Size effects in the exchange coupling between two electrons confined in quantum wire quantum dots

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 3, 2008, Pages

  Zhang, L X ^a   Melnikov, D V ^a   Agarwal, S ^a   Leburton, J P ^a  

^a United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47349086763     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.035418     Document Type: Article

References (33)

1. C. Fasth, A. Fuhrer, M. T. Björk, and L. Samuelson, Nano Lett. NALEFD 1530-6984 10.1021/nl050850i 5, 1487 (2005)
2. A. Fuhrer, C. Fasth, and L. Samuelson, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2767197 91, 052109 (2007).
3. For coupled quantum dots formed in Si/Ge core/shell nanowires, see, e.g., Y. Hu, H. O. H. Churchill, D. J. Reilly, J. Xiang, C. M. Lieber, and C. M. Marcus, Nat. Nanotechnol. NNAABX 1748-3387 10.1038/nnano.2007.302 2, 622 (2007).
4. M. T. Björk, A. Fuhrer, A. E. Hansen, M. W. Larsson, L. E. Fröberg, and L. Samuelson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.201307 72, 201307 (R) (2005).
5. C. Fasth, A. Fuhrer, L. Samuelson, V. N. Golovach, and D. Loss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.266801 98, 266801 (2007).
6. J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Science SCIEAS 0036-8075 10.1126/science.1116955 309, 2180 (2005).
7. J. M. Elzerman, R. Hanson, J. S. Greidanus, L. H. Willems van Beveren, S. De Franceschi, L. M. K. Vandersypen, S. Tarucha, and L. P. Kouwenhoven, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.161308 67, 161308 (R) (2003).
8. T. Hatano, M. Stopa, and S. Tarucha, Science SCIEAS 0036-8075 10.1126/science.1111205 309, 268 (2005).
9. M. Pi, A. Emperador, M. Barranco, F. Garcias, K. Muraki, S. Tarucha, and D. G. Austing, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.066801 87, 066801 (2001).
10. D. Bellucci, M. Rontani, F. Troiani, G. Goldoni, and E. Molinari, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.201308 69, 201308 (R) (2004).
11. G. Burkard, D. Loss, and D. P. DiVincenzo, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.2070 59, 2070 (1999).
12. X. Hu and S. Das Sarma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.062301 61, 062301 (2000).
13. D. V. Melnikov, J. P. Leburton, A. Taha, and N. Sobh, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.041309 74, 041309 (R) (2006).
14. A. Harju, S. Siljamäki, and R. M. Nieminen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.226804 88, 226804 (2002).
15. B. Szafran, F. M. Peeters, and S. Bednarek, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.205318 70, 205318 (2004).
16. W. Dybalski and P. Hawrylak, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.205432 72, 205432 (2005).
17. L.-X. Zhang, P. Matagne, J.-P. Leburton, R. Hanson, and L. P. Kouwenhoven, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.245301 69, 245301 (2004).
18. L.-X. Zhang, D. V. Melnikov, and J.-P. Leburton, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.205306 74, 205306 (2006).
19. M. Stopa and C. M. Marcus, Nano Lett. NALEFD 1530-6984 8, 1778 (2008).
20. M. J. Calderón, B. Koiller, and S. Das Sarma, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.045310 74, 045310 (2006).
21. J. Pedersen, C. Flindt, N. A. Mortensen, and A.-P. Jauho, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.125323 76, 125323 (2007).
22. G. Burkard, G. Seelig, and D. Loss, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.2581 62, 2581 (2000).
23. B. Koiller, R. B. Capaz, X. Hu, and S. Das Sarma, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.115207 70, 115207 (2004).
24. A. E. Hansen, M. T. Björk, I. C. Fasth, C. Thelander, and L. Samuelson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.205328 71, 205328 (2005).
25. An initial guess for the variational parameters is given near their nominal values and then we use the fminsearch subroutine in MATLAB, which employs the Nelder-Mead simplex method to search for the minima of the system energies with respect to these parameters. It turns out that unless the overlap between the localized s states is too large; the simplex method always finds a global minimum within the physically reasonable range of the variational parameters.
26. R. de Sousa, X. Hu, and S. Das Sarma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.042307 64, 042307 (2001).
27. We take g=8 measured in QDs with similar geometry (Ref.), although the linear dependence of J on magnetic field is clear even for g=2.
28. Recently, the VHL method has been applied to calculate the two-electron energies in a single two-dimensional elliptical QD. By comparing the results to numerical exact diagonalization results, it is shown that the VHL method is successful in reproducing the magnetic field dependence of J (Ref.).
29. I. A. Merkulov, Al. L. Efros, and M. Rosen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.205309 65, 205309 (2002)
30. P.-F. Braun, X. Marie, L. Lombez, B. Urbaszek, T. Amand, P. Renucci, V. K. Kalevich, K. V. Kavokin, O. Krebs, P. Voisin, and Y. Masumoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.116601 94, 116601 (2005).
31. C. Flindt, A. S. Sorensen, and K. Flensberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.240501 97, 240501 (2006).
32. K. V. Kavokin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.075305 64, 075305 (2001).
33. S. Agarwal, D. V. Melnikov, L.-X. Zhang, and J. P. Leburton (unpublished).