Effective Hamiltonian for Excitons with Spin Degrees of Freedom

Journal of the Physical Society of Japan

Volumn 67, Issue 10, 1998, Pages 3384-3387

  Inoue, Jun Ichi ^a,b   Brandes, Tobias ^a,b,c   Shimizu, Akira ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^c 1 Inst Theor Physik   (Germany)

Author keywords

Bosonic representation; Effective Hamiltonian; Exciton

Indexed keywords

EID: 0032274967     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.67.3384     Document Type: Article

References (24)

1. M. Stone: Bosonization (World Scientific, Singapore, 1994).
2. F. D. M. Haldane: J. Phys. C 14 (1981) 170.
3. P. Kopietz: Bosonization of Interacting Fermions in Arbitrary Dimensions (Springer, Berlin, 1997).
4. E. Hanamura and H. Haug: Phys. Rep. 33 (1977) 209.
5. M. Kuwata-Gonokami, S. Inouye, H. Suzuura, M. Shirane, R. Shimano, T. Someya and H. Sakaki: Phys. Rev. Lett. 79 (1997) 1341.
6. V. M. Axt and S. Mukamel: Rev. Mod. Phys. 70 (1998) 145.
7. A. L. Ivanov, H. Haug and L. V. Keldysh: Phys. Rep. 296 (1998) 237 and references therein.
8. This should be contrasted with liquid Helium 4: there is no doubt that an Helium 4 atom can be described by a boson operator when the superfluidity is studied, because its nuclear binding energy is much larger than typical energy scales of superfluid experiments.
9. See, for example, H. Haug and S. W. Koch: Quantum Theory of the Optical and Electric Properties of Semiconductors (World Scientific, Singapore, 1994) 3rd ed.
10. M. Lindberg and S. W. Koch: Phys. Rev. B 38 (1988) 3342.
11. Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang and D. G. Steel: Phys. Rev. B 49 (1994) 14382.
12. T. Rappen, U. B. Peter, M. Wegener and W. Schäfer: Phys. Rev. B 49 (1994) 10774.
13. W. Schäfer, D. S. Kim, J. Shah, T. C. Damen, J. E. Cunningham, K. W. Goossen, L. N. Pfeiffer and K. Köhler: Phys. Rev. B 53 (1996) 16429.
14. It should be stressed that fairly good agreement is obtained in ref. 5 between the experimental results and the lowest-order calculations based on the phenomenological Hamiltonian.
15. H. Haug and S. Schmitt-Rink: Prog. Quantum Electron. 9 (1984) 3.
16. 21)
17. S. Schmitt-Rink, D. S. Chemla and D. A. B. Miller: Adv. Phys. 39 (1989) 89.
18. Ivanov and Haug obtained this interaction without performing the projection [Phys. Rev. B 48 (1993) 1490]. However, they dropped CG coefficients of eq. (3), and determined the spin dependence using another theory of a four-body problem. Hence their derivation is not fully microscopic.
19. M. Hawton and D. Nelson: Phys. Rev. B 57 (1998) 4000.
20. M. Kuwata-Gonokami: private communication.
21. J. Inoue, T. Brandes and A. Shimizu: unpublished.
22. 1s, of course, becomes important when one measures optical processes in which higher-order terms are involved.
23. K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl and K. Ploog: Phys. Rev. B 48 (1993) 17418.
24. †ba). The eigenenergy is 2ω - |g|. Note that the existence of the bound state is independent of the sign of the interaction g.