Implementation of an all-electron GW approximation based on the projector augmented wave method without plasmon pole approximation: Application to Si, SiC, AlAs, InAs, NaH, and KH

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 15, 2003, Pages 1552081-15520810

  Lebegue S ^a,b   Arnaud, B ^c   Alouani, M ^a,d   Bloechl, P E ^d,e  

^a INSTITUT DE PHYSIQUE ET CHIMIE DES MATÉRIAUX DE STRASBOURG   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Campus de Beaulieu 35042 Cedex   (France)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e CLAUSTHAL UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALUMINUM DERIVATIVE; HYDROGEN; INDIUM; POTASSIUM DERIVATIVE; SILICON; SILICON CARBIDE; SODIUM DERIVATIVE;

ANALYTIC METHOD; ARTICLE; CALCULATION; COMPLEX FORMATION; ELECTRON TRANSPORT; ENERGY; SEMICONDUCTOR;

EID: 0038547748     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (66)

1. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, ibid. 140, A 1113 (1965).
2. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, ibid. 140, A1113 (1965).
3. L. Hedin, Phys. Rev. 139, A796 (1965).
4. L. Hedin and S. Lundquist, in Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic, New York, 1969), Vol. 23, p. 1.
5. F. Aryasetiawan and O. Gunnarsson, Rep. Prog. Phys. 61, 237 (1998).
6. W. G. Aulbur, L. Jönsson, and J. W. Wilkins, in Solid State Physics, edited by H. Ehrenreich and F. Spaegen (Academic, Orlando, 1999), Vol. 54.
7. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002).
8. F. Aryasetiawan, Advances in Condensed Matter Science, edited by I. V. Anisimov (Gordon and Breach, New York, 2000).
9. J.-L. Li, G.-M. Rignanese, E. K. Chang, X. Blase, and S. G. Louie, Phys. Rev. B 66, 035102 (2002).
10. P. van Gelderen, P. A. Bobbert, P. J. Kelly, G. Brocks, and R. Tolboom, Phys. Rev. B 66, 075104 (2002).
11. A. Marini, G. Onida, and R. Del Sole, Phys. Rev. Lett. 88, 016403 (2002).
12. M. S. Hybertsen and S. G. Louie, Phys. Rev. B 34, 5390 (1986).
13. R. W. Godby, M. Schluter, and L. J. Sham, Phys. Rev. B 37, 10 159 (1988).
14. M. Rohlfing, P. Krüger, and J. Pollmann, Phys. Rev. B 57, 6485 (1998).
15. N. Hamada, M. Hwang, and A. J. Freeman, Phys. Rev. B 41, 3620 (1990).
16. B. Arnaud and M. Alouani, Phys. Rev. B 62, 4464 (2000).
17. J. Furthmüller, G. Cappellini, H.-Ch. Weissker, and F. Bechstedt, Phys. Rev. B 66, 045110 (2002).
18. T. Kotani and M. Van Schilfgaarde, Solid State Commun. 121, 461 (2002).
19. W. Ku and A. G. Eguiluz, Phys. Rev. Lett. 89, 12 401 (2002).
20. H. N. Rojas, R. W. Godby, and R. J. Needs, Phys. Rev. Lett. 74, 1827 (1995).
21. F. Bechstedt, M. Fiedler, C. Kress, and R. Del Sole, Phys. Rev. B 49, 7357 (1994).
22. A. Fleszar and W. Hanke, Phys. Rev. B 56, 10 228 (1997).
23. P. E. Blöchl, Phys. Rev. B 50, 17 953 (1994).
24. G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
25. N. A. W. Holzwarth, G. E. Matthews, R. B. Dunning, A. R. Tackett, and Y. Zeng, Phys. Rev. B 55, 2005 (1997).
26. N. A. W. Holzwarth, G. E. Matthews, A. R. Tackett, and R. B. Dunning, Phys. Rev. B 57, 11 827 (1998).
27. S. Massidda, M. Posternak, and A. Baldereschi, Phys. Rev. B 48, 5058 (1993).
28. S. D. Adler, Phys. Rev. 126, 413 (1962); N. Wiser, ibid. 129, 62 (1963); see also D. L. Johnson, Phys. Rev. B 9, 4475 (1974).
29. S. D. Adler, Phys. Rev. 126, 413 (1962); N. Wiser, ibid. 129, 62 (1963); see also D. L. Johnson, Phys. Rev. B 9, 4475 (1974).
30. S. D. Adler, Phys. Rev. 126, 413 (1962); N. Wiser, ibid. 129, 62 (1963); see also D. L. Johnson, Phys. Rev. B 9, 4475 (1974).
31. M. S. Hybertsen and S. G. Louie, Phys. Rev. B 34, 5390 (1986).
32. W. G. Aulbur, Ph.D. thesis, Ohio State University, 1996.
33. We have used a simple four-point interpolation method. The use of a more elaborate method like the cubic spline method is shown to not influence the final results.
34. Y.-G. Jin and K. J. Chang, Phys. Rev. B 59, 14 841 (1999).
35. K.-H. Lee and K. J. Chang, Phys. Rev. B 54, 8285 (1996).
36. The reason for not using the same expression as in Ref. 19 is that our expression (15) is more general and provided us with a better stability in the fitting procedure.
37. H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976).
38. Numerical Data and Functional Relationships in Science and Technology, edited by K.H. Hellwege and O. Madelung, Landolt-Börnstein, New Series, Group III, Vol. 17, pt. a and Vol. 22, pt. a (Springer, Berlin, 1982).
39. J. L. Martins, Phys. Rev. B 41, 7883 (1990).
40. To justify the use of the present expression for F(q), we have also used the function given by Ref. 61 and found that the final QP energies differ by at most 0.02 eV for silicon. Moreover, the F(q) is specific to fcc lattice systems and therefore must be adapted for other systems according to Ref. 62, whereas the function used in this work is independent of crystallographic system. We have also checked if six points are sufficient by performing calculations using a set of 12 points; the resulting QP energies remain unchanged, proving the validity of our choice.
41. The imaginary part of the self-energy is a sum of delta functions in the plasmon-pole approximation.
42. J. E. Ortega and F. J. Himpsel, Phys. Rev. B 47, 2130 (1993).
43. W. E. Spicer and R. C. Eden, in Proceedings of the Ninth International Conference on the Physics of Semiconductors, Moscow, 1968, edited by S. M. Ryvkin (Nauka, Leningrad, 1968), Vol. 1, p. 61.
44. A. L. Wachs, T. Miller, T. C. Hsieh, A. P. Shapiro, and T. C. Chiang, Phys. Rev. B 32, 2326 (1985).
45. R. Hulthen and N. G. Nilsson, Solid State Commun. 18, 1341 (1976).
46. F. J. Himpsel, P. Heimann, and D. E. Eastman, Phys. Rev. B 24, 2003 (1981).
47. M. Rohlfing, P. Krüger, and J. Pollmann, Phys. Rev. B 48, 17 791 (1993).
48. E. L. Shirley, X. Zhu, and S. G. Louie, Phys. Rev. B 56, 6648 (1997).
49. X. Zhu and S. G. Louie, Phys. Rev. B 43, 14 142 (1991).
50. D. J. Wolford and J. A. Bradley, Solid State Commun. 53, 1069 (1985).
51. D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983); D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhatt, J. Appl. Phys. 60, 754 (1986).
52. D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983); D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhatt, J. Appl. Phys. 60, 754 (1986).
53. Notice that the same PAW method is used to compute the Si QP energies both within the RPA and the PP model.
54. 1c for SiC seems to be largely overestimated by GW calculations. In fact, we join the conclusion of Ref. 44 and claim that the experimental value is certainly less precise. This is confirmed by the fact that our calculation agrees by about 0.08 eV with their data.
55. 1c transition by more than 0.05 eV.
56. R. Ahuja, O. Eriksson, and B. Johansson, Physica B 265, 87 (1999).
57. C. O. Rodriguez and M. Methfessel, Phys. Rev. B 45, 90 (1992).
58. A. B. Kunz and D. J. Mickish, Phys. Rev. B 11, 1700 (1975).
59. J. Hama and N. Kawakami, Phys. Lett. A 126, 348 (1988).
60. N. I. Kulikov, Fiz. Tverd. Tela (Leningrad) 20, 2027 (1978).
61. Database compiled by D. A. Papaconstantopoulos and co-workers and located at http://manybody.nrl.navy.mil/esdata/database.html (the calculations were performed by the APW method including scalar-relativistic corrections within the LDA).
62. For the calculated electronic properties of NaH and KH alkali hydrides we have used 64 k points in the full BZ as well as 200 bands, and a dielectric matrix of size 169 × 169 to achieve well converged results.
63. Kunz and Mickish have also reported a band gap for LiH of 6.61 eV compared to a measured value of 4.99 eV [data reported in the paper of S. Baroni et al., Phys. Rev. B 32, 4077 (1985)].
64. S. Lebègue, M. Alouani, B. Arnaud, and W. E. Pickett, Europhys. Lett., cond-mat/0302290 (unpublished).
65. F. Gygi and A. Baldereschi, Phys. Rev. B 34, 4405 (1986).
66. B. Wenzien, G. Cappellini, and F. Bechstedt, Phys. Rev. B 51, 14 701 (1995).