Real-space finite-difference method for conductance calculations

Physical Review B - Condensed Matter and Materials Physics

Volumn 70, Issue 19, 2004, Pages 1-13

  Khomyakov, Petr A ^a   Brocks, Geert ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BOUNDARY LAYER; CHEMICAL STRUCTURE; CONDUCTANCE; ELECTRODE; ELECTRON TRANSPORT; FINITE ELEMENT ANALYSIS; HAMILTON SCALE; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; NEUTRON SCATTERING; QUANTUM MECHANICS;

EID: 12344289075     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.70.195402     Document Type: Article

References (61)

1. N. Agraït, A. Levy Yeyati, and J. M. van Ruitenbeek, Phys. Rep. 377, 81 (2003).
2. M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Phys. Rev. B 31, 6207 (1985).
3. T. N. Todorov, G. A. D. Briggs, and A. P. Sutton, J. Phys.: Condens. Matter 5, 2389 (1993).
4. K. Nicolić and A. MacKinnon, Phys. Rev. B 50, 11 008 (1994).
5. M. P. Samanta, W. Tian, S. Datta, J. I. Henderson, and C. P. Kubiak, Phys. Rev. B 53, R7626 (1996).
6. E. G. Emberly and G. Kirczenow, Phys. Rev. B 58, 10911 (1998).
7. K. Hirose and M. Tsukada, Phys. Rev. Lett. 73, 150 (1994); Phys. Rev. B 51, 5278 (1995).
8. K. Hirose and M. Tsukada, Phys. Rev. Lett. 73, 150 (1994); Phys. Rev. B 51, 5278 (1995).
9. N. D. Lang, Phys. Rev. B 52, 5335 (1995); Phys. Rev. Lett. 79, 1357 (1997).
10. N. D. Lang, Phys. Rev. B 52, 5335 (1995); Phys. Rev. Lett. 79, 1357 (1997).
11. M. Di Ventra, S. T. Pantelides, and N. D. Lang, Phys. Rev. Lett. 84, 979 (2000).
12. H. J. Choi and J. Ihm, Phys. Rev. B 59, 2267 (1999).
13. Y. G. Yoon, M. S. C. Mazzoni, H. J. Choi, J. Ihm, and S. G. Louie, Phys. Rev. Lett. 86, 688 (2001).
14. S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, U.K., 1995).
15. Y. Xue, S. Datta, and M. A. Ratner, J. Chem. Phys. 115, 4292 (2001); P. S. Damle, A. W. Ghosh, and S. Datta, Phys. Rev. B 64, 201403 (2001).
16. Y. Xue, S. Datta, and M. A. Ratner, J. Chem. Phys. 115, 4292 (2001); P. S. Damle, A. W. Ghosh, and S. Datta, Phys. Rev. B 64, 201403 (2001).
17. J. Taylor, H. Guo, and J. Wang, Phys. Rev. B 63, 245407 (2001).
18. M. Buongiorno Nardelli, J.-L. Fattebert, and J. Bernholc, Phys. Rev. B 64, 245423 (2001).
19. J. J. Palacios, A. J. Pérez-Jiménez, E. Louis, E. SanFabián, and J. A. Vergés, Phys. Rev. B 66, 035322 (2002).
20. J. Heurich, J. C. Cuevas, W. Wenzel, and G. Schön, Phys. Rev. Lett. 88, 256803 (2002).
21. M. Brandbyge, J. L. Mozos, P. Ordejón, J. Taylor, and K. Stokbro, Phys. Rev. B 65, 165401 (2002).
22. K. S. Thygesen, M. V. Bollinger, and K. W. Jacobsen, Phys. Rev. B 67, 115404 (2003).
23. D. Wortmann, H. Ishida, and S. Blügel, Phys. Rev. B 66, 075113 (2002).
24. J. P. Vigneron and Ph. Lambin, J. Phys. A 12, 1961 (1979); 13, 1135 (1980).
25. J. P. Vigneron and Ph. Lambin, J. Phys. A 12, 1961 (1979); 13, 1135 (1980).
26. C. Berthod, F. Gagel, and K. Maschke, Phys. Rev. B 50, 18 299 (1994); F. Gagel and K. Maschke, ibid. 52, 2013 (1994).
27. C. Berthod, F. Gagel, and K. Maschke, Phys. Rev. B 50, 18 299 (1994); F. Gagel and K. Maschke, ibid. 52, 2013 (1994).
28. Y. Fujimoto and K. Hirose, Phys. Rev. B 67, 195315 (2003).
29. A. A. Starikov, I. I. Yakimenko, and K.-F. Berggren, Phys. Rev. B 67, 235319 (2003).
30. J. R. Chelikowsky, N. Troullier, and Y. Saad, Phys. Rev. Lett. 72, 1240 (1994).
31. J. R. Chelikowsky, N. Troullier, K. Wu, and Y. Saad, Phys. Rev. B 50, 11355 (1994).
32. F. Gygi and G. Galli, Phys. Rev. B 52, R2229 (1995).
33. T. Ando, Phys. Rev. B 44, 8017 (1991).
34. If one uses Green functions, one has to distinguish between retarded and advanced Green functions. This can be done by subtracting or adding a (small) imaginary number to the energy.
35. K. Xia, P. J. Kelly, G. E. W. Bauer, and I. Turek, Phys. Rev. Lett. 89, 166603 (2002).
36. M. Zwierzycki, K. Xia, P. J. Kelly, G. E. W. Bauer, and I. Turek, Phys. Rev. B 67, 092401 (2003).
37. L. Molinari, J. Phys. A 30, 983 (1997).
38. H.-O. Kreiss, Math. Comput. 26, 605 (1972).
39. H. Brandén, Technical Report No. 2000-026, Department of Information Technology, Uppsala University, Uppsala, Sweden, 2000 (unpublished).
40. The size of the scattering region does not have to be an integer multiple of the size of the cell in the leads. One can choose cells of a different size in the scattering region. One also chooses differently sized cells in the left and right leads in case the leads are different. We have not introduced cells of different size here in order not to complicate the notation, but the strategy for solving the scattering problem as outlined in Appendix A 4 also works in that case.
41. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965).
42. L. D. Landau and E. M. Lifschitz, Quantum Mechanics: Non-relativistic Theory (Pergamon Press, Oxford, 1981), Sec. 25.
43. S. Wolfram, Computer code MATHEMATICA, http:// documents.wolfram.com
44. C. S. Barrett, Acta Crystallogr. 9, 671 (1956).
45. A. A. Quong, A. A. Maradudin, R. F. Wallis, J. A. Caspar, A. G. Aguiluz, and G. P. Alldredge, Phys. Rev. Lett. 66, 743 (1991).
46. N. Kobayashi, M. Brandbyge, and M. Tsukada, Phys. Rev. B 62, 8430 (2000).
47. J. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
48. 0, is used as the local potential. Tests using a nonlocal pseudopotential with s and p parts gave a virtually identical electronic structure for bulk sodium, indicating that the use of a local potential is a good approximation for sodium.
49. J. Neugebauer and M. Scheffler, Phys. Rev. B 46, 16 067 (1992).
50. N. J. Fall, N. Binggeli, and A. Baldereschi, J. Phys.: Condens. Matter 11, 2689 (1999).
51. z=3456.
52. -3 from the highly accurate results.
53. A. Levy Yeyati, A. Martín-Rodero, and F. Flores, Phys. Rev. B 56, 10 369 (1997).
54. H.-S. Sim, H.-W. Lee, and K. J. Chang, Phys. Rev. Lett. 87, 096803 (2001).
55. P. Havu, T. Torsti, M. J. Puska, and R. M. Nieminen, Phys. Rev. B 66, 075401 (2002).
56. S. Tsukamoto and K. Hirose, Phys. Rev. B 66, 161402 (2002).
57. Y. J. Lee, M. Brandbyge, M. J. Puska, J. Taylor, K. Stockbro, and R. M. Nieminen, Phys. Rev. B 69, 125409 (2004).
58. K. S. Thygesen and K. W. Jacobsen, Phys. Rev. Lett. 91, 146801 (2003).
59. -5 hartrees yields a potential that can change the conductance by up to 5% and can even suppress the even-odd oscillation almost completely.
60. G. Golub and C. F. van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, 1996).
61. 3S.