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.
Similar content being viewed by others
References
G. Onida, L. Reining, A. Rubio, Rev. Mod. Phys. 74, 601 (2002)
J. Taylor, H. Guo, J. Wang, Phys. Rev. B 63, 245407 (2001)
T. Frederiksen, M. Paulsson, M. Brandbyge, A.P. Jauho, Phys. Rev. B 75, 205413 (2007)
D.A. Broido, M. Malorny, G. Birner, N. Mingo, D.A. Stewart, Appl. Phys. Lett. 91, 231922 (2007)
G. Fugallo, M. Lazzeri, L. Paulatto, F. Mauri, Phys. Rev. B 88, 045430 (2013)
A.Y. Liu, A.A. Quong, Phys. Rev. B 53, R7575 (1996)
F. Mauri, O. Zakharov, S. de Gironcoli, S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 77, 1151 (1996)
S. Curtarolo, G.L.W. Hart, M.B. Nardelli, N. Mingo, S. Sanvito, O. Levy, Nat. Mater. 12, 191 (2013)
P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)
W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)
E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)
M. Petersilka, U.J. Gossmann, E.K.U. Gross, Phys. Rev. Lett. 76, 1212 (1996)
G. Mahan, B. Sales, J. Sharp, Phys. Today 50, 42 (1997)
F.J. DiSalvo, Science 285, 703 (1999)
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)
G.K.H. Madsen, J. Am. Chem. Soc. 128, 12140 (2006)
G.S. Pawley, W. Cochran, R.A. Cowley, G. Dolling, Phys. Rev. Lett. 17, 753 (1966)
O. Delaire et al., Nat. Mater. 10, 614 (2011)
Y. Luspin, J.L. Servoin, F. Gervais, J. Phys. C 13, 3761 (1980)
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)
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)
M. Holt, P. Zschack, H. Hong, M.Y. Chou, T.C. Chiang, Phys. Rev. Lett. 86, 3799 (2001)
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)
P.H. Ghosez, X. Gonze, J.P. Michenaud, Ferroelectrics 206, 205 (1998)
M. Calandra, I.I. Mazin, F. Mauri, Phys. Rev. B 80, 241108 (2009)
M. Calandra, F. Mauri, Phys. Rev. Lett. 106, 196406 (2011)
A.A. Maradudin, A.E. Fein, Phys. Rev. 128, 2589 (1962)
M. Calandra, M. Lazzeri, F. Mauri, Physica C 456, 38 (2007)
L. Paulatto, F. Mauri, M. Lazzeri, Phys. Rev. B 87, 214303 (2013)
D.A. Broido, T.L. Reinecke, Phys. Rev. B 70, 081310 (2004)
D.A. Broido, A. Ward, N. Mingo, Phys. Rev. B 72, 014308 (2005)
A. Ward, D.A. Broido, D.A. Stewart, G. Deinzer, Phys. Rev. B 80, 125203 (2009)
I. Errea, M. Calandra, F. Mauri, Phys. Rev. Lett. 111, 177002 (2013)
I. Errea, M. Calandra, F. Mauri, Phys. Rev. B 89, 064302 (2014)
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)
I. Errea, M. Calandra, F. Mauri, Phys. Stat. Sol. B 251, 2556 (2014)
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)
S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001)
X. Gonze, C. Lee, Phys. Rev. B 55, 10355 (1997)
G. Kresse, J. Furthmüller, J. Hafner, Europhys. Lett. 32, 729 (1995)
B. Fultz, Prog. Mater. Sci. 55, 247 (2010)
J.D. Althoff, P.B. Allen, R.M. Wentzcovitch, J.A. Moriarty, Phys. Rev. B 48, 13253 (1993)
Y. Yao, J.S. Tse, K. Tanaka, F. Marsiglio, Y. Ma, Phys. Rev. B 79, 054524 (2009)
M. Lazzeri, S. de Gironcoli, Phys. Rev. B 65, 245402 (2002)
M. Lazzeri, S. de Gironcoli, Phys. Rev. Lett. 81, 2096 (1998)
L. Paulatto, I. Errea, M. Calandra, F. Mauri, Phys. Rev. B 91, 054304 (2015)
S. Narasimhan, D. Vanderbilt, Phys. Rev. B 43, 4541 (1991)
X. Tang, C.W. Li, B. Fultz, Phys. Rev. B 82, 184301 (2010)
X. Gonze, J.P. Vigneron, Phys. Rev. B 39, 13120 (1989)
A. Debernardi, S. Baroni, E. Molinari, Phys. Rev. Lett. 75, 1819 (1995)
G. Deinzer, G. Birner, D. Strauch, Phys. Rev. B 67, 144304 (2003)
G. Lang, K. Karch, M. Schmitt, P. Pavone, A.P. Mayer, R.K. Wehner, D. Strauch, Phys. Rev. B 59, 6182 (1999)
M. Lazzeri, M. Calandra, F. Mauri, Phys. Rev. B 68, 220509 (2003)
B. Rousseau, A. Bergara, Phys. Rev. B 82, 104504 (2010)
I. Errea, B. Rousseau, A. Bergara, Phys. Rev. Lett. 106, 165501 (2011)
I. Errea, B. Rousseau, A. Bergara, J. Appl. Phys. 111, 112604 (2012)
N. Bonini, M. Lazzeri, N. Marzari, F. Mauri, Phys. Rev. Lett. 99, 176802 (2007)
D.J. Hooton, Philos. Mag. Ser. 7 46, 422 (1955)
A. Isihara, J. Phys. A 1, 539 (1968)
S. Rossano, F. Mauri, C.J. Pickard, I. Farnan, J. Phys. Chem. B 109, 7245 (2005)
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)
O. Degtyareva, M.V. Magnitskaya, J. Kohanoff, G. Profeta, S. Scandolo, M. Hanfland, M.I. McMahon, E. Gregoryanz, Phys. Rev. Lett. 99, 155505 (2007)
Z.P. Yin, S.Y. Savrasov, W.E. Pickett, Phys. Rev. B 74, 094519 (2006)
M.D. Johannes, I.I. Mazin, Phys. Rev. B 77, 165135 (2008)
M.D. Johannes, I.I. Mazin, C.A. Howells, Phys. Rev. B 73, 205102 (2006)
W. Zhong, D. Vanderbilt, K.M. Rabe, Phys. Rev. B 52, 6301 (1995)
R. Yu, H. Krakauer, Phys. Rev. Lett. 74, 4067 (1995)
L. Vocadlo, D. Alfè, M.J. Gillan, I.G. Wood, J.P. Brodholt, G.D. Price, Nature 424, 536 (2003)
W. Luo, B. Johansson, O. Eriksson, S. Arapan, P. Souvatzis, M.I. Katsnelson, R. Ahuja, Proc. Natl. Acad. Sci. USA 107, 9962 (2010)
G. Grimvall, B. Magyari-Köpe, V. Ozoliņš, K.A. Persson, Rev. Mod. Phys. 84, 945 (2012)
T.E. Markland, B.J. Berne, Proc. Natl. Acad. Sci. 109, 7988 (2012)
R. Car, M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)
C.Z. Wang, C.T. Chan, K.M. Ho, Phys. Rev. B 42, 11276 (1990)
M.P. Ljungberg, J. Íñiguez, Phys. Rev. Lett. 110, 105503 (2013)
A.M. Teweldeberhan, J.L. Dubois, S.A. Bonev, Phys. Rev. Lett. 105, 235503 (2010)
I.B. Magdău, G.J. Ackland, Phys. Rev. B 87, 174110 (2013)
D.B. Zhang, T. Sun, R.M. Wentzcovitch, Phys. Rev. Lett. 112, 058501 (2014)
O. Hellman, I.A. Abrikosov, S.I. Simak, Phys. Rev. B 84, 180301 (2011)
O. Hellman, P. Steneteg, I.A. Abrikosov, S.I. Simak, Phys. Rev. B 87, 104111 (2013)
O. Hellman, I.A. Abrikosov, Phys. Rev. B 88, 144301 (2013)
H. Dammak, Y. Chalopin, M. Laroche, M. Hayoun, J.J. Greffet, Phys. Rev. Lett. 103, 190601 (2009)
M. Ceriotti, G. Bussi, M. Parrinello, Phys. Rev. Lett. 103, 030603 (2009)
D.M. Ceperley, Rev. Mod. Phys. 67, 279 (1995)
J.C. Wojdeł, P. Hermet, M.P. Ljungberg, P. Ghosez, J. Íñguez, J. Phys.: Condens. Matter 25, 305401 (2013)
M. Allen, D. Tildesley, Computer Simulation of Liquids, Oxford Science Publ. (Clarendon Press, 1989)
T. Tadano, S. Tsuneyuki, Phys. Rev. B 92, 054301 (2015)
F. Zhou, W. Nielson, Y. Xia, V. Ozoliņš, Phys. Rev. Lett. 113, 185501 (2014)
I. Georgescu, V.A. Mandelshtam, J. Chem. Phys. 137, 144106 (2012)
J.M. Bowman, J. Chem. Phys. 68, 608 (1978)
B. Monserrat, N.D. Drummond, R.J. Needs, Phys. Rev. B 87, 144302 (2013)
S. Azadi, B. Monserrat, W.M.C. Foulkes, R.J. Needs, Phys. Rev. Lett. 112, 165501 (2014)
N.D. Drummond, B. Monserrat, J.H. Lloyd-Williams, P.L. Rios, C.J. Pickard, R.J. Needs, Nat. Commun. 6, 7794 (2015)
S.E. Brown, I. Georgescu, V.A. Mandelshtam, J. Chem. Phys. 138, 044317 (2013)
C.E. Patrick, K.W. Jacobsen, K.S. Thygesen, Phys. Rev. B 92, 201205 (2015)
P. Souvatzis, O. Eriksson, M.I. Katsnelson, S.P. Rudin, Phys. Rev. Lett. 100, 095901 (2008)
N. Antolin, O.D. Restrepo, W. Windl, Phys. Rev. B 86, 054119 (2012)
R.A. Cowley, Rep. Prog. Phys. 31, 123 (1968)
C.W. Li et al., Phys. Rev. Lett. 112, 175501 (2014)
M. Calandra, F. Mauri, Phys. Rev. Lett. 101, 016401 (2008)
V.H. Crespi, M.L. Cohen, Phys. Rev. B 48, 398 (1993)
A.P. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontov, S.I. Shylin, Nature 525, 73 (2015)
B. Stritzker, W. Buckel, Zeit. Phys. 257, 1 (1972)
J.E. Schirber, C.J.M. Northrup, Phys. Rev. B 10, 3818 (1974)
O. Degtyareva, J.E. Proctor, C.L. Guillaume, E. Gregoryanz, M. Hanfland, Solid State Commun. 149, 1583 (2009)
T. Scheler, O. Degtyareva, M. Marqués, C.L. Guillaume, J.E. Proctor, S. Evans, E. Gregoryanz, Phys. Rev. B 83, 214106 (2011)
X.F. Zhou, A.R. Oganov, X. Dong, L. Zhang, Y. Tian, H.T. Wang, Phys. Rev. B 84, 054543 (2011)
D.Y. Kim, R.H. Scheicher, C.J. Pickard, R.J. Needs, R. Ahuja, Phys. Rev. Lett. 107, 117002 (2011)
M.I. Eremets, I.A. Trojan, S.A. Medvedev, J.S. Tse, Y. Yao, Science 319, 1506 (2008)
R. Sherman, H.K. Birnbaum, J.A. Holy, M.V. Klein, Phys. Lett. A 62, 353 (1977)
A. Kolesnikov, I. Natkaniec, V. Antonov, I. Belash, V. Fedotov, J. Krawczyk, J. Mayer, E. Ponyatovsky, Physica B 174, 257 (1991)
M. Chowdhury, D. Ross, Solid State Commun. 13, 229 (1973)
D.K. Ross, V.E. Antonov, E.L. Bokhenkov, A.I. Kolesnikov, E.G. Ponyatovsky, J. Tomkinson, Phys. Rev. B 58, 2591 (1998)
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)
G. Gao, H. Wang, A. Bergara, Y. Li, G. Liu, Y. Ma, Phys. Rev. B 84, 064118 (2011)
G. Gao et al., Proc. Natl. Acad. Sci. USA 107, 1317 (2010)
G. Gao, A.R. Oganov, A. Bergara, M. Martinez-Canales, T. Cui, T. Iitaka, Y. Ma, G. Zou, Phys. Rev. Lett. 101, 107002 (2008)
H. Wang, J.S. Tse, K. Tanaka, T. Iitaka, Y. Ma, Proc. Natl. Acad. Sci. 109, 6463 (2012)
D.Y. Kim, R.H. Scheicher, R. Ahuja, Phys. Rev. Lett. 103, 077002 (2009)
Y. Li, J. Hao, H. Liu, J.S. Tse, Y. Wang, Y. Ma, Sci. Rep. 5, 9948 (2015)
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Ψk Volker Heine Young Investigator Award – 2015 Finalists”, edited by Angel Rubio and Risto Nieminen.
Rights and permissions
About this article
Cite this article
Errea, I. Approaching the strongly anharmonic limit with ab initio calculations of materials’ vibrational properties – a colloquium*. Eur. Phys. J. B 89, 237 (2016). https://doi.org/10.1140/epjb/e2016-70078-6
Received:
Published:
DOI: https://doi.org/10.1140/epjb/e2016-70078-6