Advertisement

Journal of Experimental and Theoretical Physics

, Volume 106, Issue 2, pp 296–315 | Cite as

Bose condensation of two-dimensional dipolar excitons: Simulation by the quantum Monte Carlo method

  • Yu. E. Lozovik
  • I. L. Kurbakov
  • G. E. Astrakharchik
  • M. Willander
Order, Disorder, and Phase Transition in Condensed Systems

Abstract

The Bose condensation of two-dimensional dipolar excitons in quantum wells is numerically studied by the diffusion Monte Carlo simulation method. The correlation, microscopic, thermodynamic, and spectral characteristics are calculated. It is shown that, in structures of coupled quantum wells, in which low-temperature features of exciton luminescence have presently been observed, dipolar excitons form a strongly correlated system.

PACS numbers

71.35.Lk 03.75.Hh 02.70.Ss 73.21.Fg 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. E. Lozovik and V. I. Yudson, Pis’ma Zh. Éksp. Teor. Fiz. 22, 556 (1975) [JETP Lett. 22, 274 (1975)]; Zh. Éksp. Teor. Fiz. 71, 738 (1976) [Sov. Phys. JETP 44, 389 (1976)]; Solid State Commun. 19, 391 (1976); Solid State Commun. 21, 211 (1977); Yu. E. Lozovik and V. N. Nishanov, Fiz. Tverd. Tela (Leningrad) 18, 3267 (1976) [Sov. Phys. Solid State 18, 1905 (1976)]; Yu. E. Lozovik and A. M. Ruvinskiĭ, Zh. Éksp. Teor. Fiz. 112, 1791 (1997) [JETP 85, 979 (1997)]; Yu. E. Lozovik, in Proceedings of Conference on Dielectric Electronics (FAN, Tashkent, 1973), p. 63.Google Scholar
  2. 2.
    A. Filinov, P. Ludwig, Yu. E. Lozovik, et al., J. Phys: Conf. Ser. 35, 197 (2006).CrossRefADSGoogle Scholar
  3. 3.
    S. A. Moskalenko and D. W. Snoke, Bose-Einstein Condensation of Excitons and Biexcitons and Coherent Nonlinear Optics with Excitons (Cambridge Univ. Press, Cambridge, 2000).CrossRefGoogle Scholar
  4. 4.
    D. Snoke, Science 298, 1368 (2002); R. Rapaport and G. Chen, J. Phys.: Condens. Matter 19, 295207 (2007); Z. Vörös, V. Hartwell, D. W. Snoke et al., J. Phys.: Condens. Matter 19, 295216 (2007).CrossRefADSGoogle Scholar
  5. 5.
    V. B. Timofeev, Usp. Fiz. Nauk 175, 315 (2005) [Phys. Usp. 48, 295 (2005)].Google Scholar
  6. 6.
    L. V. Butov, Solid State Commun. 127, 89 (2003); J. Phys.: Condens. Matter 16, R1577 (2004); 19, 2952002 (2007).CrossRefADSGoogle Scholar
  7. 7.
    A. V. Gorbunov, V. E. Bisti, and V. B. Timofeev, Zh. Éksp. Teor. Fiz. 128, 803 (2005) [JETP 101, 693 (2005)]; A. V. Larionov, V. B. Timofeev, J. M. Hvam, and C. Soerensen, Zh. Éksp. Teor. Fiz. 117, 1255 (2000) [JETP 90, 1093 (2000)]; Pis’ma Zh. Éksp. Teor. Fiz. 71, 174 (2000) [JETP Lett. 71, 117 (2000)]; Pis’ma Zh. Éksp. Teor. Fiz. 75, 233 (2002) [JETP Lett. 75, 200 (2002)]; A. V. Larionov and V. B. Timofeev, Pis’ma Zh. Éksp. Teor. Fiz. 73, 342 (2001) [JETP Lett. 73, 301 (2001)]; A. V. Larionov, V. B. Timofeev, P. A. Ni, et al., Pis’ma Zh. Éksp. Teor. Fiz. 75, 689 (2002) [JETP Lett. 75, 570 (2002)]; A. A. Dremin, V. B. Timofeev, A. V. Larionov, et al., Pis’ma Zh. Éksp. Teor. Fiz. 76, 526 (2002) [JETP Lett. 76, 450 (2002)]; A. V. Gorbunov and V. B. Timofeev, Pis’ma Zh. Éksp. Teor. Fiz. 83, 178 (2006) [JETP Lett. 83, 146 (2006)]; A. A. Dremin, A. V. Larionov, and V. B. Timofeev, Fiz. Tverd. Tela (St. Petersburg) 46, 168 (2004) [Phys. Solid State 46, 170 (2004)].Google Scholar
  8. 8.
    L. V. Butov and A. I. Filin, Phys. Rev. B 58, 1980 (1998); L. V. Butov, C. W. Lai, A. L. Ivanov, et al., Nature 417, 47 (2002); C. W. Lai, J. Zoch, A. C. Gossard, and D. S. Chemla, Science 303, 503 (2004); L. V. Butov, A. L. Ivanov, A. Imamoglu, et al., Phys. Rev. Lett. 86, 5608 (2001); L. V. Butov, L. S. Levitov, A. V. Mintsev, et al., Phys. Rev. Lett. 92, 117404 (2004); A. T. Hammack, M. Griswold, L. V. Butov, et al., Phys. Rev. Lett. 96, 227402 (2006); S. Yang, A. T. Hammack, M. M. Fogler, et al., Phys. Rev. Lett. 97, 187402 (2006); see also [48].CrossRefADSGoogle Scholar
  9. 9.
    V. V. Krivolapchuk, E. S. Moskalenko, and A. L. Zhmodikov, Phys. Rev. B 64, 045313 (2001); V. V. Krivolapchuk, E. S. Moskalenko, A. L. Zhmodikov, et al., Solid State Commun. 111, 49 (1999).Google Scholar
  10. 10.
    D. Snoke, S. Denev, Y. Liu, et al., Nature 418, 754 (2002); R. Rapaport, G. Chen, D. Snoke, et al., Phys. Rev. Lett. 92, 117405 (2004).CrossRefADSGoogle Scholar
  11. 11.
    D. W. Snoke, Y. Liu, Z. Vörös, et al., Solid State Commun. 134, 37 (2005).CrossRefADSGoogle Scholar
  12. 12.
    Z. Vörös, D. W. Snoke, L. Pfeiffer, and K. West, Phys. Rev. Lett. 97, 016803 (2006).Google Scholar
  13. 13.
    Z. Vörös, R. Balili, D. W. Snoke, et al., Phys. Rev. Lett. 94, 226401 (2005); G. Chen, R. Rapaport, L. N. Pfeiffer, et al., Phys. Rev. B 74, 045309 (2006).Google Scholar
  14. 14.
    A. V. Gorbunov and V. B. Timofeev, Pis’ma Zh. Éksp. Teor. Fiz. 84, 390 (2006) [JETP Lett. 84, 329 (2006)]; V. B. Timofeev and A. V. Gorbunov, J. Appl. Phys. 101, 081708 (2007).Google Scholar
  15. 15.
    D. S. Petrov, M. Holzmann, and J. V. Shlyapnikov, Phys. Rev. Lett. 84, 2551 (2000).CrossRefADSGoogle Scholar
  16. 16.
    Yu. E. Lozovik and O. L. Berman, Zh. Éksp. Teor. Fiz. 111, 1879 (1997) [JETP 84, 1027 (1997)]; Yu. E. Lozovik and O. L. Berman, Phys. Scr. 55, 491 (1997); Yu. E. Lozovik, O. L. Berman, and M. Willander, J. Phys.: Condens. Matter 14, 12457 (2002).Google Scholar
  17. 17.
    L. V. Keldysh and Yu. V. Kopaev, Fiz. Tverd. Tela (Leningrad) 6, 2791 (1965) [Sov. Phys. Solid State 6, 2219 (1964)]; A. N. Kozlov and L. A. Maksimov, Zh. Éksp. Teor. Fiz. 48, 1184 (1965) [Sov. Phys. JETP 21, 790 (1965)]; L. V. Keldysh and A. N. Kozlov, Zh. Éksp. Teor. Fiz. 54, 978 (1968) [Sov. Phys. JETP 27, 521 (1968)].Google Scholar
  18. 18.
    P. C. Hohenberg, Phys. Rev. 158, 383 (1967); N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).CrossRefADSGoogle Scholar
  19. 19.
    J. W. Kane and L. P. Kadanoff, Phys. Rev. 155, 80 (1967); F. Weling, A. Griffin, and M. Carrington, Phys. Rev. B 28, 5296 (1983).CrossRefADSGoogle Scholar
  20. 20.
    V. L. Berezinskiĭ, Zh. Éksp. Teor. Fiz. 59, 907 (1970) [Sov. Phys. JETP 32, 493 (1970)]; Zh. Éksp. Teor. Fiz. 61, 1144 (1971) [Sov. Phys. JETP 34, 610 (1972)].Google Scholar
  21. 21.
    J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973).CrossRefADSGoogle Scholar
  22. 22.
    J. M. Kosterlitz, J. Phys. C 7, 1046 (1974).CrossRefADSGoogle Scholar
  23. 23.
    D. R. Nelson and J. M. Kosterlitz, Phys. Rev. Lett. 39, 1201 (1977).CrossRefADSGoogle Scholar
  24. 24.
    V. Bagnato and D. Kleppner, Phys. Rev. A 44, 7439 (1991); W. Ketterle and N. J. van Druten, Phys. Rev. A 54, 656 (1996).CrossRefADSGoogle Scholar
  25. 25.
    G. Vignale and A. H. MacDonald, Phys. Rev. Lett. 76, 2786 (1996); S. Conti, G. Vignale, and A. H. MacDonald, Phys. Rev. B 57, R6846 (1998); A. V. Balatsky, Y. N. Joglekar, and P. B. Littlewood, Phys. Rev. Lett. 93, 266801 (2004); Y. N. Joglekar, A. V. Balatsky, and M. P. Lilly, Phys. Rev. B 72, 205313 (2005).CrossRefADSGoogle Scholar
  26. 26.
    O. L. Berman, Yu. E. Lozovik, D. W. Snoke, and R. D. Coalson, Phys. Rev. B 70, 235310 (2004); Phys. Rev. B 73, 235352 (2006); Solid State Commun. 134, 47 (2005); Physica E (Amsterdam) 34, 268 (2006).Google Scholar
  27. 27.
    Yu. E. Lozovik and M. Willander, Appl. Phys. A 71, 379 (2000); Yu. E. Lozovik, O. L. Berman, and V. G. Tsvetus, Phys. Rev. B 59, 5627 (1999); Pis’ma Zh. Éksp. Teor. Fiz. 66, 332 (1997) [JETP Lett. 66, 355 (1997)]; Yu. E. Lozovik and O. L. Berman, Pis’ma Zh. Éksp. Teor. Fiz. 64, 526 (1996) [JETP Lett. 64, 573 (1996)].CrossRefADSGoogle Scholar
  28. 28.
    J. F. Jan and Y. C. Lee, Phys. Rev. B 58, 1714 (1998); Z. G. Koinov, Phys. Rev. B 61, 8411 (2000).CrossRefADSGoogle Scholar
  29. 29.
    X. Zhu, P. B. Littlewood, M. S. Hibertsen, and T. M. Rice, Phys. Rev. Lett. 74, 1633 (1995); Y. Naveh and B. Laikhtman, Phys. Rev. Lett. 77, 900 (1996); J. Fernández-Rossier and C. Tejedor, Phys. Rev. Lett. 78, 4809 (1997); P. Pieri, D. Neilson, and G. C. Strinati, Phys. Rev. B 75, 113301 (2007).CrossRefADSGoogle Scholar
  30. 30.
    Yu. E. Lozovik, I. L. Kurbakov, G. E. Astrakharchik, et al., Solid State Commun. 144, 399 (2007).CrossRefADSGoogle Scholar
  31. 31.
    Yu. E. Lozovik and O. L. Berman, Phys. Scr. 58, 86 (1998); Fiz. Tverd. Tela (St. Petersburg) 40, 1350 (1998) [Phys. Solid State 40, 1228 (1998)]; D. V. Kulakovskiĭ, Yu. E. Lozovik, and A. V. Chaplik, Zh. Éksp. Teor. Fiz. 126, 979 (2004) [JETP 99, 850 (2004)].CrossRefADSGoogle Scholar
  32. 32.
    S. De Palo, F. Rapisarda, and G. Senatore, Phys. Rev. Lett. 88, 206401 (2002); A. I. Belousov and Yu. E. Lozovik, Pis’ma Zh. Éksp. Teor. Fiz. 68, 817 (1998) [JETP Lett. 68, 858 (1998)]; Europhys. J. D 8, 251 (2000); Yu. E. Lozovik and E. A. Rakoch, Phys. Lett. A 235, 55 (1997); A. Filinov, M. Bonitz, P. Ludwig, and Yu. E. Lozovik, Phys. Status Solidi C 3, 2457 (2006); C. Mora, O. Parcollet, and X. Waintal, Phys. Rev. B 76, 064511 (2007).Google Scholar
  33. 33.
    G. E. Astrakharchik, J. Boronat, I. L. Kurbakov, and Yu. E. Lozovik, Phys. Rev. Lett. 98, 060405 (2007); see also [46].Google Scholar
  34. 34.
    Yu. E. Lozovik, I. L. Kurbakov, G. E. Astrakharchik, and M. Willander, Fiz. Tverd. Tela (St. Petersburg) (in press).Google Scholar
  35. 35.
    Yu. E. Lozovik, S. Yu. Volkov, and M. Willander, Pis’ma Zh. Éksp. Teor. Fiz. 79, 585 (2004) [JETP Lett. 79, 473 (2004)]; G. E. Astrakharchik, J. Boronat, J. Casulleras, et al., cond-mat/07074630.Google Scholar
  36. 36.
    A. L. Ivanov, P. B. Littlewood, and H. Haug, Phys. Rev. B 59, 5032 (1999); A. V. Soroko and A. L. Ivanov, Phys. Rev. B 65, 165310 (2002); S. V. Iordanskiĭ and A. Kashuba, Pis’ma Zh. Éksp. Teor. Fiz. 73, 542 (2001) [JETP Lett. 73, 479 (2001)]; A. L. Ivanov, Europhys. Lett. 59, 586 (2002).CrossRefADSGoogle Scholar
  37. 37.
    S. I. Shevchenko, Phys. Rev. Lett. 72, 3242 (1994); Phys. Rev. B 56, 10355 (1997); Phys. Rev. B 57, 14809 (1998); Yu. E. Lozovik and E. A. Rakoch, Phys. Rev. B 57, 1214 (1998); T. Iida and M. Tsubota, Phys. Rev. B 60, 5802 (1999); J. Lumin. 87–89, 241 (2000).CrossRefADSGoogle Scholar
  38. 38.
    Yu. E. Lozovik and V. I. Yudson, Solid State Commun. 22, 117 (1977); A. V. Klyuchnik and Yu. E. Lozovik, Zh. Éksp. Teor. Fiz. 76, 670 (1979) [Sov. Phys. JETP 49, 335 (1979)]; J. Phys. C 11, L483 (1978); Yu. E. Lozovik and A. V. Poushnov, Phys. Lett. A 228, 399 (1997); see also [37].CrossRefADSGoogle Scholar
  39. 39.
    L. S. Levitov, B. D. Simons, and L. V. Butov, Phys. Rev. Lett. 94, 176404 (2005); Solid State Commun. 134, 51 (2005).Google Scholar
  40. 40.
    B. Laikhtman, Europhys. Lett. 43, 53 (1998); P. Stenius, Phys. Rev. B 60, 14072 (1999); Yu. E. Lozovik and I. V. Ovchinnikov, Pis’ma Zh. Éksp. Teor. Fiz. 74, 318 (2001) [JETP Lett. 74, 288 (2001)]; Phys. Rev. B 66, 075124 (2002); Solid State Commun. 118, 251 (2001); Yu. E. Lozovik, I. L. Kurbakov, and I. V. Ovchinnikov, Solid State Commun. 126, 269 (2003); J. Keeling, L. S. Levitov, and P. B. Littlewood, Phys. Rev. Lett. 92, 176402 (2004); R. Zimmermann, Phys. Status Solidi B 243, 2358 (2006).CrossRefADSGoogle Scholar
  41. 41.
    Yu. E. Lozovik, I. L. Kurbakov, and M. Willander, Phys. Lett. A 366, 487 (2007).CrossRefADSGoogle Scholar
  42. 42.
    Yu. E. Lozovik, O. L. Berman, and A. M. Ruvinskii, Pis’ma Zh. Éksp. Teor. Fiz. 69, 573 (1999) [JETP Lett. 69, 616 (1999)]; K. Huang and H.-F. Meng, Phys. Rev. Lett. 69, 644 (1992); M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989); see also [26, 27, 67].Google Scholar
  43. 43.
    K. Moon, H. Mori, K. Yang, et al., Phys. Rev. B 51, 5138 (1995); K. Park and S. Das Sarma, Phys. Rev. B 74, 035338 (2006); Yu. E. Lozovik and I. V. Ovchinnikov, Pis’ma Zh. Éksp. Teor. Fiz. 79, 86 (2004) [JETP Lett. 79, 76 (2004)]; H. A. Fertig and G. Murthy, Phys. Rev. Lett. 95, 156802 (2005); J. P. Eisenstein and A. H. Mac-Donald, Nature 432, 691 (2004); J. P. Eisenstein, Science 305, 950 (2004); see also [27].CrossRefADSGoogle Scholar
  44. 44.
    M. Kellogg, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 93, 036801 (2004); E. Tutuc, M. Shayegan, and D. A. Huse, Phys. Rev. Lett. 93, 036802 (2004).Google Scholar
  45. 45.
    A. Griesmaier, J. Werner, S. Hensler, et al., Phys. Rev. Lett. 94, 160401 (2005); D. Jaksch, J. I. Cirac, P. Zoller, et al., Phys. Rev. Lett. 85, 2208 (2000); H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87, 140405 (2001); S. Yi and L. You, Phys. Rev. A 63, 053607 (2001); U. R. Fischer, Phys. Rev. A 73, 031602 (2006); S. Yi and H. Pu, Phys. Rev. A 73, 061602 (2006); G. E. Astrakharchik, J. Boronat, J. Casulleras, et al., Phys. Rev. A 75, 063630 (2007).Google Scholar
  46. 46.
    H. P. Büchler, E. Demler, M. Lukin, et al., Phys. Rev. Lett. 98, 060404 (2007); D. DeMille, Phys. Rev. Lett. 88, 067901 (2002); R. V. Crems, Phys. Rev. Lett. 96, 123202 (2006); J. M. Sage, S. Sainis, T. Bergeman, and D. DeMille, Phys. Rev. Lett. 94, 203001 (2005); J. L. Bohn, Phys. Rev. A 63, 052714 (2001); T. Köhler, K. Góral, and P. S. Julienne, Rev. Mod. Phys. 78, 1311 (2006).Google Scholar
  47. 47.
    M. Schick, Phys. Rev. A 3, 1067 (1971); Yu. E. Lozovik and V. I. Yudson, Physica A (Amsterdam) 93, 493 (1978); E. B. Kolomeisky and J. P. Straley, Phys. Rev. B 46, 11749 (1992); A. Yu. Chreny and A. A. Shanenko, Phys. Rev. E 64, 027105 (2001).CrossRefADSGoogle Scholar
  48. 48.
    S. Yang, A. V. Mintsev, A. T. Hammack, et al., Phys. Rev. B 75, 033311 (2007).Google Scholar
  49. 49.
    D. S. Fisher and P. C. Hohenberg, Phys. Rev. B 37, 4936 (1988); see also [57].CrossRefADSGoogle Scholar
  50. 50.
    S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Phys. Rev. B 32, 6601 (1985).CrossRefADSGoogle Scholar
  51. 51.
    L. Reatto and G. V. Chester, Phys. Rev. 155, 88 (1967).CrossRefADSGoogle Scholar
  52. 52.
    J. Boronat and J. Casulleras, Phys. Rev. B 49, 8920 (1994).CrossRefADSGoogle Scholar
  53. 53.
    J. Casulleras and J. Boronat, Phys. Rev. B 52, 3654 (1995).CrossRefADSGoogle Scholar
  54. 54.
    G. E. Astrakharchik, J. Boronat, J. Casulleras, et al., submitted to Phys. Rev. A (2008).Google Scholar
  55. 55.
    I. M. Khalatnikov, Theory of Superfluidity (Nauka, Moscow, 1971) [in Russian].Google Scholar
  56. 56.
    R. P. Feynman, Phys. Rev. 94, 262 (1954); L. P. Pitaevskiĭ, Sov. Phys. JETP 4, 439 (1957); J. Boronat, J. Casulleras, F. Dalfovo, et al., Phys. Rev. B 52, 1236 (1995).zbMATHCrossRefADSGoogle Scholar
  57. 57.
    V. N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics (Atomizdat, Moscow, 1976; Reidel, Dordrecht, 1983).Google Scholar
  58. 58.
    P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987); Phys. Rev. B 32, 3088 (1985); P. Minnhagen and G. G. Warren, Phys. Rev. B 24, 2526 (1981).CrossRefADSGoogle Scholar
  59. 59.
    A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinskiĭ, Methods of Quantum Field Theory in Statistical Physics (Dobrosvet, Moscow, 1998) [in Russian].Google Scholar
  60. 60.
    A. V. Gorbunov and V. B. Timofeev, Pis’ma Zh. Éksp. Teor. Fiz. 80, 210 (2004) [JETP Lett. 80, 185 (2004)].Google Scholar
  61. 61.
    M. Willander, O. Nur, Yu. E. Lozovik, et al., Microelectron. J. 36, 940 (2005).CrossRefGoogle Scholar
  62. 62.
    A. T. Hammack, N. A. Gippius, S. Yang, et al., J. Appl. Phys. 99, 066104 (2006).CrossRefADSGoogle Scholar
  63. 63.
    G. Baymand and C. J. Pethick, Phys. Rev. Lett. 76, 6 (1996).CrossRefADSGoogle Scholar
  64. 64.
    G. E. Astrakharchik, Phys. Rev. A 72, 063620 (2005).Google Scholar
  65. 65.
    L. V. Butov, A. V. Mintsev, Yu. E. Lozovik, et al., Phys. Rev. B 62, 1548 (2000); L. V. Butov, C. W. Lai, D. S. Chemla, et al., Phys. Rev. Lett. 87, 216804 (2001).CrossRefADSGoogle Scholar
  66. 66.
    Yu. E. Lozovik, I. V. Ovchinnikov, S. Yu. Volkov, et al., Phys. Rev. B 65, 235304 (2002).Google Scholar
  67. 67.
    S. Giorgini, L. Pitaevskii, and S. Stringari, Phys. Rev. B 49, 12938 (1994); H.-F. Meng, Phys. Rev. B 49, 1205 (1994).Google Scholar
  68. 68.
    E. C. Svensson, V. F. Sears, A. D. B. Woods, and P. Martel, Phys. Rev. B 21, 3638 (1980).CrossRefADSGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • Yu. E. Lozovik
    • 1
  • I. L. Kurbakov
    • 1
  • G. E. Astrakharchik
    • 2
  • M. Willander
    • 3
  1. 1.Institute of SpectroscopyRussian Academy of SciencesTroitsk, Moscow oblastRussia
  2. 2.Polytechnic University of Catalonia E-08034BarcelonaSpain
  3. 3.Institute of Science and Technology (ITN)Linköping University SE-581 83Linköping, TäppanSweden

Personalised recommendations