrossRefGoogle Scholar
  42. 42.
    J.D. Althoff, P.B. Allen, R.M. Wentzcovitch, J.A. Moriarty, Phys. Rev. B 48, 13253 (1993)ADSCrossRefGoogle Scholar
  43. 43.
    Y. Yao, J.S. Tse, K. Tanaka, F. Marsiglio, Y. Ma, Phys. Rev. B 79, 054524 (2009)ADSCrossRefGoogle Scholar
  44. 44.
    M. Lazzeri, S. de Gironcoli, Phys. Rev. B 65, 245402 (2002)ADSCrossRefGoogle Scholar
  45. 45.
    M. Lazzeri, S. de Gironcoli, Phys. Rev. Lett. 81, 2096 (1998)ADSCrossRefGoogle Scholar
  46. 46.
    L. Paulatto, I. Errea, M. Calandra, F. Mauri, Phys. Rev. B 91, 054304 (2015)ADSCrossRefGoogle Scholar
  47. 47.
    S. Narasimhan, D. Vanderbilt, Phys. Rev. B 43, 4541 (1991)ADSCrossRefGoogle Scholar
  48. 48.
    X. Tang, C.W. Li, B. Fultz, Phys. Rev. B 82, 184301 (2010)ADSCrossRefGoogle Scholar
  49. 49.
    X. Gonze, J.P. Vigneron, Phys. Rev. B 39, 13120 (1989)ADSCrossRefGoogle Scholar
  50. 50.
    A. Debernardi, S. Baroni, E. Molinari, Phys. Rev. Lett. 75, 1819 (1995)ADSCrossRefGoogle Scholar
  51. 51.
    G. Deinzer, G. Birner, D. Strauch, Phys. Rev. B 67, 144304 (2003)ADSCrossRefGoogle Scholar
  52. 52.
    G. Lang, K. Karch, M. Schmitt, P. Pavone, A.P. Mayer, R.K. Wehner, D. Strauch, Phys. Rev. B 59, 6182 (1999)ADSCrossRefGoogle Scholar
  53. 53.
    M. Lazzeri, M. Calandra, F. Mauri, Phys. Rev. B 68, 220509 (2003)ADSCrossRefGoogle Scholar
  54. 54.
    B. Rousseau, A. Bergara, Phys. Rev. B 82, 104504 (2010)ADSCrossRefGoogle Scholar
  55. 55.
    I. Errea, B. Rousseau, A. Bergara, Phys. Rev. Lett. 106, 165501 (2011)ADSCrossRefGoogle Scholar
  56. 56.
    I. Errea, B. Rousseau, A. Bergara, J. Appl. Phys. 111, 112604 (2012)ADSCrossRefGoogle Scholar
  57. 57.
    N. Bonini, M. Lazzeri, N. Marzari, F. Mauri, Phys. Rev. Lett. 99, 176802 (2007)ADSCrossRefGoogle Scholar
  58. 58.
    D.J. Hooton, Philos. Mag. Ser. 7 46, 422 (1955)MathSciNetCrossRefGoogle Scholar
  59. 59.
    A. Isihara, J. Phys. A 1, 539 (1968)ADSCrossRefGoogle Scholar
  60. 60.
    S. Rossano, F. Mauri, C.J. Pickard, I. Farnan, J. Phys. Chem. B 109, 7245 (2005)CrossRefGoogle Scholar
  61. 61.
    G. Profeta, C. Franchini, N.N. Lathiotakis, A. Floris, A. Sanna, M.A.L. Marques, M. Lüders, S. Massidda, E.K.U. Gross, A. Continenza, Phys. Rev. Lett. 96, 047003 (2006)ADSCrossRefGoogle Scholar
  62. 62.
    O. Degtyareva, M.V. Magnitskaya, J. Kohanoff, G. Profeta, S. Scandolo, M. Hanfland, M.I. McMahon, E. Gregoryanz, Phys. Rev. Lett. 99, 155505 (2007)ADSCrossRefGoogle Scholar
  63. 63.
    Z.P. Yin, S.Y. Savrasov, W.E. Pickett, Phys. Rev. B 74, 094519 (2006)ADSCrossRefGoogle Scholar
  64. 64.
    M.D. Johannes, I.I. Mazin, Phys. Rev. B 77, 165135 (2008)ADSCrossRefGoogle Scholar
  65. 65.
    M.D. Johannes, I.I. Mazin, C.A. Howells, Phys. Rev. B 73, 205102 (2006)ADSCrossRefGoogle Scholar
  66. 66.
    W. Zhong, D. Vanderbilt, K.M. Rabe, Phys. Rev. B 52, 6301 (1995)ADSCrossRefGoogle Scholar
  67. 67.
    R. Yu, H. Krakauer, Phys. Rev. Lett. 74, 4067 (1995)ADSCrossRefGoogle Scholar
  68. 68.
    L. Vocadlo, D. Alfè, M.J. Gillan, I.G. Wood, J.P. Brodholt, G.D. Price, Nature 424, 536 (2003)ADSCrossRefGoogle Scholar
  69. 69.
    W. Luo, B. Johansson, O. Eriksson, S. Arapan, P. Souvatzis, M.I. Katsnelson, R. Ahuja, Proc. Natl. Acad. Sci. USA 107, 9962 (2010)ADSCrossRefGoogle Scholar
  70. 70.
    G. Grimvall, B. Magyari-Köpe, V. Ozoliņš, K.A. Persson, Rev. Mod. Phys. 84, 945 (2012)ADSCrossRefGoogle Scholar
  71. 71.
    T.E. Markland, B.J. Berne, Proc. Natl. Acad. Sci. 109, 7988 (2012)ADSCrossRefGoogle Scholar
  72. 72.
    R. Car, M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)ADSCrossRefGoogle Scholar
  73. 73.
    C.Z. Wang, C.T. Chan, K.M. Ho, Phys. Rev. B 42, 11276 (1990)ADSCrossRefGoogle Scholar
  74. 74.
    M.P. Ljungberg, J. Íñiguez, Phys. Rev. Lett. 110, 105503 (2013)ADSCrossRefGoogle Scholar
  75. 75.
    A.M. Teweldeberhan, J.L. Dubois, S.A. Bonev, Phys. Rev. Lett. 105, 235503 (2010)ADSCrossRefGoogle Scholar
  76. 76.
    I.B. Magdău, G.J. Ackland, Phys. Rev. B 87, 174110 (2013)ADSCrossRefGoogle Scholar
  77. 77.
    D.B. Zhang, T. Sun, R.M. Wentzcovitch, Phys. Rev. Lett. 112, 058501 (2014)ADSCrossRefGoogle Scholar
  78. 78.
    O. Hellman, I.A. Abrikosov, S.I. Simak, Phys. Rev. B 84, 180301 (2011)ADSCrossRefGoogle Scholar
  79. 79.
    O. Hellman, P. Steneteg, I.A. Abrikosov, S.I. Simak, Phys. Rev. B 87, 104111 (2013)ADSCrossRefGoogle Scholar
  80. 80.
    O. Hellman, I.A. Abrikosov, Phys. Rev. B 88, 144301 (2013)ADSCrossRefGoogle Scholar
  81. 81.
    H. Dammak, Y. Chalopin, M. Laroche, M. Hayoun, J.J. Greffet, Phys. Rev. Lett. 103, 190601 (2009)ADSCrossRefGoogle Scholar
  82. 82.
    M. Ceriotti, G. Bussi, M. Parrinello, Phys. Rev. Lett. 103, 030603 (2009)ADSCrossRefGoogle Scholar
  83. 83.
    D.M. Ceperley, Rev. Mod. Phys. 67, 279 (1995)ADSCrossRefGoogle Scholar
  84. 84.
    J.C. Wojdeł, P. Hermet, M.P. Ljungberg, P. Ghosez, J. Íñguez, J. Phys.: Condens. Matter 25, 305401 (2013)Google Scholar
  85. 85.
    M. Allen, D. Tildesley, Computer Simulation of Liquids, Oxford Science Publ. (Clarendon Press, 1989)Google Scholar
  86. 86.
    T. Tadano, S. Tsuneyuki, Phys. Rev. B 92, 054301 (2015)ADSCrossRefGoogle Scholar
  87. 87.
    F. Zhou, W. Nielson, Y. Xia, V. Ozoliņš, Phys. Rev. Lett. 113, 185501 (2014)ADSCrossRefGoogle Scholar
  88. 88.
    I. Georgescu, V.A. Mandelshtam, J. Chem. Phys. 137, 144106 (2012)ADSCrossRefGoogle Scholar
  89. 89.
    J.M. Bowman, J. Chem. Phys. 68, 608 (1978)ADSCrossRefGoogle Scholar
  90. 90.
    B. Monserrat, N.D. Drummond, R.J. Needs, Phys. Rev. B 87, 144302 (2013)ADSCrossRefGoogle Scholar
  91. 91.
    S. Azadi, B. Monserrat, W.M.C. Foulkes, R.J. Needs, Phys. Rev. Lett. 112, 165501 (2014)ADSCrossRefGoogle Scholar
  92. 92.
    N.D. Drummond, B. Monserrat, J.H. Lloyd-Williams, P.L. Rios, C.J. Pickard, R.J. Needs, Nat. Commun. 6, 7794 (2015)ADSCrossRefGoogle Scholar
  93. 93.
    S.E. Brown, I. Georgescu, V.A. Mandelshtam, J. Chem. Phys. 138, 044317 (2013)ADSCrossRefGoogle Scholar
  94. 94.
    C.E. Patrick, K.W. Jacobsen, K.S. Thygesen, Phys. Rev. B 92, 201205 (2015)ADSCrossRefGoogle Scholar
  95. 95.
    P. Souvatzis, O. Eriksson, M.I. Katsnelson, S.P. Rudin, Phys. Rev. Lett. 100, 095901 (2008)ADSCrossRefGoogle Scholar
  96. 96.
    N. Antolin, O.D. Restrepo, W. Windl, Phys. Rev. B 86, 054119 (2012)ADSCrossRefGoogle Scholar
  97. 97.
    R.A. Cowley, Rep. Prog. Phys. 31, 123 (1968)ADSCrossRefGoogle Scholar
  98. 98.
    C.W. Li et al., Phys. Rev. Lett. 112, 175501 (2014)ADSCrossRefGoogle Scholar
  99. 99.
    M. Calandra, F. Mauri, Phys. Rev. Lett. 101, 016401 (2008)ADSCrossRefGoogle Scholar
  100. 100.
    V.H. Crespi, M.L. Cohen, Phys. Rev. B 48, 398 (1993)ADSCrossRefGoogle Scholar
  101. 101.
    A.P. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontov, S.I. Shylin, Nature 525, 73 (2015)ADSCrossRefGoogle Scholar
  102. 102.
    B. Stritzker, W. Buckel, Zeit. Phys. 257, 1 (1972)ADSCrossRefGoogle Scholar
  103. 103.
    J.E. Schirber, C.J.M. Northrup, Phys. Rev. B 10, 3818 (1974)ADSCrossRefGoogle Scholar
  104. 104.
    O. Degtyareva, J.E. Proctor, C.L. Guillaume, E. Gregoryanz, M. Hanfland, Solid State Commun. 149, 1583 (2009)ADSCrossRefGoogle Scholar
  105. 105.
    T. Scheler, O. Degtyareva, M. Marqués, C.L. Guillaume, J.E. Proctor, S. Evans, E. Gregoryanz, Phys. Rev. B 83, 214106 (2011)ADSCrossRefGoogle Scholar
  106. 106.
    X.F. Zhou, A.R. Oganov, X. Dong, L. Zhang, Y. Tian, H.T. Wang, Phys. Rev. B 84, 054543 (2011)ADSCrossRefGoogle Scholar
  107. 107.
    D.Y. Kim, R.H. Scheicher, C.J. Pickard, R.J. Needs, R. Ahuja, Phys. Rev. Lett. 107, 117002 (2011)ADSCrossRefGoogle Scholar
  108. 108.
    M.I. Eremets, I.A. Trojan, S.A. Medvedev, J.S. Tse, Y. Yao, Science 319, 1506 (2008)ADSCrossRefGoogle Scholar
  109. 109.
    R. Sherman, H.K. Birnbaum, J.A. Holy, M.V. Klein, Phys. Lett. A 62, 353 (1977)ADSCrossRefGoogle Scholar
  110. 110.
    A. Kolesnikov, I. Natkaniec, V. Antonov, I. Belash, V. Fedotov, J. Krawczyk, J. Mayer, E. Ponyatovsky, Physica B 174, 257 (1991)ADSCrossRefGoogle Scholar
  111. 111.
    M. Chowdhury, D. Ross, Solid State Commun. 13, 229 (1973)ADSCrossRefGoogle Scholar
  112. 112.
    D.K. Ross, V.E. Antonov, E.L. Bokhenkov, A.I. Kolesnikov, E.G. Ponyatovsky, J. Tomkinson, Phys. Rev. B 58, 2591 (1998)ADSCrossRefGoogle Scholar
  113. 113.
    D. Duan, Y. Liu, F. Tian, D. Li, X. Huang, Z. Zhao, H. Yu, B. Liu, W. Tian, T. Cui, Sci. Rep. 4, 6968 (2014)ADSCrossRefGoogle Scholar
  114. 114.
    G. Gao, H. Wang, A. Bergara, Y. Li, G. Liu, Y. Ma, Phys. Rev. B 84, 064118 (2011)ADSCrossRefGoogle Scholar
  115. 115.
    G. Gao et al., Proc. Natl. Acad. Sci. USA 107, 1317 (2010)ADSCrossRefGoogle Scholar
  116. 116.
    G. Gao, A.R. Oganov, A. Bergara, M. Martinez-Canales, T. Cui, T. Iitaka, Y. Ma, G. Zou, Phys. Rev. Lett. 101, 107002 (2008)ADSCrossRefGoogle Scholar
  117. 117.
    H. Wang, J.S. Tse, K. Tanaka, T. Iitaka, Y. Ma, Proc. Natl. Acad. Sci. 109, 6463 (2012)ADSCrossRefGoogle Scholar
  118. 118.
    D.Y. Kim, R.H. Scheicher, R. Ahuja, Phys. Rev. Lett. 103, 077002 (2009)ADSCrossRefGoogle Scholar
  119. 119.
    Y. Li, J. Hao, H. Liu, J.S. Tse, Y. Wang, Y. Ma, Sci. Rep. 5, 9948 (2015)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Fisika Aplikatua 1 Saila, EUITI Bilbao, University of the Basque Country (UPV/EHU)Basque CountrySpain
  2. 2.Donostia International Physics Center (DIPC), Manuel Lardizabal Pasealekua 4Basque CountrySpain

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