Self-consistent Overhauser model for the pair distribution function of an electron gas in dimensionalities D=3 and D=2

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 7, 2002, Pages 751101-751108

  Davoudi, B ^a   Polini, M ^a   Asgari, R ^a   Tosi, M P ^a  

^a SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; ACCURACY; ARTICLE; ELECTRON; ENERGY; GAS; MAGNETISM; MOLECULAR DYNAMICS; MOLECULAR MODEL; NUCLEAR OVERHAUSER EFFECT; QUANTUM MECHANICS;

EID: 0037104292     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.075110     Document Type: Article

References (47)

1. For reviews focused on many-body aspects of electron-gas theory, see K.S. Singwi and M.P. Tosi, in Solid State Physics edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic, New York, 1981), Vol. 36, p. 177; S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982); M. P. Tosi, in Electron Correlation in the Solid State, edited by N. H. March (Imperial College Press, London, 1999), p. 5.
2. For reviews focused on many-body aspects of electron-gas theory, see K.S. Singwi and M.P. Tosi, in Solid State Physics edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic, New York, 1981), Vol. 36, p. 177; S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982); M. P. Tosi, in Electron Correlation in the Solid State, edited by N. H. March (Imperial College Press, London, 1999), p. 5.
3. For reviews focused on many-body aspects of electron-gas theory, see K.S. Singwi and M.P. Tosi, in Solid State Physics edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic, New York, 1981), Vol. 36, p. 177; S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982); M. P. Tosi, in Electron Correlation in the Solid State, edited by N. H. March (Imperial College Press, London, 1999), p. 5.
4. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965); O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4724 (1976); S. Lundqvist and N,H. March, Theory of Inhomogeneous Electron Gas (Plenum, New York, 1983); E.K.U. Gross and W. Kohn, Adv. Quantum Chem. 21, 255 (1990).
5. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965); O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4724 (1976); S. Lundqvist and N,H. March, Theory of Inhomogeneous Electron Gas (Plenum, New York, 1983); E.K.U. Gross and W. Kohn, Adv. Quantum Chem. 21, 255 (1990).
6. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965); O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4724 (1976); S. Lundqvist and N,H. March, Theory of Inhomogeneous Electron Gas (Plenum, New York, 1983); E.K.U. Gross and W. Kohn, Adv. Quantum Chem. 21, 255 (1990).
7. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965); O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4724 (1976); S. Lundqvist and N,H. March, Theory of Inhomogeneous Electron Gas (Plenum, New York, 1983); E.K.U. Gross and W. Kohn, Adv. Quantum Chem. 21, 255 (1990).
8. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965); O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4724 (1976); S. Lundqvist and N,H. March, Theory of Inhomogeneous Electron Gas (Plenum, New York, 1983); E.K.U. Gross and W. Kohn, Adv. Quantum Chem. 21, 255 (1990).
9. O. Gunnarsson, M. Jonson, and B.I. Lundqvist, Phys. Rev. B 20, 3136 (1979); J.P. Perdew and A. Zunger, ibid. 23, 5048 (1981); E. Chacón and P. Tarazona, ibid. 37, 4013 (1988); J.P. Perdew, K. Burke, and Y. Wang, ibid. 54, 16 533 (1996); J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396 (1997).
10. O. Gunnarsson, M. Jonson, and B.I. Lundqvist, Phys. Rev. B 20, 3136 (1979); J.P. Perdew and A. Zunger, ibid. 23, 5048 (1981); E. Chacón and P. Tarazona, ibid. 37, 4013 (1988); J.P. Perdew, K. Burke, and Y. Wang, ibid. 54, 16 533 (1996); J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396 (1997).
11. O. Gunnarsson, M. Jonson, and B.I. Lundqvist, Phys. Rev. B 20, 3136 (1979); J.P. Perdew and A. Zunger, ibid. 23, 5048 (1981); E. Chacón and P. Tarazona, ibid. 37, 4013 (1988); J.P. Perdew, K. Burke, and Y. Wang, ibid. 54, 16 533 (1996); J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396 (1997).
12. O. Gunnarsson, M. Jonson, and B.I. Lundqvist, Phys. Rev. B 20, 3136 (1979); J.P. Perdew and A. Zunger, ibid. 23, 5048 (1981); E. Chacón and P. Tarazona, ibid. 37, 4013 (1988); J.P. Perdew, K. Burke, and Y. Wang, ibid. 54, 16 533 (1996); J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396 (1997).
13. O. Gunnarsson, M. Jonson, and B.I. Lundqvist, Phys. Rev. B 20, 3136 (1979); J.P. Perdew and A. Zunger, ibid. 23, 5048 (1981); E. Chacón and P. Tarazona, ibid. 37, 4013 (1988); J.P. Perdew, K. Burke, and Y. Wang, ibid. 54, 16 533 (1996); J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396 (1997).
14. O. Gunnarsson, M. Jonson, and B.I. Lundqvist, Phys. Rev. B 20, 3136 (1979); J.P. Perdew and A. Zunger, ibid. 23, 5048 (1981); E. Chacón and P. Tarazona, ibid. 37, 4013 (1988); J.P. Perdew, K. Burke, and Y. Wang, ibid. 54, 16 533 (1996); J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396 (1997).
15. U. von Barth and L. Hedin, J. Phys. C 5, 1629 (1972); M.M. Pant and A.K. Rajagopal, Solid State Commun. 10, 1157 (1972); R.M. Dreizler and E.K.U. Gross, Density Functional Theory, An Approach to the Quantum. Many-Body Problem (Springer, Berlin, 1990).
16. U. von Barth and L. Hedin, J. Phys. C 5, 1629 (1972); M.M. Pant and A.K. Rajagopal, Solid State Commun. 10, 1157 (1972); R.M. Dreizler and E.K.U. Gross, Density Functional Theory, An Approach to the Quantum. Many-Body Problem (Springer, Berlin, 1990).
17. U. von Barth and L. Hedin, J. Phys. C 5, 1629 (1972); M.M. Pant and A.K. Rajagopal, Solid State Commun. 10, 1157 (1972); R.M. Dreizler and E.K.U. Gross, Density Functional Theory, An Approach to the Quantum. Many-Body Problem (Springer, Berlin, 1990).
18. L.J. Lantto and P.J. Siemens, Nucl. Phys. A 317, 55 (1979); L.J. Lantto, Phys. Rev. B 22, 1380 (1980).
19. L.J. Lantto and P.J. Siemens, Nucl. Phys. A 317, 55 (1979); L.J. Lantto, Phys. Rev. B 22, 1380 (1980).
20. K.S. Singwi, M.P. Tosi, R.H. Land, and A. Sjölander, Phys. Rev. 176, 589 (1968); R. Lobo, K.S. Singwi, and M.P. Tosi, ibid. 186, 470 (1969).
21. K.S. Singwi, M.P. Tosi, R.H. Land, and A. Sjölander, Phys. Rev. 176, 589 (1968); R. Lobo, K.S. Singwi, and M.P. Tosi, ibid. 186, 470 (1969).
22. D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566 (1980); B.J. Alder, D.M. Ceperley, and E.L. Pollock, Int. J. Quantum Chem. 16, 49 (1982).
23. D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566 (1980); B.J. Alder, D.M. Ceperley, and E.L. Pollock, Int. J. Quantum Chem. 16, 49 (1982).
24. G. Ortiz and P. Ballone, Phys. Rev. B 50, 1391 (1994); 56, 9970 (1997); G. Ortiz, M. Harris, and P. Ballone, Phys. Rev. Lett. 82, 5317 (1999); P. Gori-Giorgi, F. Sacchetti, and G.B. Bachelet, Phys. Rev. B 61, 7353 (2000).
25. G. Ortiz and P. Ballone, Phys. Rev. B 50, 1391 (1994); 56, 9970 (1997); G. Ortiz, M. Harris, and P. Ballone, Phys. Rev. Lett. 82, 5317 (1999); P. Gori-Giorgi, F. Sacchetti, and G.B. Bachelet, Phys. Rev. B 61, 7353 (2000).
26. G. Ortiz and P. Ballone, Phys. Rev. B 50, 1391 (1994); 56, 9970 (1997); G. Ortiz, M. Harris, and P. Ballone, Phys. Rev. Lett. 82, 5317 (1999); P. Gori-Giorgi, F. Sacchetti, and G.B. Bachelet, Phys. Rev. B 61, 7353 (2000).
27. G. Ortiz and P. Ballone, Phys. Rev. B 50, 1391 (1994); 56, 9970 (1997); G. Ortiz, M. Harris, and P. Ballone, Phys. Rev. Lett. 82, 5317 (1999); P. Gori-Giorgi, F. Sacchetti, and G.B. Bachelet, Phys. Rev. B 61, 7353 (2000).
28. B. Tanatar and D.M. Ceperley, Phys. Rev. B 39, 5005 (1989); S. Moroni, D.M. Ceperley, and G. Senatore, Phys. Rev. Lett. 69, 1837 (1992); F. Rapisarda and G. Senatore, Aust. J. Phys. 49, 161 (1996); D. Varsano, S. Moroni, and G. Senatore, Europhys. Lett. 53, 348 (2001); C. Attaccalite, S. Moroni, P. Gori-Giorgi, and G. Bachelet, Phys. Rev. Lett. 88, 256601 (2002).
29. B. Tanatar and D.M. Ceperley, Phys. Rev. B 39, 5005 (1989); S. Moroni, D.M. Ceperley, and G. Senatore, Phys. Rev. Lett. 69, 1837 (1992); F. Rapisarda and G. Senatore, Aust. J. Phys. 49, 161 (1996); D. Varsano, S. Moroni, and G. Senatore, Europhys. Lett. 53, 348 (2001); C. Attaccalite, S. Moroni, P. Gori-Giorgi, and G. Bachelet, Phys. Rev. Lett. 88, 256601 (2002).
30. B. Tanatar and D.M. Ceperley, Phys. Rev. B 39, 5005 (1989); S. Moroni, D.M. Ceperley, and G. Senatore, Phys. Rev. Lett. 69, 1837 (1992); F. Rapisarda and G. Senatore, Aust. J. Phys. 49, 161 (1996); D. Varsano, S. Moroni, and G. Senatore, Europhys. Lett. 53, 348 (2001); C. Attaccalite, S. Moroni, P. Gori-Giorgi, and G. Bachelet, Phys. Rev. Lett. 88, 256601 (2002).
31. B. Tanatar and D.M. Ceperley, Phys. Rev. B 39, 5005 (1989); S. Moroni, D.M. Ceperley, and G. Senatore, Phys. Rev. Lett. 69, 1837 (1992); F. Rapisarda and G. Senatore, Aust. J. Phys. 49, 161 (1996); D. Varsano, S. Moroni, and G. Senatore, Europhys. Lett. 53, 348 (2001); C. Attaccalite, S. Moroni, P. Gori-Giorgi, and G. Bachelet, Phys. Rev. Lett. 88, 256601 (2002).
32. B. Tanatar and D.M. Ceperley, Phys. Rev. B 39, 5005 (1989); S. Moroni, D.M. Ceperley, and G. Senatore, Phys. Rev. Lett. 69, 1837 (1992); F. Rapisarda and G. Senatore, Aust. J. Phys. 49, 161 (1996); D. Varsano, S. Moroni, and G. Senatore, Europhys. Lett. 53, 348 (2001); C. Attaccalite, S. Moroni, P. Gori-Giorgi, and G. Bachelet, Phys. Rev. Lett. 88, 256601 (2002).
33. A.W. Overhauser, Can. J. Phys. 73, 683 (1995),
34. J.C. Kimball, Phys. Rev. A 7, 1648 (1973).
35. H. Yasuhara, Solid State Commun. 11, 1481 (1972); B.B.J. Hede and J.P. Carbotte, Can. J. Phys. 50, 1756 (1972).
36. H. Yasuhara, Solid State Commun. 11, 1481 (1972); B.B.J. Hede and J.P. Carbotte, Can. J. Phys. 50, 1756 (1972).
37. M. Polini, G. Sica, B. Davoudi, and M.P. Tosi, J. Phys.: Condens. Matter 13, 3591 (2001).
38. P. Gori-Giorgi and J.P. Perdew, Phys. Rev. B 64, 155102 (2001).
39. P. Ziesche, J. Tao, M. Seidl, and J.P. Perdew, Int. J. Quantum Chem. 77, 819 (2000).
40. In our calculations we have found that satisfying Eq. (9) at the level of a percent may require as many as 40 angular momentum states in 3D and even more in 2D.
41. S. Conti, Ph.D. thesis, Scuola Normale Superiore, Pisa, 1997.
42. B.J. Verhaar, J.R.H.W. van den Eijnde, M.A.J. Voermans, and M.M.J. Schaffrath, J. Phys. A 17, 595 (1984).
43. L.P. Kouwenhoven, D.G. Austing, and S. Tarucha, Rep. Prog. Phys. 64, 701 (2001) and references therein; L. Jacak, P. Hawrylak, and A. Wojs, Quantum Dots (Springer, Berlin, 1998).
44. L.P. Kouwenhoven, D.G. Austing, and S. Tarucha, Rep. Prog. Phys. 64, 701 (2001) and references therein; L. Jacak, P. Hawrylak, and A. Wojs, Quantum Dots (Springer, Berlin, 1998).
45. C.A. Ullrich and G. Vignale, Phys. Rev. Lett. 87, 037402 (2001) and references therein.
46. S. Luin, V. Pellegrini, F. Beltram, X. Marcadet, and C. Sirtori, Phys. Rev. B 64, 041306 (2001) and references therein.
47. M. Nekovee, W.M.C. Foulkes, and R.J. Needs, Phys. Rev. Lett. 87, 036401 (2001).