Spin-orbit coupling effects in two-dimensional circular quantum rings: Elliptical deformation of confined electron density

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 19, 2009, Pages

  Nowak, M P ^a   Szafran, B ^a  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954702272     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.195319     Document Type: Article

References (57)

1. S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990). 10.1063/1.102730
2. J. Schliemann, J. C. Egues, and D. Loss, Phys. Rev. Lett. 90, 146801 (2003). 10.1103/PhysRevLett.90.146801
3. K. C. Nowack, F. H. L. Koppens, Yu. V. Nazarov, and L. M. K. Vandersypen, Science 318, 1430 (2007). 10.1126/science.1148092
4. S. Bednarek and B. Szafran, Phys. Rev. Lett. 101, 216805 (2008). 10.1103/PhysRevLett.101.216805
5. P. Földi, B. Molnar, M. G. Benedict, and F. M. Peeters, Phys. Rev. B 71, 033309 (2005) 10.1103/PhysRevB.71.033309
6. P. Földi, O. Kalman, M. G. Benedict, and F. M. Peeters, Nano Lett. 8, 2556 (2008). 10.1021/nl801858a
7. S. Bellucci and P. Onorato, Phys. Rev. B 77, 165305 (2008). 10.1103/PhysRevB.77.165305
8. E. Tsitsishvili, G. S. Lozano, and A. O. Gogolin, Phys. Rev. B 70, 115316 (2004). 10.1103/PhysRevB.70.115316
9. P. Pietiläinen and T. Chakraborty, Phys. Rev. B 73, 155315 (2006). 10.1103/PhysRevB.73.155315
10. M. S. Kushwaha, J. Appl. Phys. 104, 083714 (2008). 10.1063/1.3003086
11. W. H. Kuan, C. S. Tang, and W. Xu, J. Appl. Phys. 95, 6368 (2004). 10.1063/1.1710726
12. T. Chakraborty and P. Pietiläinen, Phys. Rev. Lett. 95, 136603 (2005). 10.1103/PhysRevLett.95.136603
13. M. Valin-Rodriguez, A. Puente, and L. Serra, Phys. Rev. B 69, 153308 (2004). 10.1103/PhysRevB.69.153308
14. P. Lucignano, B. Jouault, A. Tagliacozzo, and B. L. Altshuler, Phys. Rev. B 71, 121310 (R) (2005). 10.1103/PhysRevB.71.121310
15. C. F. Destefani, S. E. Ulloa, and G. E. Marques, Phys. Rev. B 70, 205315 (2004). 10.1103/PhysRevB.70.205315
16. D. V. Bulaev and D. Loss, Phys. Rev. B 71, 205324 (2005) 10.1103/PhysRevB.71.205324
17. M. Florescu and P. Hawrylak, Phys. Rev. B 73, 045304 (2006) 10.1103/PhysRevB.73.045304
18. J. I. Climente, A. Bertoni, G. Goldoni, M. Rontani, and E. Molinari, Phys. Rev. B 76, 085305 (R) (2007) 10.1103/PhysRevB.76.085305
19. M. Prada, R. H. Blick, and R. Joynt, Phys. Rev. B 77, 115438 (2008). 10.1103/PhysRevB.77.115438
20. T. Bergsten, T. Kobayashi, Y. Sekine, and J. Nitta, Phys. Rev. Lett. 97, 196803 (2006). 10.1103/PhysRevLett.97.196803
21. M. F. Borunda, X. Liu, A. A. Kovalev, X. J. Liu, T. Jungwirth, and J. Sinova, Phys. Rev. B 78, 245315 (2008). 10.1103/PhysRevB.78.245315
22. D. Frustaglia and K. Richter, Phys. Rev. B 69, 235310 (2004). 10.1103/PhysRevB.69.235310
23. O. Kalman, P. Földi, M. G. Benedict, and F. M. Peeters, Phys. Rev. B 78, 125306 (2008). 10.1103/PhysRevB.78.125306
24. R. Citro and F. Romeo, Phys. Rev. B 75, 073306 (2007). 10.1103/PhysRevB.75.073306
25. U. Aeberhard, K. Wakabayashi, and M. Sigrist, Phys. Rev. B 72, 075328 (2005). 10.1103/PhysRevB.72.075328
26. K. Niemelä, P. Pietiläinen, P. Hyvönen, and T. Chakraborty, Europhys. Lett. 36, 533 (1996). 10.1209/epl/i1996-00265-7
27. J. I. Climente, J. Planelles, and W. Jaskólski, Phys. Rev. B 68, 075307 (2003). 10.1103/PhysRevB.68.075307
28. A. Puente, L. Serra, and R. G. Nazmitdinov, Phys. Rev. B 69, 125315 (2004). 10.1103/PhysRevB.69.125315
29. S. Viefers, P. Koskinen, P. Singa Deo, and M. Manninen, Physica E (Amsterdam) 21, 1 (2004).
30. T. Chakraborty and P. Pietiläinen, Phys. Rev. B 50, 8460 (1994). 10.1103/PhysRevB.50.8460
31. A. O. Govorov, S. E. Ulloa, K. Karrai, and R. J. Warburton, Phys. Rev. B 66, 081309 (R) (2002). 10.1103/PhysRevB.66.081309
32. J. I. Climente, J. Planelles, and J. L. Movilla, Phys. Rev. B 70, 081301 (R) (2004). 10.1103/PhysRevB.70.081301
33. Y. V. Pershin and C. Piermarocchi, Phys. Rev. B 72, 125348 (2005). 10.1103/PhysRevB.72.125348
34. V. M. Fomin, V. N. Gladilin, S. N. Klimin, J. T. Devreese, N. A. J. M. Kleemans, and P. M. Koenraad, Phys. Rev. B 76, 235320 (2007). 10.1103/PhysRevB.76.235320
35. V. M. Fomin, V. N. Gladilin, J. T. Devreese, N. A. J. M. Kleemans, and P. M. Koenraad, Phys. Rev. B 77, 205326 (2008). 10.1103/PhysRevB.77.205326
36. N. A. J. M. Kleemans, I. M. A. Bominaar-Silkens, V. M. Fomin, V. N. Gladilin, D. Granados, A. G. Taboada, J. M. Garcia, P. Offermans, U. Zeitler, P. C. M. Christianen, J. C. Maan, J. T. Devreese, and P. M. Koenraad, Phys. Rev. Lett. 99, 146808 (2007). 10.1103/PhysRevLett.99.146808
37. J. Splettstoesser, M. Governale, and U. Zülicke, Phys. Rev. B 68, 165341 (2003). 10.1103/PhysRevB.68.165341
38. J. S. Sheng and K. Chang, Phys. Rev. B 74, 235315 (2006). 10.1103/PhysRevB.74.235315
39. G. H. Ding and B. Dong, Phys. Rev. B 76, 125301 (2007). 10.1103/PhysRevB.76.125301
40. Q. F. Sun, X. C. Xie, and J. Wang, Phys. Rev. Lett. 98, 196801 (2007). 10.1103/PhysRevLett.98.196801
41. G. Y. Huang and S. D. Liang, EPL 86, 67009 (2009). 10.1209/0295-5075/86/ 67009
42. A. G. Aronov and Y. B. Lyanda-Geller, Phys. Rev. Lett. 70, 343 (1993). 10.1103/PhysRevLett.70.343
43. F. E. Meijer, A. F. Morpurgo, and T. M. Klapwijk, Phys. Rev. B 66, 033107 (2002). 10.1103/PhysRevB.66.033107
44. S.-R. Eric Yang, Phys. Rev. B 74, 075315 (2006). 10.1103/PhysRevB.74. 075315
45. J. D. Koralek, C. Weber, J. Orenstein, A. Bernevig, S. Zhang, S. Mack, and D. Awschalom, Nature (London) 458, 610 (2009). 10.1038/nature07871
46. B. A. Bernevig, J. Orenstein, and S. C. Zhang, Phys. Rev. Lett. 97, 236601 (2006). 10.1103/PhysRevLett.97.236601
47. A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M. Garcia, and P. M. Petroff, Phys. Rev. Lett. 84, 2223 (2000). 10.1103/PhysRevLett.84.2223
48. W. Knap, C. Skierbiszewski, A. Zduniak, E. Litwin-Staszewska, D. Bertho, F. Kobbi, J. L. Robert, G. E. Pikus, F. G. Pikus, S. V. Iordanskii, V. Mosser, K. Zekentes, and Yu. B. Lyanda-Geller, Phys. Rev. B 53, 3912 (1996). 10.1103/PhysRevB.53.3912
49. S. Saikin, M. Shen, M. C. Cheng, and V. Privman, J. Appl. Phys. 94, 1769 (2003). 10.1063/1.1589581
50. M. J. Snelling, E. Blackwood, C. J. McDonagh, R. T. Harley, and C. T. B. Foxon, Phys. Rev. B 45, 3922 (1992). 10.1103/PhysRevB.45.3922
51. M. Bayer, M. Korkusinski, P. Hawrylak, T. Gutbrod, M. Michel, and A. Forchel, Phys. Rev. Lett. 90, 186801 (2003). 10.1103/PhysRevLett.90.186801
52. T. Chwiej and B. Szafran, Phys. Rev. B 78, 245306 (2008). 10.1103/PhysRevB.78.245306
53. For α = β and g = 0 each energy level is twofold degenerate with respect to the s parity. The degenerate states corresponding to even and odd s parities have the same charge densities, and the spin-up and spin-down densities are exchanged.
54. The eigenstates of σ x - σ y can be constructed from the odd and the even s-parity eigenstates which in the case of α = β and g = 0 correspond to degenerate energy levels. The eigenstates of σ x - σ y are no longer s -parity eigenstates.
55. B. Szafran, M. P. Nowak, S. Bednarek, T. Chwiej, and F. M. Peeters, Phys. Rev. B 79, 235303 (2009). 10.1103/PhysRevB.79.235303
56. T. Chwiej and B. Szafran, Phys. Rev. B 79, 085305 (2009). 10.1103/PhysRevB.79.085305
57. Figure presents the case of pure Rashba coupling and g = 0. For the pure Dresselhaus coupling the energy spectrum is identical, the average z component of the spin and the s parity are inverted.