P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). 10.1103/PhysRev.136.B864
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). 10.1103/PhysRev.140.A1133
R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, 2nd ed. (Dover Publications, 1976).
G. D. Mahan, Many-Particle Physics (Springer, 2000).
L. Hedin and S. Lundqvist, in Solid State Physics, edited by F. Seitz, D. Turnbull, and H. Ehrenreich (Academic Press, New York, 1969), Vol. 23, pp. 1-181.
M. Shishkin, M. Marsman, and G. Kresse, Phys. Rev. Lett. 99, 246403 (2007). 10.1103/PhysRevLett.99.246403
M. Rohlfing and S. G. Louie, Phys. Rev. B 62, 4927 (2000). 10.1103/PhysRevB.62.4927
F. Giustino, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 105, 265501 (2010). 10.1103/PhysRevLett.105.265501
G. Antonius, S. Poncé, P. Boulanger, M. Côté, and X. Gonze, Phys. Rev. Lett. 112, 215501 (2014). 10.1103/PhysRevLett.112.215501
G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002). 10.1103/RevModPhys.74.601
S. Poncé, G. Antonius, Y. Gillet, P. Boulanger, J. Laflamme Janssen, A. Marini, M. Côté, and X. Gonze, Phys. Rev. B 90, 214304 (2014). 10.1103/PhysRevB.90.214304
P. B. Allen and V. Heine, J. Phys. C: Solid State Phys. 9, 2305 (1976). 10.1088/0022-3719/9/12/013
P. B. Allen and M. Cardona, Phys. Rev. B 23, 1495 (1981). 10.1103/PhysRevB.23.1495
P. B. Allen and M. Cardona, Phys. Rev. B 27, 4760 (1983). 10.1103/PhysRevB.27.4760
A. Marini, Phys. Rev. Lett. 101, 106405 (2008). 10.1103/PhysRevLett.101.106405
S. Poncé, G. Antonius, P. Boulanger, E. Cannuccia, A. Marini, M. Côté, and X. Gonze, Comput. Mater. Sci. 83, 341 (2014). 10.1016/j.commatsci.2013.11.031
X. Gonze, P. Boulanger, and M. Côté, Ann. Phys. 523, 168 (2011). 10.1002/andp.201000100
E. Cannuccia and A. Marini, Phys. Rev. Lett. 107, 255501 (2011). 10.1103/PhysRevLett.107.255501
E. Cannuccia and A. Marini, Eur. Phys. J. B 85, 1 (2012). 10.1140/epjb/e2012-30105-4
A. Marini, S. Poncé, and X. Gonze, Phys. Rev. B 91, 224310 (2015). 10.1103/PhysRevB.91.224310
B. Monserrat, N. D. Drummond, and R. J. Needs, Phys. Rev. B 87, 144302 (2013). 10.1103/PhysRevB.87.144302
R. Ramírez, C. P. Herrero, E. R. Hernández, and M. Cardona, Phys. Rev. B 77, 045210 (2008). 10.1103/PhysRevB.77.045210
M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, 1954).
R. M. Sternheimer, Phys. Rev. 96, 951 (1954). 10.1103/PhysRev.96.951
S. Zollner, M. Cardona, and S. Gopalan, Phys. Rev. B 45, 3376 (1992). 10.1103/PhysRevB.45.3376
P. B. Allen, Phys. Rev. B 18, 5217 (1978). 10.1103/PhysRevB.18.5217
G. Antonius, S. Poncé, E. Lantagne-Hurtubise, G. Auclair, X. Gonze, and M. Côté, " Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure," Phys. Rev. B (submitted); e-print arXiv:1505.07738 (2015).
G. Grimvall, The Electron-Phonon Interaction in Metals (North-Holland Publishing Company, 1981).
X. Gonze and C. Lee, Phys. Rev. B 55, 10355 (1997). 10.1103/PhysRevB.55.10355
R. Zallen, R. M. Martin, and V. Natoli, Phys. Rev. B 49, 7032 (1994). 10.1103/PhysRevB.49.7032
X. Gonze, Phys. Rev. B 55, 10337 (1997). 10.1103/PhysRevB.55.10337
See supplementary material at http://dx.doi.org/10.1063/1.4927081 E-JCPSA6-143-013597 for the convergence studies.
L. He, F. Liu, G. Hautier, M. J. T. Oliveira, M. A. L. Marques, F. D. Vila, J. J. Rehr, G.-M. Rignanese, and A. Zhou, Phys. Rev. B 89, 064305 (2014). 10.1103/PhysRevB.89.064305
X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.-M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M. Verstraete, G. Zerah, and J. Zwanziger, Comput. Phys. Commun. 180, 2582 (2009). 10.1016/j.cpc.2009.07.007
S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001). 10.1103/RevModPhys.73.515
X. Gonze, G.-M. Rignanese, and R. Caracas, Z. Kristallogr. 220, 458 (2005). 10.1524/zkri.220.5.458.65077
G.-M. Rignanese, J.-P. Michenaud, and X. Gonze, Phys. Rev. B 53, 4488 (1996). 10.1103/PhysRevB.53.4488
P. Boulanger, " Etudes ab initio des effets de la température sur le spectre optique des semi-conducteurs," Ph.D. thesis, Université Catholique de Louvain and Université de Montréal, 2010.
A. Wright and J. Nelson, Phys. Rev. B 51, 7866 (1995). 10.1103/PhysRevB.51.7866
A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, APL Mater. 1, 011002 (2013). 10.1063/1.4812323
G. Yu, in Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, SiGe, edited by M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur (John Wiley & Sons, 2001).
I. Petrov, E. Mojab, R. C. Powell, J. E. Greene, L. Hultman, and J. Sundgren, Appl. Phys. Lett. 60, 2491 (1992). 10.1063/1.106943
H. Schulz and K. Thiemann, Solid State Commun. 23, 815 (1977). 10.1016/0038-1098(77)90959-0
W. R. L. Lambrecht and B. Segall, in Properties of Group III Nitrides, edited by J. H. Edgar (EMIS Datareviews Series, London, 1994).
K. Kim, W. Lambrecht, and B. Segall, Phys. Rev. B 53, 16310 (1996). 10.1103/PhysRevB.53.16310
C. Stampfl and C. Van de Walle, Phys. Rev. B 59, 5521 (1999). 10.1103/PhysRevB.59.5521
G. Cappellini, G. Satta, M. Palummo, and G. Onida, Phys. Rev. B 64, 035104 (2001). 10.1103/PhysRevB.64.035104
T. Soma, A. Sawaoka, and S. Saito, Mater. Res. Bull. 9, 755 (1974). 10.1016/0025-5408(74)90110-X
J. Furthmüller, J. Hafner, and G. Kresse, Phys. Rev. B 50, 15606 (1994). 10.1103/PhysRevB.50.15606
Numerical Data and Functional Relationships in Science and Technology- Crystal and Solid State Physics, Vol. III of Landolt-Börnstein, edited by O. Madelung (Springer, 1972).
R. Wentzcovitch, K. Chang, and M. Cohen, Phys. Rev. B 34, 1071 (1986). 10.1103/PhysRevB.34.1071
Y.-N. Xu and W. Ching, Phys. Rev. B 44, 7787 (1991). 10.1103/PhysRevB.44.7787
X. Liu, L. Li, Q. Li, Y. Li, and F. Lu, Mater. Sci. Semicond. Process. 16, 1369 (2013). 10.1016/j.mssp.2013.04.017
G. Gildenblat and P. Schmidt, Handbook Series on Semiconductor Parameters (World Scientific, 1996), pp. 58-76.
C. E. Patrick and F. Giustino, J. Phys.: Condens. Matter 26, 365503 (2014). 10.1088/0953-8984/26/36/365503
R. Wyckoff, in Crystal Structures (John Wiley & Sons, 1963), Vol. 1.
M. Fuchs and M. Scheffler, Comput. Phys. Commun. 119, 67 (1999). 10.1016/S0010-4655(98)00201-X
H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976). 10.1103/PhysRevB.13.5188
J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). 10.1103/PhysRevB.23.5048
M. Cardona and M. L. W. Thewalt, Rev. Mod. Phys. 77, 1173 (2005). 10.1103/RevModPhys.77.1173
D. Vogel, P. Krüger, and J. Pollmann, Phys. Rev. B 55, 12836 (1997). 10.1103/PhysRevB.55.12836
P. B. Perry and R. F. Rutz, Appl. Phys. Lett. 33, 319 (1978). 10.1063/1.90354
F. Litimein, B. Bouhafs, Z. Dridi, and P. Ruterana, New J. Phys. 4, 64 (2002). 10.1088/1367-2630/4/1/364
N. E. Christensen and I. Gorczyca, Phys. Rev. B 50, 4397 (1994). 10.1103/PhysRevB.50.4397
N. E. Christensen and I. Gorczyca, Phys. Rev. B 47, 4307 (1993). 10.1103/PhysRevB.47.4307
A. Rubio, J. Corkill, M. Cohen, E. Shirley, and S. Louie, Phys. Rev. B 48, 11810 (1993). 10.1103/PhysRevB.48.11810
C. Prasad and J. Dubey, Phys. Status Solidi B 125, 629 (1984). 10.1002/pssb.2221250223
N. L. Coleburn and J. W. Forbes, J. Chem. Phys. 48, 555 (1968). 10.1063/1.1668682
R. Chrenko, Solid State Commun. 14, 511 (1974). 10.1016/0038-1098(74)90978-8
Y. Gillet, M. Giantomassi, and X. Gonze, Phys. Rev. B 88, 094305 (2013). 10.1103/PhysRevB.88.094305
G. E. Jellison and F. A. Modine, Phys. Rev. B 27, 7466 (1983). 10.1103/PhysRevB.27.7466
C. D. Clark, P. J. Dean, and P. V. Harris, Proc. R. Soc. A 277, 312 (1964). 10.1098/rspa.1964.0025
S. Logothetidis, J. Petalas, H. M. Polatoglou, and D. Fuchs, Phys. Rev. B 46, 4483 (1992). 10.1103/PhysRevB.46.4483
B. Monserrat, G. J. Conduit, and R. J. Needs, Phys. Rev. B 90, 184302 (2014). 10.1103/PhysRevB.90.184302
J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992). 10.1103/PhysRevB.45.13244
B. Monserrat and R. J. Needs, Phys. Rev. B 89, 214304 (2014). 10.1103/PhysRevB.89.214304
W. Bludau, A. Onton, and W. Heinke, J. Appl. Phys. 45, 1846 (1974). 10.1063/1.1663501
G. Macfarlane, T. McLean, J. Quarrington, and V. Roberts, Phys. Rev. 111, 1245 (1958). 10.1103/PhysRev.111.1245
P. Lautenschlager, P. B. Allen, and M. Cardona, Phys. Rev. B 33, 5501 (1986). 10.1103/PhysRevB.33.5501
K. Karch and F. Bechstedt, Phys. Rev. B 56, 7404 (1997). 10.1103/PhysRevB.56.7404
L. E. McNeil, M. Grimsditch, and R. H. French, J. Am. Ceram. Soc. 76, 1132 (1993). 10.1111/j.1151-2916.1993.tb03730.x
O. Brafman, G. Lengyel, S. Mitra, P. Gielisse, J. Plendl, and L. Mansur, Solid State Commun. 6, 523 (1968). 10.1016/0038-1098(68)90503-6
P. Pavone, K. Karch, O. Schütt, D. Strauch, W. Windl, P. Giannozzi, and S. Baroni, Phys. Rev. B 48, 3156 (1993). 10.1103/PhysRevB.48.3156
J. L. Warren, J. L. Yarnell, G. Dolling, and R. A. Cowley, Phys. Rev. 158, 805 (1967). 10.1103/PhysRev.158.805
S. A. Solin and A. K. Ramdas, Phys. Rev. B 1, 1687 (1970). 10.1103/PhysRevB.1.1687
G. Nilsson and G. Nelin, Phys. Rev. B 6, 3777 (1972). 10.1103/PhysRevB.6.3777
P. Giannozzi, S. de Gironcoli, P. Pavone, and S. Baroni, Phys. Rev. B 43, 7231 (1991). 10.1103/PhysRevB.43.7231
D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, O. Dimitrov, R. Ambacher, and M. Stutzmann, J. Appl. Phys. 82, 5090 (1997). 10.1063/1.366309
Q. Guo and A. Yoshida, Jpn. J. Appl. Phys., Part 1 33, 2453 (1994). 10.1143/JJAP.33.2453
M. Cardona, Solid State Commun. 133, 3 (2005). 10.1016/j.ssc.2004.10.028
G. Nenciu, Rev. Mod. Phys. 63, 91 (1991). 10.1103/RevModPhys.63.91
R. W. Nunes and X. Gonze, Phys. Rev. B 63, 155107 (2001). 10.1103/PhysRevB.63.155107
I. Souza, J. Íñiguez, and D. Vanderbilt, Phys. Rev. Lett. 89, 117602 (2002). 10.1103/PhysRevLett.89.117602
M. S. Hybertsen and S. G. Louie, Phys. Rev. B 35, 5585 (1987). 10.1103/PhysRevB.35.5585
J. Lindhard, Mat.-Fys. Medd. K. Dan. Vidensk. Selsk. 28, 1 (1954), available online at http://www.sdu.dk/media/bibpdf/Bind%2020-29%5CBind%5Cmfm-28-8.pdf.