Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

optical recombination of the exciton ground state. The polarization propertiesof this PL are determined by the symmetry of admixed states. We nowconsider the effect of an external magnetic field on the fine structure of theband-edge exciton.III.FINE STRUCTURE OF THE BAND-EDGE EXCITONSIN MAGNETIC FIELDSFor nanosize quantum dots, the effect of an external magnetic field, H, on theband-edge exciton is well described as a molecular Zeeman effect:HˆH ¼ 1 2 g el B sˆ H g h l ˆ B KHð36Þwhere g e is the g factor of the 1S electron state, g h is the g factor of the hole1S 3/2 state, and l B is the Bohr magneton. For bulk CdSe, the electron g factorg eb = 0.68 [25]; however, due to the nonparabolicity of the conduction band, itdepends strongly on the nanocrystal size [26,27]. The value of the hole g factordepends strongly on the structure of the valence band. The Appendix showsthe expression for g h that was derived in the Luttinger model [28] using theresults of Ref. 29. In Eq. (29), we neglect the diamagnetic, H 2 , terms becausethe dots are significantly smaller than the magnetic length [f115 A˚ at 10 T].Treating the magnetic interaction as a perturbation, we can determinethe influence of the magnetic field on the unperturbed exciton state using theperturbation matrix Eˆ HV =hC a,M jl B 1 Hˆ HjC aV , MV i:z; 3=2 z; 1=2 z; 1=2 z; 3=2 #; 3=2 #; 1=2 #; 1=2 #; 3=2pffiffiffiH z ðg e 3g h Þ i 3 gh Hg e Hz; 3=20 00 0 0222pffiffiffii 3 gh H þ H z ðg e g h Þg e Hz; 1=2ig h H 0 00 0222pffiffiffiH z ðg e þ g h Þ i 3 gh Hg e Hz; 1=2 0 ig h H þ 0 00222pffiffiffii 3 gh H þ H z ðg e þ 3g h Þg e Hz; 3=2 0 00 0 0222pffiffiffig e H þH z ðg e þ 3g h Þ i 3 gh H#; 3=20 0 00 0222pffiffig e H þi 3 gh H þ H z ðg e þ g h Þ#; 1=2 00 0ig h H 0222pffiffiffig e H þH z ðg e g h Þ i 3 gh H#; 1=2 0 00 0 ig h H þ222pffiffiffig e H þi 3 gh H þ H z ðg e 3g h Þ#; 3=2 0 0 00 0222ð37ÞCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.