Topological stability of the half-vortices in spinor exciton-polariton condensates

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 4, 2010, Pages

  Flayac, H ^a,b   Shelykh, I A ^c,d   Solnyshkov, D D ^a,b   Malpuech, G ^a,b  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b UNIVERSITÉ BLAISE PASCAL   (France)

^c UNIVERSITY OF ICELAND   (Iceland)

^d ST PETERSBURG ACADEMIC UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954821601     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.045318     Document Type: Article

References (50)

1. For review on the subject see, e.g., F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999) 10.1103/RevModPhys.71.463
2. A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001) 10.1103/RevModPhys.73.307
3. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, New York, 2003).
4. Yu. S. Kivshar and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, New York, 2003).
5. P. G. Savvidis, J. J. Baumberg, R. M. Stevenson, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, Phys. Rev. Lett. 84, 1547 (2000). 10.1103/PhysRevLett.84.1547
6. A. Imamoglu and J. R. Ram, Phys. Lett. A 214, 193 (1996). 10.1016/0375-9601(96)00175-2
7. G. Malpuech, A. Di Carlo, A. Kavokin, J. J. Baumberg, M. Zamfirescu, and P. Lugli, Appl. Phys. Lett. 81, 412 (2002). 10.1063/1.1494126
8. M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, Phys. Rev. B 65, 161205 (R) (2002). 10.1103/PhysRevB.65.161205
9. M. Richard, J. Kasprzak, R. Andre, R. Romestain, L. S. Dang, G. Malpuech, and A. Kavokin, Phys. Rev. B 72, 201301 (R) (2005). 10.1103/PhysRevB.72.201301
10. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymanska, R. Andre, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, Nature (London) 443, 409 (2006). 10.1038/nature05131
11. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, Science 316, 1007 (2007). 10.1126/science.1140990
12. S. Utsunomiya, L. Tian, G. Roumpos, C. W. Lai, N. Kumada, T. Fujisawa, M. Kuwata-Gonokami, A. Loffler, S. Hofling, A. Forchel, and Y. Yamamoto, Nat. Phys. 4, 700 (2008). 10.1038/nphys1034
13. J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butte, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Hoger von Hogersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, Phys. Rev. Lett. 101, 136409 (2008). 10.1103/PhysRevLett.101.136409
14. G. Christmann, R. Butte, E. Feltin, J. F. Carlin, and N. Grandjean, Appl. Phys. Lett. 93, 051102 (2008). 10.1063/1.2966369
15. J. Kasprzak, D. D. Solnyshkov, R. Andre, Le Si Dang, and G. Malpuech, Phys. Rev. Lett. 101, 146404 (2008). 10.1103/PhysRevLett.101.146404
16. E. Wertz, L. Ferrier, Dmitry D. Solnyshkov, P. Senellart, D. Bajoni, A. Miard, A. Lemaitre, G. Malpuech, and J. Bloch, Appl. Phys. Lett. 95, 051108 (2009). 10.1063/1.3192408
17. G. Malpuech, Y. G. Rubo, F. P. Laussy, P. Bigenwald, and A. Kavokin, Semicond. Sci. Technol. 18, S395, (2003), special issue on microcavities, edited by, J. J. Baumberg, and, L. Vina,. 10.1088/0268-1242/18/10/314
18. G. Malpuech, D. D. Solnyshkov, H. Ouerdane, M. M. Glazov, and I. Shelykh, Phys. Rev. Lett. 98, 206402 (2007). 10.1103/PhysRevLett.98.206402
19. D. Sanvitto, A. Amo, L. Vina, R. Andre, D. Solnyshkov, and G. Malpuech, Phys. Rev. B 80, 045301 (2009). 10.1103/PhysRevB.80.045301
20. C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007). 10.1038/nature06334
21. M. H. Szymańska, J. Keeling, and P. B. Littlewood, Phys. Rev. Lett. 96, 230602 (2006). 10.1103/PhysRevLett.96.230602
22. M. Wouters and I. Carusotto, Phys. Rev. Lett. 99, 140402 (2007). 10.1103/PhysRevLett.99.140402
23. I. Carusotto and C. Ciuti, Phys. Rev. Lett. 93, 166401 (2004). 10.1103/PhysRevLett.93.166401
24. D. D. Solnyshkov, I. A. Shelykh, N. A. Gippius, A. V. Kavokin, and G. Malpuech, Phys. Rev. B 77, 045314 (2008). 10.1103/PhysRevB.77.045314
25. A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, Nature (London) 457, 291 (2009). 10.1038/nature07640
26. K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. Andre, Le Si Dang, and B. Deveaud-Pledran, Nat. Phys. 4, 706 (2008). 10.1038/nphys1051
27. J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401 (2008). 10.1103/PhysRevLett.100.250401
28. Yu. G. Rubo, Phys. Rev. Lett. 99, 106401 (2007). 10.1103/PhysRevLett.99. 106401
29. G. Panzarini, L. C. Andreani, A. Armitage, D. Baxter, M. S. Skolnick, V. N. Astratov, J. S. Roberts, Alexey V. Kavokin, Maria R. Vladimirova, and M. A. Kaliteevski, Phys. Rev. B 59, 5082 (1999). 10.1103/PhysRevB.59.5082
30. See, however, the work where it was argued that dark states can sometimes play substantial role, I. A. Shelykh, L. Vina, A. V. Kavokin, N. G. Galkin, G. Malpuech, and R. Andre, Solid State Commun. 135, 1 (2005). 10.1016/j.ssc.2005. 04.012
31. K. V. Kavokin, I. A. Shelykh, A. V. Kavokin, G. Malpuech, and P. Bigenwald, Phys. Rev. Lett. 92, 017401 (2004). 10.1103/PhysRevLett.92.017401
32. M. D. Martín, G. Aichmayr, L. Viña, and R. André, Phys. Rev. Lett. 89, 077402 (2002) 10.1103/PhysRevLett.89.077402;
33. for a recent review on the subject see I. A. Shelykh, A. V. Kavokin, Yuri G. Rubo, T. C. H. Liew, and G. Malpuech, Semicond. Sci. Technol. 25, 013001 (2010). 10.1088/0268-1242/25/1/013001
34. M. Z. Maialle, E. A. de Andrada e Silva, and L. J. Sham, Phys. Rev. B 47, 15776 (1993). 10.1103/PhysRevB.47.15776
35. C. Leyder, M. Romanelli, J.-Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007). 10.1038/nphys676
36. W. Langbein, I. A. Shelykh, D. Solnyshkov, G. Malpuech, Yu. Rubo, and A. Kavokin, Phys. Rev. B 75, 075323 (2007). 10.1103/PhysRevB.75.075323
37. T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 75, 241301 (R) (2007). 10.1103/PhysRevB.75.241301
38. M. Combescot and O. Betbeder-Matibet, Phys. Rev. B 74, 125316 (2006). 10.1103/PhysRevB.74.125316
39. D. N. Krizhanovskii, D. Sanvitto, I. A. Shelykh, M. M. Glazov, G. Malpuech, D. D. Solnyshkov, A. Kavokin, S. Ceccarelli, M. S. Skolnick, and J. S. Roberts, Phys. Rev. B 73, 073303 (2006). 10.1103/PhysRevB.73.073303
40. F. P. Laussy, I. A. Shelykh, G. Malpuech, and A. Kavokin, Phys. Rev. B 73, 035315 (2006). 10.1103/PhysRevB.73.035315
41. J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973). 10.1088/0022-3719/6/7/010
42. Half-quantum vortices were first discussed for superfluid helium 3 in: G. E. Volovik and V. P. Mineev, JETP Lett. 24, 561 (1976)
43. and were observed first in cuprate superconductors: J. R. Kirtley, C. C. Tsuei, M. Rupp, J. Z. Sun, Lock See Yu-Jahnes, A. Gupta, M. B. Ketchen, K. A. Moler, and M. Bhushan, Phys. Rev. Lett. 76, 1336 (1996) at the intersection of three grain boundaries 10.1103/PhysRevLett.76.1336
44. for a complete review on the subject see G. E. Volovik, The Universe in a Helium Droplet (Clarendon Press, Oxford, 2003).
45. K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, Science 326, 974 (2009). 10.1126/science.1177980
46. In realistic situations usually α 1 is about 10-20 times bigger then α 2, see P. Renucci, T. Amand, X. Marie, P. Senellart, J. Bloch, B. Sermage, and K. V. Kavokin, Phys. Rev. B 72, 075317 (2005). 10.1103/PhysRevB.72. 075317
47. G. E. Pikus and G. L. Bir, Zh. Eksp. Teor. Fiz. 60, 195 (1971)
48. G. E. Pikus and G. L. Bir, [Sov. Phys. JETP 33, 108 (1971)].
49. I. A. Shelykh, Yu. G. Rubo, G. Malpuech, D. D. Solnyshkov, and A. V. Kavokin, Phys. Rev. Lett. 97, 066402 (2006). 10.1103/PhysRevLett.97.066402
50. We supposed that m t > m l and thus χ < 0. In the case of the vortex in which the pseudospin is oriented antiparallel to effective magnetic field, one should replace m t by m l.